Coach's Corner

Is the Future, Digital Learning?

2011-11-11T11:45:00.000-08:00

I just finished reading, Stacey Roshan's thoughts on Online and Blended Courses and Education Next's Jeb Bush, Melinda Gates, Sal Khan and the Coming Digital Learning Battle. I was very surprised by the opening paragraph of the Education Next article,

"The debate over digital learning will soon enter a new phase. No longer will educators debate whether or not digital learning has the capacity to transform the American education system. Just about gone are the anti-technology Luddites who insist that every classroom be self-contained, with students and teachers left to their own devices, save for the help of pencils, chalk, blackboards and weighty textbooks stuffed into 10 kilo backpacks."

And as much as I would like to think that Stacey's classroom was not the exception, I think it is.

Let me make one important point, I do believe that technology, online learning, and a new classroom model are the future of education, but I do not have as much confidence that it will be a swift conversion. I think there are currently too many forces vying for attention and focus, the primary force being NCLB or National Testing whatever form it takes over the next five years, to allow instructional models that are this radical to find a foothold in mass education settings.

Stacey makes the great point that one reason she loves teaching is,

"I love hearing their thoughts, I love playing with their ideas, and I love being there to help them feel stronger than they ever thought they could be. Sometimes I fear that I’ll lose this tight connection I feel with my students…"

I too think it's important that we recognize the human factor of teaching as well as the human factor of learning. We focus on making conditions that are maximally effective for learning and do not always include the important conditions that need to exist for great teaching. Without that kind of connection with students many great teachers will not go into the field unless they know they can create those experiences in the online/blended environments. I know I love teaching math, but I would love teaching history or science or English (OK, not English) just as much, because it is about the learner for me as much as it is about the content. (I do have a dual major in math and history, so I am not fibbing when I say I would be just as happy, I love both contents for different reasons.)

When I think back to the many great memories I have of the classroom, it is never about the skill, or content that I remember, but the students asking the great questions, making the subtle observation, or connecting something seemingly unconnected. Without those kinds of experiences, I wouldn't have stayed in teaching for 20+ years. I do think we can create those kinds of interactions in online environments, but they will look and feel different because the experience of the students are different.

I do think it is crucial though that we begin to move away from the kind of instruction that I see in many classrooms today. I don't know the exact reason why I see so many classrooms in which students sit and receive simple content, have very little interaction with creating understanding, and very seldom have opportunity to experience the power of technology, but I do see this every time I'm in a school (I will see approximately 400 classrooms this academic year). If we put students in a blended or fully online environment we could rescue them from the 6 hours of sit and get they experience currently for at least part of the time. We would force them to share their thinking because that's a characteristic of good online instruction (interaction with other students and teacher).

I know this post is more a rant than anything, but the articles touched two very interesting thought processes for me: the hoped for wave of digital learning options that are 'coming', and the love of teaching and interacting with students that it a central tenant of my love for teaching. I hope both authors are correct and most importantly I hope students benefit from any changes in education that will arise in the future.

Video Games, Fun, and Learning!

2011-10-17T09:25:00.001-07:00

I've long been a proponent of using games and simulations to engage students in learning (1, 2). Let's face it, we all like to play games, and we all want our students to be successful learners. Does it matter if they have fun while they are learning? I don't think so, and there is mounting evidence that gaming not only teaches facts more effectively than rote memorization, but it also teachers logic, problem solving, and creativity.

Kurt Squire (2003a), in a widely cited study on Video Games in Education, shares, "When educators have discussed games, they have focused on the social consequences of game play, ignoring important educational potentials of gaming." It is something we, as educators, need to move beyond. We didn't learn this way because the kinds of games that exist now, didn't exist a generation ago, and honestly many of the early computer-based games weren't very good. Good games have structures that make them great learning vehicles.

clear goals that students find

meaningful,

Squire outlines several key characteristics of educational games:

multiple goal structures and scoring to give students feedback on their progress,
multiple difficulty levels to adjust the game difficulty to learner skill,
random elements of surprise,
emotionally appealing fantasy and metaphor that is related to game skills.

In their study, Whitehall and McDonald (1993) argued that incorporating a variable payoff schedule into a simulation game led to increased risk taking among students, which resulted in greater persistence on the task and improved performance. This kind of perseverance in problem-solving is a skill that many American mathematics students have traditionally been poor at in standardized testing situations. If we find games that accomplish the learning goals we've set for our students and they include these kinds of structures then why not make them an integral component of our instructional process?

This infographic from Online Colleges, shares much of the anecdotal evidence around video gaming as an educational tool.

Via: Online Colleges Guide

Traditionally, many computer games have been drill and practice games, aimed at increasing a students basic knowledge recall, and teachers were pretty comfortable with those simple lower level learning targets. There will continue to be a role for drill and practice games (Savery & Duffy, 1995), but the opportunity to have students explore microworlds, problem-solving simulations, and design/creation (Papert 1980; Rieber 1996) is more suited to the new capabilities of technology in education.

Can you imagine using games to get student's to read and understand Shakespeare? Prospero’s Island, a partnership between the Royal Shakespeare Company and the Massachusetts Institute of Technology & a work-in-progress, is an interactive reinterpretation of Shakespeare’s classic, The Tempest that draws players into a playful and exploratory re-engagement with the classic text.

Civilizations III allows players to lead a civilization from 4000 BC to the present. Students win by making political, scientific, military, cultural, and economic gains, and balancing the different aspects of a complex system that is a nationstate. Players seek out geographical resources, manage economies, plan the growth of their civilization, and engage in diplomacy.

Squire (2003a, 2003b) in his evaluation of simulation games identified that students made connections between the different aspects of the simulations that were not prevalent in other learning scenarios.

Looking beyond the 'engagement' factor, gaming in education has the potential to strengthen student understanding of a variety of different areas, and educators need to look beyond traditional ways of learning and take advantage of opportunities to get students involved in the learning process any way we can.

Look for games that will help students do something in your content area that they can do other ways, but are likely to do more if they can play a game and do it at the same time, I know I am!

References:

Papert, S. (1981). Mindstorms: Children, computers and powerful ideas. Brighton: Harvester Press.

Rieber, L. P. (1996). Seriously considering play: Designing interactive learning environments based on the blending of microworlds, simulations, and games. Educational Technology Research and Development, 44, 43-58.

Savery, J.R., & Duffy, T.M. (1995). Problem based learning: An instructional model and its constructivist framework. Educational Technology, 35(5), 31-37.

Squire, K. (2003a). Video games in education. International Journal of Intelligent Simulations and Gaming, 2(1), 49-62.

Squire, K. (2003b). Formative Evaluation of Biohazard” (report delivered at the Microsoft Faculty Research Summit, 29 July.

Whitehall, B., & McDonald, B. (1993). Improving learning persistence of military personnel by enhancing motivation in a technical training program. Simulation & Gaming, 24, 294-313.

Update on Project 365

2011-01-12T09:21:00.000-08:00

A short update on my first two weeks doing Project 365. I love it! I'm not saying it hasn't been a challenge a couple of days getting things posted, but I like always having in the back of my mind "looking for a photo op". Several times over the last couple of days, I've driven by something that I thought was interesting and wishing I had stopped to capture a pic.

When I was younger I was an avid photographer, but when my trusty old 35 mm camera developed a light leak, I essentially quit thinking that way. I kept taking easy pics of my kids but haven't really been looking to capture what I see around me. I like being back in that mode and am looking forward to the rest of the year. Yes, I realize this is only two weeks into 365 days, but it's a start.

As far as the tools that I'm using and how they are working: I'm using my iPhone 3GS for most of my pictures and it is severely limited in its quality and capacity. That is not a major issue because I just have to be a little more creative in how I frame my shots and how I edit them. I can say that most of these images are not going to be landscape or general shots because the camera just isn't of a high quality. If I upgrade in June like I intend to do, then I think the quality of the images is likely to increase at that point.

The posting tool I'm using is Tumblr (http://rlodan01.tumblr.com/) and it is working well. I don't post directly from Tumblr often because I use Instagram for most of my uploads. Instagram allows me to immediately cross load to flickr and any other site I choose (primarily twitter or facebook). I usually get to flickr once a week or so to manage images or do some uploading and that's when I move my 365 photos into the 365 photos set and tag them. It's easy with the bulk tools on flickr. I'm, also, tagging the photos I upload to Tumblr, but that requires me to go to Tumblr or upload from the Tumblr app on my iPhone, which just isn't as easy because it requires me to use multiple tools to cross-load.

Here's looking towards the rest of the year. I, also, want to thank Dean Shareski for offering some points of advice. I'm using several that he and Wes Fryer both recommended: using an iPhone, light editing (if Instagram doesn't do it, I generally won't), using an easy uploading tool to cross-post on flickr and tumblr, and tagging the photos.

(My favorite target so far! My grandson Jase!)

If you remember I got back into this idea by reading Wes Fryer's post on committing to the project this year, and I'm following him on tumblr to help keep me motivated. I'm also following several tumblr bloggers to help give me ideas and motivation, but haven't found a way to think about taking images beyond, "oh gosh it's 7:00 and I haven't taken one." I haven't found a group to follow or include in the process yet, that's on my agenda.

I'll keep you posted on how things are going.

Project 365

2010-12-20T11:37:00.000-08:00

I've been wanting to commit to this project since I read about it several years ago. I don't remember where I read about it, but I know several bloggers that I follow have done it Darren Kuropatwa, Chris Lehman, Silvia Tolisano, and Wes Fryer's committing to it this year. When I ready Wes' post a couple of days ago, I knew I had to put it into motion. I had to do it. It's a daunting task, thinking about taking a picture everyday for a year. I don't know that I have the ability to maintain the focus, but I'm going to give it a try.

Besides, it gives me the opportunity to use a couple of tools that I've been wanting to explore more. My daughter continues to extol the uses of Tumblr and when I read Wes' idea of using Tumblr as his 365 blog, I was convinced. It gives me a purpose to use my Tumblr. I got it set to cross post to twitter and facebook to save myself having to multiple post things, but I do want to make sure that all of my pics go to flickr. I like to make sure I can easily embed and share images that I take and I haven't found a tool I like better than flickr.

On the 365 Project blog, they make 6 suggestions:
Pick a theme- I don't know that I can pick a theme for an entire year, but I'm likely to switch between my family and my work. It's all I really think about. I won't be trying to do a lot of artsy photos, for several reasons; my camera isn't that good (see above), and I don't think that will sustain me for a year.

Learn to use your camera- I think I've got this one, but I'll keep working on it. I might try some different filters.

Organize your photos- I will definitely try to organize the images on flickr. I am getting better about that as I compile more and more images. It becomes more important all the time to tag and organize them. This suggestion should be relatively easy to do.

Update regularly- I like that it doesn't require updating daily, but it is the spirit of the mission to take one daily. I can see taking them and posting at least to tumblr daily, but getting the uploaded and organized in flickr might be a weekly mission.

Find inspiration- this is my concern. I don't know that I have inspiration on a daily basis. Yes, I am often inspired to take pics of my grandson, but I don't see him everyday. I have wanted for a long time to take more pics of my kids as they get older, but it is much more difficult now that I don't see them regularly or they don't want to be photographed (yes, they are very much girls in this sense). My wife is also a big part, but she is anti-photograph and it's not worth a battle. That leaves work and my dog. I've got too many pics of him already, but we'll see what comes my way!

Keep your eye on the prize- what prize? Oh yah, self-motivation. I'm doing it because I want to see what I saw as important or interesting or just mundane over the course of a year.

So here it goes!

Redesigning Pedagogy: Chapter 16- The Model Method

2010-12-13T06:38:00.000-08:00

Currently reading:
Redesigning Pedagogy:Reflections on Theory and Praxis
By Wendy D. Bokhorst-Heng, National Institute of Education, Singapore,
Margery D. Osborne, University of Illinois at Urbana-Champaign,USA,
Kerry Lee, National Institute of Education, Singapore

"Many aspects of mathematics make use of pictorial representation to solve various problems (Booth & Thomas, 2000)."

The intentional use of pictorial representations to solve arithmetic problems is a cornerstone of the Singaporean mathematics curriculum. This chapter studies the transition into high school level algebra and the role that the bar model heuristic plays in developing students ability to problem solve using symbolic notation.

Over the past two decades as students have grown up using the bar model method and then gone on to algebra there have been mixed results in moving students away from the bar model method to a more symbolic method of solving problems. (Need a citation for this statement) Many secondary school teachers deal with the dilemma by banning the use of the bar model method to force students to use symbolic representation.

In research by Ng (2003), ten primary and ten secondary teachers were asked to solve problems by using the bar model and symbolic algebra respectively. Once the teachers had solved the problems successfully they were asked to use the alternative method to solve the problems. The primary teachers were generally more successful at solving the problems using symbolic representation than the secondary teachers were at solving the problems using the bar model method.

The primary teachers were aware of the connection between the two methods, but had trouble articulating the connection. The predetermined stance that the bar model method was a primary tool, inhibited the secondary teachers from creating model drawings to solve the problems, and considerable more help was needed to create the bar models from the equations than was needed to create the equations from the bar models (p 234). The study did determine that secondary teachers were surprised at the close connections between the two methods for solving problems (p. 235).

When students are not able to use the model to create an algebraic equation and then use the algebraic methodology to solve the problem is one inhibition to successful problem solving (p 238). The research is incomplete as to whether without the bar model if the students would have been able to create the equations to begin with. So, whether the bar modeling the inhibitor or was the students inability to understand the algebraic approach the inhibitor is not know.

"From a pedagogical perspective, these findings are supportive of the use of the model method as an introductory tool (p 237)."

Overall the findings offer some evidence that modeling is potentially less demanding on cognitive resources and an acceptable bridge to symbolic algebra. The recommendations suggest that rather than prohibiting the bar model at the secondary level, students use the model method to solve word problems with explicit support to creating algebraic solutions accompanying the process, and making the connections an integral component of the problem solving process for students who are not yet able to produce the algebraic solutions (p 239).

Lincoln Archive

2010-12-09T07:17:00.000-08:00

Lincoln Archive

Looking for primary source materials to use with students when teaching the civil war? The Lincoln Archive is an excellent source for documents that show how our national leaders were communicating during the war, and insights into Lincoln's thinking as he made incredibly difficult decisions.

QR Code in Education

2010-12-08T05:34:00.000-08:00

I want to thank Tom Barrett (@tombarrett) for sharing his Google presentation on QR codes.

You might be wondering, what are QR codes? They are related to bar codes in the sense that they are displays of data. However QR codes can be read from multiple directions instead of just left to right. I'm no expert on QR codes, and in fact didn't know much about them until I perused Tom's presentation.

I don't have a lot to add to the information that Tom is presenting, but I do want to share some of the great resources that he's put together for our use. I love this video from McGuffey School District in Claysville, PA:

I continue to pursue ways of helping teachers create easy access points for students to resources. Creating simple links, sharing links via twitter, wikis, RSS, email. These are all great for virtual environments where the student is accessing the link from a computer, but what about drawing a student to a site from a poster? How do I draw a student, easily to a site that has a long tedious URL from a print environment? I'll answer that QR code!

Happy Surfing!

TEDxKC - Michael Wesch - From Knowledgeable to Knowledge-Able

2010-11-15T09:04:00.000-08:00

This is Michael Wesch's TEDxKC talk. As always, Michael has a way with words and images. I just love how he goes at the state of education. The world is changing and how knowledge is conveyed/communicated is changing, but schools don't seem to be able to handle the changing landscape effectively. I don't have a lot to add to Dr. Wesch's message, but to say, I hope he teaches my children some day!

Rational Number Development Instructional Routine Model

2010-09-12T10:00:00.000-07:00

In previous posts (1, 2) I outlined my ideas for creating an instructional routine that engaged students through some type of game to work on skills that need practice or are often 'boring' for students to gain enough experience with. The online game Geosense prompted my thinking and in working with the iPod Touch I came across several math games that I thought would capture student attention for the purpose of practicing number sense skills.

I laid out the main components of the plan: Monitoring and Goal Setting, Practice and Formative Assessment, and Strategy/Skill Development and developed the plan. In this post I wanted to provide what a typical set of classroom activities might look like. These are general ideas, and can be modified depending on your goals and time you want to set aside for the routine.

During the course of one week students:

Day 1:

Play a game for 5 minutes, capturing the highest score of the game through the screen capture process on the iPod Touch.
Record and update their progress through a Google Form
Identify 1-2 problems, numbers, representations they struggled with during the game they played that day

Day 2:

Students evaluate their progress towards their goal, being sure to analyze their performance as it relates to specific learning standards in the student goals
Submit their reflection to their progress blog via Word Press along with a graph of their progress

Day 3:

Students utilize 5-10 minutes of class time to create a representation of the kind of problem they are working to improve that intentionally includes a process/strategy, or multiple representations including; model/diagram, written description, and a symbolic representation of the problem
Students share their example in small groups and/or whole group, being sure to talk about how they are applying the process/strategy to solve this kind of problem more efficiently/effectively

9 Week Period:

Repeat the cycle weekly with a focus on just two or three games during the quarter so students get enough experience during the course of a nine week grading period to identify progress. If students have access to the games outside of class time, I encourage the capture of how much time the student plays the game on their own just as added incentive.

I hope to address student rational number sense with this routine as the year progresses, and will be tracking student progress on MAPS (or some equivalent formative assessments) to determine the efficacy of the plan. The components of the plan are a compilation of procedural fluency research and formative assessment research from Wiliam and Black as well as Marzano.

Developing a Number Sense Routine using the iPod Touch

2010-09-08T12:21:00.000-07:00

I have the distinct pleasure of working with Bate Middle School in Danville, Kentucky with their iPod Touch Literacy Program. They are piloting for the second semester the use of iPods with middle school students to increase opportunities in classroom instruction to have students reading/writing/speaking & listening about content.

I’ve been very interested in working with the teachers to develop instructional routines for use with students that take advantage of the multiple tools available to students with an iPod Touch. Students have access to so many different media, games, processing tools, and they have an equal opportunity to create information as they do to consume information.

In a post on this blog, I discussed using games to engage students to help them learn facts that might not otherwise be memorized or that need extra practice by students. The two cases I discussed are geography and multiplication tables, but this concept isn’t limited to those categories. It is limited by the teachers’ imagination and access to games students’ might find enjoyable. Luckily with the iPod Touch there are lots of math games that deal with number sense and number relations (computation), understanding of estimation, relationships between number forms, and applying strategies for computation to large/complex problems.

A second set of goals that we think are critical to success of mathematics students is to help students be aware of their skills and strategies, and to work at getting better at these skills. It is the ideas of meta-cognition and perseverance in problem solving that we know are now part of the new Common Core Academic Standards in mathematics that we want to begin to instill in students.

The question becomes how do we achieve these goals with the students?

Process/routine:

is more than just practice/memorization,
has built in identification and monitoring of goals and progress,
is fun as well as educational,
addresses several skill sets during the course to meet the needs of multiple students, and
is developmental and provides students opportunities to address specific strategy development as well as reinforcement.

Here is my initial take on a Rational Number Improvement Plan:

The routine has three components: Monitoring and Goal Setting, Practice and Formative Assessment, and Strategy/Skill Development

Part 1: Monitoring and goal setting- Students:

Set goals based on their strengths/weaknesses and performance over the course of the year
Monitor their progress/scores using Google Forms and create broken line graph to represent their performance
As part of the Google Form students reflect on their performance on the game, identifying specific problems they thought were easy, had difficulty in answering, or were not sure about how to answer.

Part 2: Practice and formative assessment- I identified an initial five games on the iPod Touch to help students work on their rational number development:

Number line by Todd Bowden- ordering rational numbers

(Students move the numbers into the correct order on the number line; if they move the numbers incorrectly the numbers turn red; indicating the need to reorder the number)

Fraction Factory by Radford University, Games Lab- estimating values of fractions in decimal number form and on a number line

(Note that students move the fraction from the assembly line to the appropriate spot on the number line; in the second image you see that students are provided an accuracy score to reinforce their skill in estimating the value of the fraction)

Freddy Fraction by Radford University, Games Lab- finding equivalent number forms for fractions, decimals, percents

Pearl Diver by New Mexico State University, Learning Games Lab- Equality and order on the number line, Number line properties(In this game players are asked to identify the correct value for the integer given and dive to get the pearl; if successful without being electrocuted by the eel the diver is given another number to dive for until four pearls have been collected moving on to a new level)

Alien Equation by funnerlabs- number relationships that form computation equations

(Players slide numbers and operators up/down and left/right to form relationships that make equations; when a correct equation is formed it disappears providing new numbers for the player to turn into new relationships; the game progresses in difficulty and operators as it progresses)

Part 3: Strategy/skill development- Students identify one or two problems they struggled with during the day’s practice/game session and create a model of the problem that utilizes multiple representations and/or models a strategy that students could have brought to bear on that problem. This allows students to learn to identify problems that they realize are harder for them, have practice with specific strategies that help them to solve related problems, learn to apply strategies to a variety of problem types, and uses multiple representations to deepen student understanding of rational number.

(This is an example of what a student analysis of one problem might look like; in this case the student is learning to estimate values of fractions using an upper and lower benchark; additionally the student is using multiple models for representing the value)

(In this example a student is using a chunking strategy or distributive property to learn to turn multiplication facts into easier problems, using a verbal description, a model, and a symbolic representation. It is likely that the student will need some support, but in future analysis the student will return to this strategy until they feel comfortable with doing it on their own during the game.)

In a future post, I will describe what typical week of classroom activities entails.

Proportional Thinking/Algebraic Reasoning- Using the Computer to Generate the “Average Face”

2010-09-08T05:40:00.000-07:00

A while ago, I shared my thoughts on drawing the human form and more specifically the human face. I mentioned in the post that I liked the idea of students collecting the image of a face on the computer to do this activity using the Paint program and a spreadsheet. I like paint because of its simplicity and availability. If you have a different program you like then you can still easily adapt these ideas.

I like to have students use spreadsheets whenever possible to record data, if for no other reason than it provides access to data in an on-going way. We can pull up the spreadsheet of data we collected, review what we found or how we organized the information, or analyze the information differently; all because we saved it in a spreadsheet. Most spreadsheet software have the capability of inserting formulas, producing a variety of graphs/data displays, and can be used to share text based information. I prefer Microsoft Excel because it has a wide array of analysis tools available, but for this project the analysis is rather simple.

So, here are my thoughts on how I made the 'Average Face' a paperless activity.

Step 1- I created two spreadsheets with the desired measurements on them to share with the students. (I created 2 because it depends on the grade level and content strand I want to focus on:

In both spreadsheets we will use formulas to perform certain operations, for instance subtracting the ‘Bottom of Chin’ from the ‘Top of Head’ to determine ‘Length of Face’, or compare length from 'Bottom of Nose' to 'Chin' to 'Length of Face'.

How much information or guidance you provide for determining the formulas that go into the spreadsheet depends on your instructional goals and your student experiences with spreadsheets. In the sample provided below I generate several of the formulas using different syntax options.

If you aren’t ready to have students enter the information in the spreadsheet it would be just as acceptable to provide them with the worksheet to gather their data on (although I highly recommend using the spreadsheet to do this).

Step 2- Open and Resize the image I want to measure in Paint. It is not necessary for people’s images to be the same size if we are doing simple ratios. However if I want to find ‘average’ lengths of faces then it would be wise to resize images too approximately the same size. (Image, Attributes, to determine height of the image. In this case the image is 352 pixels high and I would like the images to be approximately 600 pixels tall. Divide 600 by 352 to get the percent change 170%. (Note you can change measure to inches or

centimeters if you so desire, but I like having students

use pixels to confirm that the proportions work no matter what measurement system you are using)

Choose Image, Stretch/Skew, type 170 in each field to maintain proper image ratios, and your image will now be about the same size for all students.

Step 3- Measuring facial attributes

Place the cursor over the spot that I want to measure to get the position information. The program shows me my exact position in pixels on the photo in an ordered pair, horizontal position, vertical position with upper left corner of the image being 0,0. Therefore as you see, the bottom of my chin is 198 pixels from the left side of the image and 539 pixels from the top edge of the image.

If using the spreadsheet, gather vertical position data in the spreadsheet and then extrapolate the information needed. Note that G4 has ‘=C4-B4’ as its entry. This introduces the idea of developing formulas to gather the necessary information for calculating the measurements. We could also introduce another column that would convert from pixels to mm or inches, if you were so inclined.

Step 4- Calculating the ratios for the average face. In this next step I just began asking students the different measurements that artists use and how we could check to see if the face we were measuring was close to those measures.

Step 5- Finding the Average Face in the crowd. By collecting the data from each spreadsheet students can begin using formulas that identify important univariate components. Here I entered some fictitious data to play with:

I don’t think it is out of the question to expect 7^th or 8^th graders to express these ideas using a spreadsheet, and think asking freshman to manipulate the data using spreadsheets given a goal of finding the average face, and a little (I mean very little) access to formulas would be an interesting approach .

Note the first spreadsheet was very simple and it was meant to be for younger students, who would need more scaffolding in how to develop a formula. Even if the development were done without the express connection to algebra students in would garner considerable algebraic reasoning from the activity.

I have attached both spreadsheets here: simple human face proportions, speadsheet with more options.

Dissertation Thoughts

2010-05-10T07:56:00.000-07:00

I thought when I began my pursuit of a PhD that the coursework would be the hardest part, but I was wrong! The coursework was an easy goal to work through. It was laid out, handed out in small manageable chunks, and was more or less a long hike.

Comps didn't even cause me much angst; they just took my weekends away for a month. Even those challenges were for the most part served up in small (OK these might have been medium sized) chunks with definite goals and timelines. Pound out 24 hours of intense research/writing/editing and submit.

My dissertation on the other hand is a very different story. This is not clearly defined, and involves me staying focused for an extended period of time on something that I just don't have clearly defined in my head. It's very frustrating that I've gone six months and don't feel like I've accomplished anything. Therefore, I'm changing my approach. I am GOING to graduate and I'm going to graduate in May of 2011.

Here's my plan: get myself back into dissertation mode and set clearly achievable goals, make the process more transparent (looking to add some accountability with this one!), and finally set aside time to make this happen rather than thinking I can do this without interrupting my work and family schedule. I just don't have the energy to do it that way. (I do applaud those who are able to make that happen.)

What does this mean for this blog? I'm hoping to do much of my work right here. I am going to attempt to post a lot of my work/thinking right here for lots of reasons, but mostly, just trying to make my work visible to myself so I can keep my momentum going. If I get feedback and support great, but I don't know that I'm prolific enough to develop that kind of a following.

Developing Problem Solving in math students

2010-05-07T09:26:00.000-07:00

I've written several posts recently about problem solving recently and I am still working through my thinking. I have mentioned that I agree with the approach that Dan Meyer espouses in his wonderful TEDx talk. I think Dan is espousing problem solving not only as a cornerstone of a mathematics classroom, but problem solving that is rich, complicated, open-ended, and varied so that students work through the processes. I think he's right but I think there are other issues of equal importance.

It is important that we provide teachers with tools to help them work bridge the gap in problem solving in their classrooms. We can't just expect teachers to start asking students harder and more complicated problems in their classrooms and expect them to be successful. So the question for me is how do we support teachers in becoming more rigorous?

I've been a long-time proponent of Singapore Math for a variety of reasons; one of which is the model method they use in their elementary program. The heuristic alone isn't a cure all, but it does offer some interesting parallels to Dan's approach to more open ended problem solving situations in classrooms.

Let me try to illustrate my point. I came across this problem "134 girls and 119 boys took part in an art
competition. How many children took part in the competition?" in Bill Jackson's PowerPoint on the Model Method on the Daily Riff. It's not a difficult problem but in the Singapore approach the problem will be explored from a variety of relationships, so that students are comfortable looking at a situation from multiple perspectives and are used to modeling situations from a variety of points of view.

For example a related problem might be, "119 boys took part in an art competition. 15 more girls than boys took part. How many girls took part in the competition?"

or "253 children took part in an art competition. There are 134 girls. How many boys are there?"

I would, also, look to the research by John Sweller that discusses the difference between novice and expert thinkers. He encourages the use of the open ended approach to help students look at situations not from a focus on the solution or answer but from a perspective of what are the relationships that I can see, to help students become more flexible in their learning and approach to problem solving.

The expectation that students will routinely look at problems and identify different relationships, I believe will lend itself to helping students look at problems with the understanding that there are different relationships available here, potentially resulting in a student being more flexible in their problem solving approach.

I have always valued problem solving and think it's critical that we continue to push students to problem solve more effectively, and more importantly push teachers to expand their approach to problem solving.

Showcasing Student Products

2010-05-04T08:10:00.000-07:00

I'm not a huge fan of any particular product, but my experiences with teachers integrating new tools into their instructional routine over the past two years has taught me that if there is a simple tool available then encourage teachers to use it.

Again, let me say, I don't care what tools teachers use as long as they are having students create products that showcase the student's thinking, that encourages students to analyze processes, makes the student's thinking transparent, and lets students use the tools that are available to them. As long as a teacher is doing these things, I don't care what tools they are using. In fact, one of the best examples that I've seen was a simple piece of chart paper with graph paper taped to it. It's the thinking that I'm after and not the use of technology.

All of that said, having students create Voicethreads is a great way for students to present what they are learning. I'm working with several schools to incorporate Voicethreads into their instruction as a tool to help students create products that showcase their learning. It lends itself well to the comfort level of some of the teachers. They already have students do some work with PowerPoint and Voicethread is such a natural extension of that product that I openly encourage teachers to push to the next level.

I've been very impressed with some of the great ways teachers have used Voicethreads. In one classroom, Ms. Mullins is having her algebra II students showcase the process of factoring trinomials; making their decision making very transparent as they go through the process. Being able to factor the trinomial is important, but being able to make clear the thinking process is as important so that the student is able to work through the process with different problems next time.

In another class, Mr. Hoskins, is having his students present their career PowerPoints and their presentations via Voicethread. It's not a huge difference from delivering the speeches in front of the class, but what it is forcing the students to do it so practice and to hear themselves before they get in front of the class. Mr. Hoskins has been excited about how much effort students have put into the "speeches" they are doing on Voicethread and the impact it has had on the quality of their presentations. He is now able to showcase those presentations for other students and parents.

One very nice addition was the ability for students to grade Mr. Hoskins' Voicethread prior to the process, so students were very familiar with what the rubric meant and were able to discuss the differences between the different categories!

It is an interesting and very profitable next step to showcase that work intentionally in a wiki or blog format. The wiki especially allows the students (and teacher) opportunities to share what they have been doing with their parents and family. Not all teachers are ready for this next step, but I keep encouraging teachers to think about the entire cycle and how they can use this collection of information and materials to make the idea of having students showcase their learning an integral part of the learning processes in the classroom.

It's funny as I read this post it's nothing new or earth shattering, but it is yet another example of the process of instructional change and how difficult it is for teachers to implement while they are teaching a class. Which brings me back to my initial point, "Make it simple" and that's what Voicethread does. I know I said I don't usually advocate a particular product, but I may have to make an exception for Voicethreads.

http://www.flickr.com/photos/theunquietlibrary/ / CC BY-NC-SA 2.0

Problem Solving is Better When It's Complicated

2010-05-04T07:45:00.000-07:00

Dan Meyer presented at the TEDxNYED conference recently and delivered this talk on teaching problem solving in US schools:

Let me say I couldn’t agree with Dan more!

His approach to developing problem solving is simple. Let students focus on figuring out what the relationships are, let them work through the details themselves and create their own understanding, instead of handing them the answer masked in a couple of simple computations.
I agree with everything that he espouses here and am glad that he is saying it because he says it so much more eloquently than I am able to.

My agreement means a lot to me but I understand others may be less swayed by my position, so I looked to research to back up these simple ideas. I found several pieces of research that add to this discussion. Notably John Sweller wrote in, Cognitive Science, 1998, about the difference between novice and experts when they are problem solving. Novices tend to work backwards from the answer to identify relationships they understand that they use to work their way back to the information provided. Interestingly, an expert tends to work forward from the information provided to direct themselves toward the target answer.

These two divergent perspectives become enlightening when compared to Dan’s approach. Instead of falsely providing novice learners an expert approach (by asking them questions that guide them from the information provided toward the solution) Dan espouses to let them progress through the novice stage, and let them build their cognitive understanding themselves. I would like to add that making this process a point of reflection for students may hasten their transition to the expert approach.

Sweller goes on to write that students who are asked to just determine as many relationships as they can are more likely to take an expert approach to a problem solving situation because there isn’t that focus on the one correct answer. This ‘brainstorming’ approach also more closely mirrors real life research in many ways in that direction is often established by observing relationships that can be determined rather than already knowing a direction to go.

This focus on process is critical to Schoenfeld (1987), and Garofola and Lester (1985) have suggested that students are largely unaware of the processes involved in problem solving and that addressing this issue within problem solving instruction is an important step in helping students progress through the different stages of learning.

All of the research is predicated on the fact that we allow students to work their way through problems, struggle with outcomes, and learn from the process. How can students take on this challenge if we as teachers continue to ask them simple problems and guide them through the process like an expert when they aren’t?

Garfola, J. & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163-176.

Schoenfeld, A. H. (1987). Cognitive science and mathematics education: An overview. In A. H. Schoenfeld, Cognitive science and mathematics education. Hillsdale, NJ: Lawrence Erlbaum.

Sweller, J. (1988). Cognitive load during problem solving: effects on Learning. Cognitive Science, 12, 257-285.

Is your thinking as dynamic as Geogebra?

2010-03-12T10:15:00.000-08:00

I've been planning my session for the upcoming Kentucky Gearup Alliance Institute, Use of GeoGebra: free mathematics software to help students understand and apply concepts in geometry, algebra, and calculus.

Geogebra is an incredibly powerful dynamic mathematics software (DMS) designed for teaching and learning mathematics at the secondary and college levels. It combines mathematics disciplines of Geometry and Algebra, hence the name Geometry Algebra. As I plan my session I keep coming back to the changes that occur in high school mathematics for students. Much of the work they have done to this point is very concrete; real number operations, data analysis, simple geometric relationships, measurement, and proportional thinking. In algebra I there is a major shift to a very abstract approach to algebra instruction, especially in the United States (National Research Committee, 2005). Additionally, the new CCSSO standards that many states are adopting place an increased emphasis on conceptual understanding and development of student ability to work holistically with functions rather than work primarily from a skill based approach.

So why do a session on Geogebra? Why is it different?

Technology has progressed a long way in recent years, and the dynamic nature of tools that are available make them powerful learning tools. Eighteen years ago James Kaput, a leader in the use of technology in the mathematics classroom, "predicted that in regard to continuing growth of electronic technology, "major limitations of computer use in the coming decades are likely to be less a result of technological limitations than a result of limited human imagination and the constraints of old habits and social structures (Priener, 2008)." I think Geogrebra may be the tool that more teachers of mathematics will be able to see as viable in their classroom.

The reason I think Geogebra may be a game changer in creating opportunities for students to interact with content differently and the reason I think it is the exception to Kaput's prediction is it's simplicity and flexibility. Yes, I know I'm a technology geek, and I know I'm an evangel of dynamic applets, but Geogebra does what no other tool has been able to do, does it easier, cheaper, and more flexibly. Let my provide you a case in point.

Let me take a few moments to show you a quick sample of what Geogebra can do: In an algebra I course developing understanding of linear functions is a major focus of the course, and creating contextual understanding has been proven to help students creating deeper understanding.

Notice in the example pic that students not only see the graphical representation in connection to the story problem. Students can manipulate the situation by changing car speeds using the sliders on the left, can see the impact of their changes as the cars move and as the time/distance graph changes.

Here is an example of just how easy it is to create objects using Geogebra. If teachers want to have students create objects to explore slope it can be as easy as...

As I put more planning into my presentation, I'm reading "How Students Learn: Mathematics in the Classroom" by the National Research Council, and I keep coming back to making connections between the different representations, having students create objects, manipulate those objects, and observe the characteristics of those objects as being central to the principles that the National Research Council has identified as being crucial to deep student learning and understanding.

Finally, we have a tool that is only limited by our own imaginations, so even if you aren't very imaginative, let your students be and let their learning soar with the endless possibilities of a tool like Geogebra.

Creating Conversation, Gathering Evidence of Learning, and Algebra!

2009-11-19T06:30:00.000-08:00

I recently had a conversation about formative assessment with two algebra II teachers. It was a great conversation about creating opportunities for students to make products to show what they know, how teachers can use these products to learn more about the thinking of their students, and how to intentionally integrate these kinds of products routinely into instruction. One reason the conversation was so strong is because we started off talking about what we wanted to know about what the students were learning and moved to what that might look like, before we ever discussed strategy or instruction. It gave us several ideas to pursue. The conversation wasn't about what we were or weren't doing but about how we can tell what the students know and use that to help us inform what happens next in the classroom. Wiliam and Black (1998) identified five simple factors for effective formative assessment:

immediate, effective feedback to students
involvement of students in their own learning
adjust instruction based on results of assessment
student self assessment and understand how to improve performance
recognize influence assessment has on the motivation and self esteem of students

The result of the conversation was a matrix that looked at the learning cycle (access prior knowledge, during learning, synthesis/summary) along one dimension and process, algorithm/computation, and multiple representation/communication along the other. We then proceeded to identify different strategies, products, and uses for each category. It was interesting to look at different aspects of the learning cycle and then think about how we create opportunities to have students show what they know during that cycle with the express purpose of having students give and get feedback that is timely and influences next instructional steps.

One strategy identified by one of the teachers stood out for me. She had different rows of students solve a problem using specific methods (i.e. row 1 solved the linear system using graphing, row 2 solved the same problem using substitution, and row 3 solved the problem using linear combination). She then had students from the different rows come together to explain how they solved the problem, compare answers, and compare processes. At the end of the activity she had group products that solved each problem in multiple ways, had an explanation of what the solution meant from the different perspectives, and to my great joy, an analysis of the strengths and weaknesses of each method for solving that particular problem.

She built into the conversation a quick student reflection on what they learned about the characteristics of the problem that made a particular method most effective, and which method made most sense to the student. I almost stopped our conversation right here, because for me that was it! Students were involved in the process, were able to talk about the strengths of a particular method, the teacher is able to use what she heard during the conversations to clear up any misconceptions and point to any insights, and post the products for extended conversations/models.

I think it's very important to have students communicate what they know, but without a responsive teacher being willing and able to use that information to make their instruction more responsive then deeper learning may not be able to occur. This teacher gets it, she understands the need for extended conversation, organization of ideas, developing group understanding, providing immediate feedback, and making students responsible for their learning.

Picture: "linear system multiple representation” by rodaniel,

http://www.flickr.com/photos/rlodan01/ / CC BY-NC-ND 2.0

Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5 (1), 7–74.

Coach's Corner 11/10/2009

2009-11-09T22:30:00.001-08:00

iPod Touch Schoolwide Implementation - Classroom 2.0
iPodTouch in education conversation. Lot of great information.
tags: web2.0, technology, differentiation, ipod, touch, instruction
Differentiated Instruction | Teaching and Learning in the Digital Age
tags: web2.0, technology, blogging, differentiation, learning, instruction, pedagogy, education
Blogging About The Web 2.0 Connected Classroom: The Essential Tools For The Connected Teacher-Part 1
Some nice ideas about using web2.0 in the classroom. Worth visiting for ideas.
tags: web2.0, technology, blogging
Center for Technology and Teacher Education || Macromedia Flash Activities
Some great applets for use with math classes.

From basic arithmetic modeling to modeling of integrals.

From the University of Virginia these flash based apps will work on almost any platform except the iPod system (currently).
tags: math, web2.0, applets, technology
Illuminations: Dynamic Paper
Neat tool for teachers. Need a quickly designed number line or graph paper. From NCTM and Illuminations,
easy to create different options,
easy to download as a jpg and then cut and paste if you want to use in another file.

Good for basic graphics needs that you might not be able to create on your own like nets and spinners.
tags: math, instruction, worksheets, dynamic, illuminations
Learning in Hand - iPod touch Applications
iPod Touch in the Classroom ideas.
tags: ipodtouch
Mathematics Knowledge Networks (MKNs) - Using assessment to promote learning in mathematics - NCETM
Always looking for resources that help math teachers think about how to promote learning in the classroom. This synopsis of formative assessment research starts with Wiliam and Black, "Inside the Black Box" from 1998 and progresses forward from there. Some nice specific tasks that are supported by links to examples.
tags: mathematics, assessment, math, instruction, knowledge

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/30/2009

2009-10-29T23:30:00.001-07:00

SpringerLink - Journal Article
Links between math and art, current research, worth reading.
tags: math, art

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/23/2009

2009-10-22T23:30:00.001-07:00

Tools for Differentiation / Mathematics
tags: differentiation, wiki, pd

Posted from Diigo. The rest of my favorite links are here.

Presenting at KCTM

2009-10-22T09:21:00.000-07:00

I had the opportunity to present at the KCTM Conference, October 10th, 2009 at Bourbon County High School. I presented about using regression modeling to support algebraic understanding and thought it was a good presentation, although I would liked to have had a few more people present.

The keynote speaker was Jon Wray, and he spoke about the hot topic of disruptive technologies. I enjoyed his talk and am sure that for the given population it was pretty radical. (I don't think most math teachers look at the influx of technologies as a good thing in their classroom, which is unfortunate!) The opportunity to go beyond the basic explanation about all the different ways people are using technology outside of the classroom has been done as has the Did You Know videos. Again, I like those videos, but I need more!!! It's not good enough anymore for me to continue to see the presentations, and to see people go "Wow", and to then see them go back to their classroom, shut the door, and NOT plug in their students.

During Jon's session later that day, I continued to tweet my thoughts with the hash tag #kctm. An amazing thing happened. I was joined! Two other educators-@dcraigschroeder and @STEMeducator, in the presentation were doing the same thing. We had an interesting conversation. I just wish others could have joined in. I, unfortunately, had to leave early to present and was unable to say "Hi" in person (although I did see them across the room). It was a great example of disruptive technologies and the power they can bring. We've continued to share and my PLN has grown by two very strong contributors.

This is what it's all about, but how do we expand beyond the 3 of us to include more? This is the question that has been troubling me ever since the conference. I keep going back to disruptive technologies and how do we use them to make what we are doing stronger and more effective. I think about the effort that I and so many other presenters put forth to prepare our sessions and wonder if KCTM could create a blended conference for next year. Could we have the day where we all come together but use that as the first day of the conference rather than the only day of the conference? Could be make the goal to be extension, application, adaptation, and sharing? What would it take? Would others be willing to join the conversation? Or would it be the three of us talking?

This has been floating around in my head for several days and I know I need to get it out so I can either be part of the solution or part of the unsolution!

Let Students Measure

2009-10-22T08:32:00.000-07:00

Measuring is a skill that continues to appear as one of the weaker domains for fourth graders in the 2007 TIMSS data. As students progress through school geometry replaces measurement as the weakest area for eighth graders with ten more countries outperforming American students in geometry than compared to the number content domain. Regarding the cognitive domains, American students performed well in the knowledge domain in comparison to other countries and less well in the applying and reasoning in both the fourth and eighth grades. It is laudable that American students are making gains on the TIMSS assessments, and I believe a testament to the fact that American mathematics teachers are pushing their students to learn more rigorous content.

Measurement is a domain that requires extensive practice and context for students. Providing opportunities for students to measure in the context of learning other material allows students to practice and become more fluent in the domain. Actually measuring things also provides context for which to learn and understand new content. The idea of chunking concepts together is not new, and is a great way of helping students understand material more effectively. The processes involved in actually getting students moving around measuring objects reinforces what we know from the latest brain research as well. Novel movements (movements that are new, fine motor, and can be complex) involve the prefrontal cortex and the rear two-thirds of the frontal lobes, the areas of the brain involved in problem-solving, planning, and sequencing (Jensen, 1998). Additionally, involving more aspects of the brain allows for more and stronger connections to be developed when learning new material making the learning more flexible and easier for students to retrieve.

The skills involved in measuring go beyond identifying the length or width of an object, but also provide context for students to deal with rational numbers, ratios and proportions, geometric relationships, and important science concepts like precision and accuracy. Having students measure their own heights in both the metric system and the English system is not a complex task, but allows teachers to create engagement, have immediate conversations about relationships between the two measurements, and something as simple as have students discuss the ordering of students from least to greatest in height.

If we know that a content domain such as measurement is a weakness for our students then we need to develop a plan that allows the students to address those concerns while at the same time continuing to learn new material. Measuring is a great tool for creating opportunities for students to learn more effectively, so why not let them measure today!

What Mountain Should We Be Climbing in Math Ed?

2009-10-22T06:24:00.000-07:00

I want to thank Mike Falick for posting this TED talk last week. I've argued for years that probability and statistics is the best unheralded math class in high school mathematics. We push our top notch students toward calculus because it is the gatekeeper to engineering, physics/sciences, and mathematics degrees, but what about the other 97% of students who aren't going to become engineers and scientists? (sources: wolfram alpha; US dept of labor) Do we push them toward the utopian goal of calculus so we can justify the course? Or do we push them toward a rigorous statistics class that will challenge them, and prepare them for using mathematics in the fields they will actually choose to enter?

Statistics is one of the fastest growing fields in mathematics, and an easy field for students to see application. For high level students who want to continue to push themselves, but know math is not their primary focus, probability and statistics provides a golden opportunity to make rigorous mathematics an option.

Why not approach mathematics education differently? Why not make probability and statistics a goal unto itself rather than the course we push students into if they can't handle calculus? Would it hurt the top notch math students? I don't think so, I am not espousing to do away with calculus; I am arguing that we just do not make the penultimate high school mathematics course. Wouldn't it be better to teach to the 97% rather than the 3%?

I think it's worth a discussion and I agree with Arthur Benjamin that it is time we changed our focus in American mathematics to embrace probability and statistics in a rigorous way in high school mathematics. Let's add a mountain to our range and see if we can't get more people to become mountain climbers!

Writing in Math Class

2009-10-21T06:37:00.000-07:00

I captured some ideas about writing in math classes several years ago on a wiki for a class I was taking (Teaching Transactive Writing). It is interesting as I looked through my Google Analytics account today that that wiki continues to be one of the most visited sites that I've created. There continue to be almost 75 visitors a month to the site. I haven't updated it in almost two years, so they aren't coming for new information.

There is no doubt they come because the topic is a tough one for mathematics teachers. We aren't trained to teach writing, and I will say that many of us don't feel comfortable with the process (note my attempts here at writing and writing consistently), but we know that communicating understanding must involve having students write about mathematics.

I, also, believe that there aren't a lot of good writing examples available to teachers in middle and high school level mathematics classes. If you are a blogger then you know of Darren Kuropatwa's classes at Daniel McIntyre Collegiate Institute, but what other examples do you find as real integrated routines? I think Darren does some fantastic things and is a great thinker, but is he the only math teacher out there who can pull it off? Maybe, but I think there are some other capable teachers out there.

I am in the process of working with several teachers to develop note taking routines in their classes to allow students to learn how to take notes, but more importantly learn the content more effectively as a result of taking notes. It's this kind of writing that I think a lot of math teachers are already doing with their students that can have immediate impact and efficacy. It's, also, a great place to start if someone is interested in doing more writing with their students.

One of the teachers (I will call him Dave because I haven't asked permission to use his name in my blog yet) has developed a very intentional plan to support his students in the process of writing notes and using those notes to make connections, to expand/extend their thinking, and to very intentionally help the class synthesize the learning from the day.

After Dave gets an opportunity to get his routine in place, I hope to share more examples of what he's doing and share more about the routine. From looking at the number of people going to a wiki that is limited in scope and old, I think there will definitely be an audience for Dave's work.

Photo source by solofotones

Addendum: I wanted to make sure I put these into the post itself. Darren was kind enough to comment and pointed out several blogs to look at:
The blog love is spreading; check out:

Derrick Willard's class blog
Jim Homan's Cathoilic Morality wiki
Mr. Marti's precalculus class blog
Reversearp's (an alias I believe) precalculus class blog
Mrs. Everard's AP Calculus class blog

Every new day brings more new math bloggers. This is a small, and woefully incomplete list. ;-)

Yes, everyday brings more new bloggers and builds a foundation of what it can look like for those teachers still lurking in the shadows. I hope others will point me toward more blogs to check out!

Coach's Corner 10/21/2009

2009-10-20T23:30:00.001-07:00

MathSite: Polygon Dissection Gallery
tags: web2.0, geometry, math, applet, Berkley, smartboard, technology
Soople; easy search in Google. Advanced calculator
tags: web2.0, search, reference
- - post by geneboy
- - post by svartling

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/08/2009

2009-10-07T23:30:00.001-07:00

copyrightconfusion - Reasoning
How do I know if my use is a fair use?This tool has been developed to help teachers and students reason through the fair use process. You can see an example of how this tool is being used HEREUse the form online. The data from this form feeds into a google spreadsheet so you can compare how individuals or groups reason the fair use of copyrighted material in a work. If you would like to use this form in your work you can click here. If you have a google account, you can sign in and copy into your google account.
tags: fair, use, copyrightconfusion, copyright, administration, instruction
» Would You Please Block? Bud the Teacher
Another great post from Bud, actually calling attention to the issue of classroom management rather than the tool being the issue. How dare students express their boredom by doing something rather than daydreaming...Make sure you read the comments, especially Dave Truss' response.
tags: filtering, blocking, blogging, administration, instruction

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/06/2009

2009-10-05T23:30:00.001-07:00

Posterous - The place to post everything. Just email us. Dead simple blog by email.
Blending lines in how you post to the web. Moving toward a truly interactive web.
tags: blogging, web2.0, tools, posterous
Teacher Online Training
More Smartboard resources from Teacher Online Training. Some nice easy to understand videos, easy navigation, and great exemplar files. I still need to do some exploring of the files, but liked the two I looked at today.
tags: web2.0, smartboard, IWB, instruction
PinDax - Online Message Board
Post it notes site similar to Wallwisher
tags: web2.0, write2learn, visualization, instruction
SHOW®USA - A New Way To Look At The USA
Lots of data displayed in an interactive way. Great for use with an interactive white board. Easy for students to gather data, display, and report.
tags: math, SocialStudies, instruction, web2.0, technology, Statistics, Data, maps, geography, visualization
podOmatic - Create, Find, Share Podcasts!
tags: web2.0, technology, podcasts, fluency, dialog, instruction, write2learn
Create and share flashcards - ediscio.com
Create and share flashcards online, make the flashcard idea more interactive, allows you to capture some metadata and track how you are doing. If students are going to memorize something this might be a way of making it more interesting. Enables the input of video, audio files into flashcards.
tags: web2.0, technology, memory, education, flashcards
wetoku
Great way to create podcasts with students when they interview someone for their class. They can "meet" experts online and record the conversation so they can revisit the conversation and share with others.
tags: web2.0, technology, videoconference, interviews, videoconferencing, skype
Defence Dynamics - Multimedia Library
tags: web2.0, technology, math, science
Read free books online: The Call of the Wild, by Jack London
"BookRix allows writers to create their own projects and display their work to others. The BookRix-Format enables users to design individual books. All one needs is a web browser to easily publish and showcase their work."

Book-like interface, where readers can "turn pages". Great way of showcasing student work, getting feedback, producing rather than just consuming material. The interface does provide a more formal presentation of material and makes a more published feel.
tags: write2learn, instruction, web2.0, technology, write2pub

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/03/2009

2009-10-02T23:30:00.001-07:00

Education Community Blog: Search Results
Obviously,I'm not a writing expert, but I love how this post describes the writing process this teacher is using at Duke with her students. The peer editing process is tested and this approach uses a screencast (video that can include audio of what is happening on a computer- mouse movements, ability to highlight text while commenting, etc.)

I think it's right up our alley and incorporates free technology.
tags: instruction, write2learn, peer editing, web2.0, technology, dialog
Starting Point-Teaching Entry Level Geoscience
Geared toward developing good instructional strategies for entry level geo-science courses at the post-secondary setting, the suggestions can easily be applied to 6-12 setting and are just good instructional practices.
Well organized and includes different perspectives and connected content.

I thoroughly agree with the mathematical modeling discussion. It's worth reading
tags: education, geoscience, science, web2.0, math, instruction, high, middlegrades

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/02/2009

2009-10-01T23:30:00.001-07:00

DEN Blog Network » Experience the Adventures With Your Students
Discovery Educator Network projects.
tags: blog, inter-classroom, web2.0
Technology's Impact on Effective Teaching Strategies -- THE Journal
"The United States Department of Education published a report over the summer titled, "Evaluation of Evidence-Based Practices in Online Learning; A Meta-Analysis and Review of Online Learning Studies" (Center for Technology in Learning, 2009). What's interesting about this report is that it confirms what those of us who teach or have taught either distance or online courses already know and moves us beyond what is often commonly believed: that there is no significant difference between online learning and the face-to-face experience. "
tags: online, instruction, meta-analysis
Microsoft WorldWide Telescope Web Client
Directly from Time Magazine: "Like Google Earth for the heavens, WWT aggregates terabytes of astronomical data from the world's biggest telescopes to create a single virtual scope that anyone can look through. WWT is not a model of the known universe, but rather a centralized repository for just about everything known about the universe. The idea is to democratize the science of astronomy with a single tool that can be used by students and scientists. Who knows, when everyone has access to the same data, maybe the next big discovery in astronomy will be made by an amateur? There are hundreds of terabytes of digitized sky — enough data for everyone. "
tags: gifted, telescope, Astronomy, science
Aardvark
New type of search engine. Ask your friends/students/peers a question and find out what their online response might be. Not sure of the usability for the classroom, but let me know if you think I'm way off base.
tags: web2.0, collaboration, aardvark, crowdsourcing
Photosynth: Your photos, automatically in 3D.
Been a fan of this site for a while and didn't realize I hadn't bookmarked it yet. Instead of arranging photos in a traditional album,Synth finds relationships among pictures and digitally composites them to create a 3-D experience. Awesome!
tags: web2.0, collaboration, digital, photgraphy
Simple private real-time sharing and collaboration by drop.io
Great file sharing option for those who like to have access to files on different computers or want to create backups. Also, great for collaborating with others.
tags: storage, filesharing, web2.0, collaboration
- - post by mingqing
- - post by yyensen
- - post by angelamaiers
- - post by paulpomeroy
FiveThirtyEight: Politics Done Right
Another polling site. This one is the brainchild of Nate Silver. His predictions during the 2008 presidential election were consistently more accurate than the national media outlets. He must be doing something correctly. BTW, he's a baseball statistician by trade.
tags: polls, election, socialstudies
Pollster.com - Political Surveys and Election Polls, Trends, Charts and Analysis
Aggregation of poll data. Great way of exploring data with lots of social studies/current events connections. Time rates this as one of the fifty best sites this year. Worth a few minutes of exploration.
tags: statistics, polls, news, elections
- - post by docbadwrench
Kiva - 50 Best Websites 2009 - TIME
tags: kiva, microlending
MetaFilter | Community Weblog
There are lots of collaborative voting and comment sites out there — Digg, Reddit, StumbleUpon and Metafilter is another one. It costs five dollars to join, but that cost keeps lots of spammers and ads off the site. A great plus.
tags: blogging, news, community, comprehension
- - post by calebism
- - post by abaklg
Academic Earth | Online Courses | Academic Video Lectures
University lectures available online from all over the world, including MIT, Harvard, etc.

Not necessarily great lectures all the time, but great sources of information and sometimes great examples of lecture done well.
tags: university, opencourseware, web2.0, interactive, scholars, academic, education, lectures
Boing Boing
...is a deliberately eclectic mix of tech commentary, sci-fiction nerd-outs, fringe culture, gadgets, and serious news items. It is, according to its own description, a "directory of wonderful things."
tags: web2.0, interactive, comprehension, write2pub
- - post by dscrimshaw
- - post by nannaner
- - post by mistersite
- - post by pablopowell
- - post by minichaos
- - post by ilia11
Triangles with Specified Side Lengths
"This applet is designed to visualize triangle construction where the lengths of the sides of the triangle are specified.

The right sides of the top 4 lines of the applet are draggable. This lets you modify the scale used for measuring and the lengths of the three sides.

The applet displays the length of the sides and the size of the angles in the constructed triangle."
tags: web2.0, math, triangles, geometry
Applets for math courses below calculus
"These following collection of applets are designed for use in mathematics courses below the level of calculus. Some of the applets were developed at SLU and some have been developed elsewhere and are included by permission. If you would like to host the applets locally, please contact Mike May, S.J. "
tags: math, web2.0, applets, algebra, slu, calculus
Calculus Applets at SLU
"Math Applets for Calculus at SLU"
tags: math, web2.0, mathematics, algebra, slu, calculus, applets
- - post by pennmanormath
YesICan Polar Science 2009
Great opportunity to collaborate online with scientists researching real questions: "the team is trying to answer the question - how do the skeletal muscles of seals develop to work during deep dives, even when the animal is not breathing for long periods of time. The researchers believe the answers to this question may have tremendous implications for human medicine. By understanding how another mammal has successfully overcome the debilitating effects of working under low oxygen conditions, we may be able to learn new therapeutic approaches to assist humans with heart or lung disease. "
tags: biology, chemistry, instruction, inter-classroom, web2.0, technology

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 10/01/2009

2009-09-30T23:30:00.001-07:00

Spezify
Really interesting way of doing a multimedia search. Not sure it's classroom safe, even with safe search on there were several images that were beyond borderline. When I did compound search "algebra" + "linear" much tighter and deleted virtually all inappropriate material.

I just like the way you can explore the information. If you have students gathering information and tagging with specific tags like "wjhsconlit09" then you could pull up all of that material without interference. I think it's a great tool for that kind of exploration.
tags: search, visualization, spezify, mashup, visual

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/30/2009

2009-09-29T23:30:00.001-07:00

Handbook for Mathematics
Singapore Math in the US site. Several books for ordering.
tags: singapore, textbook, teacher training, math
Comparative Studies on U.S. and Chinese Mathematics Learning and the Implications for Standards-Based Mathematics Teaching Reform -- Wang and Lin 34 (5): 3 -- Educational Researcher
Chinese students often outperform U.S. students on international tests in mathematics. Chinese students’ mathematics performances are assumed to be related directly to their teachers’ deep mathematics understanding and ability to represent concepts flexibly in their classrooms, which, in turn, are thought to be influenced by Chinese mathematics curriculum and policies. The authors examine this theoretical assumption through a systematic review of relevant literature and attempt to identify the relationship between Chinese students’ mathematics performance and the factors that contribute to their achievement. On the basis of their review, the authors raise questions about the assumption and propose research that can lead to a better understanding of the relationship between the quality of students’ mathematics learning and the contexts in which their learning occurs.
tags: student performance, chinese, math, standards
http://math.nie.edu.sg/lhfan/Publication%20in%20PDF%20files/Inservice%20training%20in%20Alternative%20assessment%20(Final%20version%20for%20ME).pdf
In-service Training in Alternative Assessment withSingapore Mathematics TeachersFan LianghuoNational Institute of Education, Nanyang Technological University, SingaporeAbstract: Fifty-nine primary mathematics teachers of three intakes participated in in-service training in alternative assessment newly offered at a university in Singapore. A study, action research in nature, was undertaken to examine the effects of the in-service training and investigate relevant issues in promoting teachers' use of alternative assessment in classrooms. Data were mainly collected through questionnaire surveys, the participants’ work on an authentic alternative assessment task, and field-notes of the training. The results indicate that systematic training in alternative assessment is highly needed for school teachers, and inservice training can be an effective way to promote their professional growth in this area, especially through their integrating authentic alternative assessment tasks into their actual classroom teaching as part of the training. In addition, the study reveals that the current school curriculum does not well reflect the new development of assessment and therefore there is a need to integrate the concept and content of alternative assessment into school curriculum to facilitate teachers’ use of alternative assessment in classroom. Some other relevant issues, including advantages and disadvantages of in-service training, are also documented in the article.
tags: teacher training, singapore, math
SpringerLink - Journal Article
Lianghuo Fan1 and Yan Zhu1Centre for Research in Pedagogy and Practice, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore, 637616, SingaporeAbstract: This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layers – general strategies, which adopted Pólya’s four-stage problem-solving model, and specific trategies, which consisted of 17 different problem-solving heuristics such as ‘acting it out,’ ‘looking for a pattern,’ ‘working backwards,’ etc. Both similarities and differences in the representation of problem-solving procedures in the textbooks across the three countries were revealed and compared. The possible reasons for the similarities and especially for the differences were explored. Suggestions about how to improve the representation of problem-solving in mathematics textbooks were provided at the end of the study. Comparative study, Mathematical problem-solving, Mathematics textbooks,Curricular contents, Pólya’s problem-solving, model, Problem-solving heuristics, Textbook analysis, Lower-secondary mathematics
tags: problem solving, singapore, textbook
Miracle Math: A Successful Program from Singapore Tests the Limits of School Reform in the Suburbs
Miracle Math: A Successful Program from Singapore Tests the Limits of School Reform in the SuburbsAuthors:Personal author, compiler, or editor name(s); click on any author to run a new search on that name.Garelick, Barry
tags: singapore, textbook, math
ccsso math standards - Google Search
Alignment Content Analysis of TIMSS and PISA Mathematics and Science Assessments, Using the Surveys of Enacted Curriculum MethodologyFebruary 2009, A CCSSO paperPrepared for National Center for Education Statisticsand American Institutes for Research
tags: no_tag
Top News - ED announces student video contest
Great opportunity to have students showcase their skills, their learning, and for teachers to maximize an engagement opportunity. I would love to collaborate with someone interested in making this a class assignment. Looking for someone to help provide guidance, let me know!
tags: write2pub, web2.0, video
sean.blog: Diigo 4.0 Release
We introduced Diigo to WJHS this summer and I thought I would pass this news along to everyone, but especially that group.
I still think Diigo is an incredible tool for collaboration in the classroom for research, group work/accountability, formative assessment, reaching beyond classroom walls both with students and colleagues.

Additionally, Sean does some nice simple video production (with totally FREE tools) that I want to share with other teachers. It's easy to do, is a way of getting information to your students easily and in a manner that allows them to access the information as many times as they like/need.
tags: diigo, socialbookmarking, research, write2learn, write2pub, dialog, blogging, bookmarking
- - post by qncenterlab14
Miracle Math : Education Next
tags: singapore, math, textbook, algebra
Study: Wikipedia as accurate as Britannica - CNET News
I've been an advocate for Wikipedia for a long time, yet more information saying it is a valid source (as with all sources we need to teach students to find corroborating sources before using the source).

Not without error, but does go to show that even more trusted sites have errors, so don't hold Wikipedia to a different standard!

Finally, what makes Wikipedia a better source is a shear volume of information on the site as compared to other 'encyclopedias'.
tags: wikipedia, research, write2learn, comprehension, encyclopedia
Heilbrunn Timeline of Art History | The Metropolitan Museum of Art
I've always liked timelines as an educational tool. They offer the ability to show related threads compared to each other easily. I loved having students investigate a single topic, create a timeline for that topic, mash the timelines together in a BIG overarching timeine, and then have students start to look for connections. I stole the concept early in my career from the TV show Connections (too bad it didn't make it, GREAT GREAT show).
tags: timeline, art, arthistory, socialstudies, history, write2pub, write2learn
Learning in Hand - iPod touch in Education
tags: ipodtouch, technology

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Coach's Corner 09/29/2009

2009-09-28T23:30:00.001-07:00

Screenr - @jameshollis: Activity example using Smartboard, Notebook, Wordle, and a reveal technique from Teacher Online Training.
An easy to create activity for use with a smartboard. I like the Guess the Wordle of the Day concept, I like that students try to guess based on contextual clues, and I like that it uses the Smartboard (although it's a relatively low level usage, it's still interactive.)
tags: wordle, web2.0, vocabdev, iwb
ModuMath Algebra 11
Modumath as linked from Wisconsin Online learning resources. Interesting videos of algebra concepts, not a huge library but well worth the exploration. You must join http://www.wisc-online.com/ to gain access, but it's free and very interesting.
tags: web2.0, math, technology, applet
Webquests
Webquests from the National Portrait Gallery, United Kingdom. Some Webquests designed with specific age/content groups in mind. Worth a look if you like using Webquests with your students.
tags: social studies, webquest, technology

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/28/2009

2009-09-27T23:30:00.001-07:00

Education / American Art
I guess the original link I bookmarked changed. Here is another one from the museum
tags: Smithsonian, socialstudies

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Coach's Corner 09/25/2009

2009-09-24T23:30:00.001-07:00

picturing the thirties
• “Picturing the 1930s,” a new educational web site created by the Smithsonian American Art Museum in collaboration with the University of Virginia, allows teachers and students to explore the 1930s through paintings, artist memorabilia, historical documents, newsreels, period photographs, music, and video. Using PrimaryAccess, a web-based teaching tool developed at the university’s Curry Center for Technology and Teacher Education, visitors can select images, write text, and record narration in the style of a documentary filmmaker.
tags: web2.0, socialstudies, primary source, smithsonian, museum
The Beginner's Guide to Tricking Out Your WordPress Blog - Blogs - Lifehacker
tags: blogging, CTL blog
MIT Students Explain How to Photograph Space for $150 - $150 Space Photo - Gizmodo
Follow-up to the BEAR-4 near space video from amateur radio enthusiasts from Edmonton, CA. These students (yes, MIT students) capture still photos from space for $150 worth of equipment. Again, it's all about letting students solve problems, using technology that is available to them, and sharing it! Talk about engaging!!!!!
tags: web2.0, science, technology, MIT
BEAR-4
A group of amateur radio enthusiats launch an HD video camera into space and track it back down to earth. I think it's incredible and a great example of what people with an interest in something can do. What could we do if we gave students goals like this to accomplish? Any thoughts about how we use this incredible example of curiosity with students? Also, note that they send it to space, share their work via YouTube, blog about it, get picked up on the Discovery channel for relatively little cost!
tags: science, technology, amateur, geography

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Coach's Corner 09/24/2009

2009-09-23T23:30:00.001-07:00

Asteroid Watch - jpl.nasa.gov
tags: nasa, asteroids

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Coach's Corner 09/18/2009

2009-09-17T23:30:00.001-07:00

Show your Apprication Blogs » Appreciation for 365 Days of Astronomy Podcast
A project called 365 Days of Astronomy Podcast received an appreciation by being hailed as the Best Infotainment 2009 given by the Parsec Award.
tags: astronomy, science, podcasting, instruction, web2.0

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/17/2009

2009-09-16T23:30:00.001-07:00

3-6 Student Interactives - Science - UEN
Science apps for Science grades 3-6.
tags: science, web2.0
remix my lit
Not many books begin with a word of warning. Through the Clock's Workings does. This anthology of literature is not some textual tome, frozen in time and space. It is alive, evolving organically in a constant state of flux. Why? Because each story is available under a Creative Commons licence, giving you rights to share and reuse the book as you see fit. This is a world first: a remixed and remixable short fiction anthology. Buy your copy here or download the electronic version.
tags: comprehension, write2learn, write2pub, web2.0, technology
Amazing Space: Hubble Is Back in Business
Always looking for reading resources to share with the Striving Readers group. Here is a great online resource that has short readings that are applicable and topical. May not be user friendly for students 2 years or more behind grade level, but very applicable to the content area classrooms! Very interactive, combine pictures with text, updated constantly.
tags: comprehension, science
HubbleSite - NewsCenter - Hubble Opens New Eyes on the Universe (09/09/2009) - Introduction
I know the Hubble is not new, but the addition of the new spectroscope adds new life to this old tool (yes it's almost 20 years old). If nothing else exposing students to the different pictures that Hubble generates would be an addition. If you can use the pictures to help develop math/science connections then what a powerful tool.

Take one picture a day and ask students to calculate how long it would take a human to get to that point in space traveling at 100,000 miles per hour (twice as fast a any human has ever gone) or at 1,000,000 miles per hour (way faster than we can currently travel)...
tags: math, science, tech, hubble
100 Best Blogs for Tech-Savvy Teachers - Online Courses
"While there are still some educators who dispute the importance of technology in the classroom, there is no dispute over the fact that technology is here to stay in schools. Whether you are one of those tech-savvy teachers who can’t get enough of technology news and ideas or you are a teacher just learning to embrace technology in the classroom, these blogs offer a wealth of information straight from teachers and other professionals in the education field themselves."
tags: blog, instruction, write2pub, write2learn

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/12/2009

2009-09-11T23:30:00.001-07:00

Teachers Love SMART Boards: SMARTBoards and MP3 Audio Resources
tags: iwb, smartboard, podcasting, dialog, write2learn
twtpoll :: How do you MOST OFTEN teach a novel to your class? (via @KyleneBeers)
Just want to pass along this idea to everyone. It's a poll sent out to teachers via Twitter (from Kylene Beers no less) to see how they teach novels. Simple way of collecting some self-reported data. I just think it's an interesting way of using social networking professionally.
tags: socialnetworking, pd, instruction

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/09/2009

2009-09-08T23:30:00.001-07:00

Google Maps Mania: Design Portfolios on Google Maps
Using an application, like CASA's Image Cutter or the Automatic Tile Cutter, you can create your own map tiles for Google Maps. It is therefore possible to replace Google Maps tiles with other maps.
tags: maps, googlemaps, instruction, web2.0, technology
INSITE MAIN - Web 2.0 Tools - New Possibilities for Teaching and Learning - Confluence
What is Web 2.0, how to use it, and some great analysis of different tools. In-depth and very comprehensive.
tags: web2.0, instruction, pedagogy, technology
EdTechSandyK: Top 10 Social Networking Guidelines for Educators Who Wish to Keep Their Career Intact
tags: socialnetworking, instruction, pedagogy

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/05/2009

2009-09-04T23:30:00.001-07:00

MrsA - Internet Safety Curriculum Resources
tags: safety, wiki, web2.0, instruction
I Am What I Learn -- Coming Soon
On September 8, the U.S. Department of Education will ask students to respond to the President’s Back to School challenge by creating videos, up to two minutes in length, describing the steps they will take to improve their education and the role education will play in fulfilling their dreams. Watch this page for more information about the “I Am What I Learn” video contest for students.
tags: obama, education, history, digitalstorytelling, dialog, write2learn, write2pub

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/03/2009

2009-09-02T23:30:00.001-07:00

How to Plan For Differentiate Instruction
Some great examples/suggestions for planning differentiated instruction.
tags: instruction, differentiation, tutorials, resources
DIFFERENTIATION TOOLBOX
Set of tools from VA department of ed to help construct exciting, engaging, meaningful lessons for students.
tags: differentiation, resources, education
The Differentiator
Updated Bloom's Taxonomy. Helps identify the kinds of questions we ask and expectations we have for our students.
tags: bloom's taxonomy, differentiation, instruction, tools
- Useful not only for students… - post by grahamperrin
- Wow, I love this tool - post by leingang
Differentiated Instruction
Four Ways to Differentiate Instruction: Differentiation can occur in the content, process, product or environment in the classroom.1. Differentiating the Content/Topic2. Differentiating the Process/Activities 3. Differentiating the Product 4. Diffferentiating By Manipulating The Environment or Through Accommodating Individual Learning Styles
tags: differentiation, instruction, math, process, content, environment
Thirty-Four Interesting Ways* to Use Search Engines in the Class
tags: googledocs, searchengines, web2.0, write2learn
guessthewordle / FrontPage
Wordle is a great tool for using in the classroom, and this is just another example of how it can be used. I want to point out several aspects of this site-- it uses a wiki as the hosting site (easy to create)- is centered on using a tool called wordle- embeds wordles within the wiki- uses a Google form (go to "Today's Wordle" page) to have people submit information- has created a twitter account to advertise/keep participants up to date with information- has created an RSS for those who want to follow new wordles daily
tags: wordle, web2.0, write2learn, write2pub, vocabdev
A GeekyMomma's Blog: VoiceThread: Where do you fit in?
Great explanation of Voicethread and some very scaffolded examples of how we can use Voicethread in our classrooms. Lee does a wonderful job of developing a compelling reason for using Voicethread and how to accomplish your goals.
tags: dialog, web2.0, write2learn, write2pub
Mozilla Labs » Blog Archive » Introducing Prism
A tool for looking at information differently than we've ever done so before. Next step in web browsing? Just remember that things don't always stay the same in the virtual environment.
tags: web2.0, graphorg
Lockhart's Lament
This article was brought to my attention by Tim Ferree this summer and I thought I would pass it along. It's not necessarily content literacy, but I think it is about good instruction. Happy reading.
tags: math, reform
The Business Trip | Dr. Jeff's Blog on the Universe
Great post about teachable moments and what that looks like when you are an astronaut and your child asks you where you are going for work... beats Hazard! Read through the post and make sure click on the "checked" link for a great way of giving students some perspective on a shuttle flights speed and location.
tags: math, science, web2.0

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Coach's Corner 09/02/2009

2009-09-01T23:30:00.001-07:00

50 Awesome Ways to Use Skype in the Classroom
tags: web2.0, technology, skype, dialog
gettingtrickywithwikis - Background Colour in Tables
When you want to make your wiki do things that aren't necessarily easy to do this is a great site! I added a background graphic to a wiki with the help of this site. It was very helpful in getting the basic code added and with a little tinkering it did the things I needed it to do! Great resource
tags: wiki, web2.0, technology

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 09/01/2009

2009-08-31T23:30:00.001-07:00

Half of Americans use social networks - Technology Live - USATODAY.com
Killing two birds with one stone. Here are some interesting facts about social networking and use among 35-54 yo age group growing by 60% recently according to Forrester. Also, if you are looking for a read-aloud to do with math students, here's a great example to use with them. The topic is social media, the content is proportional reasoning, data analysis, and interpreting real-world data. For example if usage among 35-54 yos has grown by 60% what does that mean among the sample of 4500, what does that mean among the sample of the US population, if previous usage was 15% of that age group, what percentage of that age group now use it? Etc. Good math/science reading is as close as your local USA Today/Yahoo homepage/iGoogle/news RSS
tags: math, comprehension, write2pub, write2learn, instruction, readaloud
Teaching With Technology: Educational Technology Services at MIT
Different categories on the MIT teaching with technology page. Great way of thinking about different issues and ways of solving some of those issues from MIT's perspective.
tags: technology, mit, edtech, web2.0
Stanford Study of Writing - Home
Thought provoking analysis of writing by current students.
tags: writing
Math Central - Welcome!
tags: math, technology, resources

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Coach's Corner 08/30/2009

2009-08-29T23:30:00.001-07:00

COPD - MayoClinic.com
tags: copd
- Chronic obstructive pulmonary disease (COPD)
- Emphysema and chronic bronchitis are the two main conditions that make up COPD, but COPD can also refer to damage caused by chronic asthmatic bronchitis. In all cases, damage to your airways eventually interferes with the exchange of oxygen and carbon dioxide in your lungs.

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Coach's Corner 08/29/2009

2009-08-28T23:30:00.001-07:00

Cool Cat Teacher Blog: The Wheels Never Stop Turning: Inside the Mind of Lisa Parisi, Teacher Heroine and UDL Pro
Differentiated instruction and universal learning by design comparison. Thanks Viki for sharing Lisa's great work.
tags: instruction, assessment, planning
50 Ways to Use Wikis for a More Collaborative and Interactive Classroom | Smart Teaching
Want to thank Michelle Desilva for finding this site. Great resource and full of practical ideas and important processes/structures to think about if implementing with a class of students.
tags: wiki, web2.0, instruction, inter-classroom

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Coach's Corner 08/28/2009

2009-08-27T23:30:00.001-07:00

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 08/27/2009

2009-08-26T23:30:00.001-07:00

Google Tutor: Tutorials and Tips for Google Users
If you use Google tools a lot then this is a great place to go to get some tips/tricks. I learned two things about Google Calendar that I wasn't aware of: attaching Google docs to items and showing free/busy as my status.
tags: google, web2.0
- Google tutorials, tips, techniques and advice. Updated daily. - post by kl75214
- Tips, Techniques and Advice for Google Users - post by iberolynx
GraphSketch
Easy to use graphing utility. No adds easy to setup different windows, graph multiple functions.
tags: math, graph, algebra, web2.0

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 08/25/2009

2009-08-24T23:30:00.001-07:00

SMART Board Templates
tags: smartboard, iwb, instruction
Chatzy - Start Quick Chat
tags: web2.0, socialnetworking, communication, dialog, write2learn
Smartboard Templates
These templates require the Smart Notebook software, Kidspiration. Inspiration,Microsoft PowerPoint Viewer and KidPix to use. Most have a preview for you to decide if it is something you would like. I would suggest creating folders on your desktop called SmartNoteBookTemplates, InspirationTemplates, and KidspirationTemplates. You can then save the templates in the appropriate folder for later use.
tags: iwb, smartboard
50+ Ways To Create Digital Stories With Students | The Edublogger
Creating stories using web tools is fun and engaging for student while also teaching them new skills. Best of all you can embed them in blog posts to grab readers; including something a bit different makes reading posts more interesting.
tags: web2.0, digitalstorytelling, write2learn, write2pub
Regifting Robin
If you are looking for an activity to have your students investigate, then this is a great little activity. Let them investigate (try a couple of examples), look for a pattern with the numbers (any two digit number minus the sum of the digits will produce a number with some very identifiable characteristics), then explore the second page of the challenge for what happens each time regarding those numbers... great fun, very educational, great way for students to look for patterns/make observations.
tags: math, algebra, web2.0
Wonderful Web 2.0 Tools / FrontPage
Yet another list of web resources. Relatively up to date and comprehensive. Worth looking at if you want choices for tool usage.
tags: instruction, web2.0, wiki, blogging
blogmodel.htm
If looking for a system or classroom routine to develop student eportfolio this mosdel is a nice way of organizing the 'tech' aspect of the routine. Have students write blog posts as writing to learn component, get feedback for editing, organize them according theme/topic (allows for cross-referencing), post final products as portfolio pieces. Very transparent, easy to track, allows for built-in feedback/reflection.
tags: instruction, web2.0, write2learn, write2pub, blogging

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Coach's Corner 08/23/2009

2009-08-22T23:30:00.001-07:00

Doodle: Easy Scheduling
A very simple poll generating tool. Doodle helps finding suitable dates and times for group events, e.g., an appointment, a conference call, a family reunion, etc. In addition to scheduling events, Doodle also supports polls in general. That is, groups can conveniently decide on options other than dates. - comment by Rob Reynolds
tags: web2.0, write2learn
Wordle Blog: How to make Wordle safe for classroom use.
FROM the Creator/Owner of WORDLE: "I’m happy to announce that from now on, the Wordle front page will never feature images or links that are inappropriate for classroom use. It's now possible to configure an institution's "site-blocking" software to keep Wordle safe for classroom use." Simply have your networking administrator block the following base URLs1: * http://www.wordle.net/gallery * http://www.wordle.net/next * http://www.wordle.net/random -
tags: wordle, blog, web2.0, vocabdev, graphorg, instruction
Qualifications : GCSE : GCSE from 2010 : Mathematics : Edexcel - Annotated
tags: edexcel, assessment, math
- Draft Sample Assessment Material - Unit 1 (Foundation)
  
  Draft Sample Assessment Material - Unit 1 (Higher)
  - Does anybody know what grade levels these would be used with, so I could have a valid comparison? - post by lainlev
HippoCampus - Homework and Study Help - Free help with your algebra, biology, environmental science, American government, US history, physics and religion homework
tags: math, science, education, elearning, web2.0
K12 Online Conference 2009 | Week in the Classroom“Wiki Collaboration Across the Curriculum”
As we further incorporate technology and online tools into content literacy. Here is a great set of tools/resources from Vicky Davis on using a wiki in your classroom. She even goes so far as to include a rubric, lesson planning ideas, and examples.
tags: web2.0, wikis, instruction, graphorg

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Coach's Corner 08/22/2009

2009-08-21T23:30:00.001-07:00

Screenr - Create screencasts and screen recordings the easy way
Create quick screencasts and share via twitter or embed. Quic, easy to use, great way of introducing basic software, functions.
tags: screencast, twitter, web2.0, technology
- It comes in very handy! - post by charmaine_lim

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Coach's Corner 08/21/2009

2009-08-20T23:30:00.001-07:00

ThemesongSoundtrack - Google Docs
Thought I would share this with you. I like it because it uses a simple way of sharing the document: tweeted it to her students as well as shared on a Ning link, great assignment, they can all see as well as parents can see it and didn't kill a tree. Deborah, this is the kind of use of technology that NAEP is looking for.
tags: no_tag
LiveSide.net
Windows live Movie Maker, is even easier than it used to be. Great FREE tool for making videos with students.
tags: web2.0, write2pub, write2learn, instruction
Foundation Center - Knowledge to Build On
Opportunity to identify potential funders for grants (small and large).
tags: Foundations, philanthropy, funding, nonprofit, grants
Template 2 - Single Column
that over 700,000 historical images from The New York Public Library's Digital Gallery are now freely and instantly available whenever you're creating a VoiceThread. Our new Media Browser allows you to search or browse these primary source materials - maps, photos, drawings, paintings, posters and more, and then import them directly into any VoiceThread. Links back to the original location of the images on the web are automatically inserted to make citing and attribution easier for you and your students.
tags: web2.0, digitalstorytelling, dialog, write2learn, write2pub
Teaching with Technology / Index
List of resources. Lots of options. Always good to look around and find any new resources I'm not familiar with.
tags: web2.0, instruction

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 08/20/2009

2009-08-19T23:30:00.001-07:00

SMARTboard Resources
Collection of Smartboard resources. Some of the resources are really good! Worth taking the time to look at and identify a few that would be helpful to you.
tags: iwb, smartboard, instruction

Posted from Diigo. The rest of my favorite links are here.

Coach's Corner 08/18/2009

2009-08-17T23:30:00.001-07:00

Education Week: NAEP Draft on Technological Literacy Unveiled
A discussion draft of the framework for the national assessment of technological literacy, the first to gauge students’ understanding of and skill in using a range of tools, has been presented to theboard that oversees the testing program.
tags: web2.0, technology
Fuel Our Future Now - Jumpstart Students' STEM Education with Free Teacher Resources
Resources from the department of energy and Discovery Education for use with STEM classes
tags: stem, science, education, interactive, web2.0

Posted from Diigo. The rest of my favorite links are here.

Measurement: Fixed Area/Perimeter: Relationships

2009-08-17T05:53:00.000-07:00

Standards:
The standards for this activity come from the Kentucky Program of Studies for Grade 7:
- Students will investigate and demonstrate fixed area with changing perimeter and fixed perimeter with changing area.
- Students will explain how measurements and measurement formulas are related or different
- Students will read and use measurement tools (e.g., rulers, scales, protractors, angle rulers)
- Students will represent, analyze and generalize functional relationships (input/output) through tables, graphs and verbal rules.
- Students will recognize, create and extend patterns and generalize the pattern by determining the rule for any term.
- Students will simplify numeric and algebraic expressions.
Lesson Description:
In this lesson students use a grid to create a rectangle with a fixed perimeter. Students work individually after modeling by the teacher to create a rectangle, share the dimensions, perimeter, and area of the rectangle to create a class database/spreadsheet of information, and then students work together in small groups to begin comparing their information/find relationships between the different measurements, make attempts to determine the exact relationship between the length/width for a fixed perimeter, etc.

Accessing Prior Knowledge:
Students use words from the Word Wall to identify components/characteristics of a rectangle
If students don't identify the terms/characteristics area, square units, perimeter, formula, relationships then the teacher will want to pull those terms and ask how they relate to the rectangle or how students might use them with the rectangle to prompt discussion abut the concepts that will be critical for today's lesson. This conversation should be led by students to identify what they already know and are able to do. Consider using a T/P/W/S strategy with students if they are reluctant or slow to respond by having students work together to remember two things they remember about the different prompted terms.

New Learning:
- After the initial conversation direct students to get out rulers, graph paper, fold the paper into quarters, and create a rectangle in the first quadrant
- Ask students to find the perimeter of their rectangle with the goal of discussing that all the rectangles have different perimeters and we want to analyze rectangles that all have the same dimensions
- Have students create a rectangle that has a perimeter of 40 units (the rectangle needs to be large enough that students will be able to create multiple versions of the rectangle but not so large as to be limited in how many rectangles students can create) I would encourage students who want to create a rectangle that is longer or wider than one quadrant to unfold their paper and feel free to do so
- Have students determine the length, width, area (if based on your accessing conversation students are still struggling with finding area then have them count the blocks inside the rectangle), and perimeter
- After students gather their information, have them enter the data in a spreadsheet on the classroom computer or Smartboard.
- Now that students have created their data base of information, have them work together to identify common characteristics of the rectangles (everyone should have the same perimeter, there are different rectangles but a limited number, etc.)
- Working together in pairs have students look at the data and try to determine the relationship between the length and width.
- Stop work after 5 minutes to bring everyone up to a similar place by asking questions like:
- What relationships have we noticed (as one gets bigger the other gets smaller, etc.)?
- Does the width change by the same amount each time the length changes?
- How much does it change each time?
(this conversation will allow students who are already developing the rule to make sure they can express their understanding so that others can also understand them, and allow others to answer questions that will help them understand connections; it's also a great opportunity for some formative assessment)
- Be sure to model capturing the discussion in their notes on the whiteboard, this is a good spot to use a think aloud that might help students make some connections (i.e. "When I'm trying to figure out a relationship, I don't look at all the pairs of data, but i look at one and try to figure out a relationship, then I look at another pair to see if the relationship works for that pair too...")
- Give students more time to develop a rule for determining the relationship and to quantify the rule (W = (P - 2L)/2, for a perimeter of 40 it will likely be W = 20 - L)
- Show students that you can use the rule they developed to create more rectangles that have a perimter of 40 but adding the formula (=20-"Cell for Length")

- By adding the formula in several cells (cutting, pasting, dragging the cell down, lost of different ways) you can show students that you can confirm the relationship by typing in known lengths to determine corresponding widths
- Students can figure out if the rectangles work by drawing the new rectangles in the third or fourth quadrant of their graph paper. They can also use this time to determine the area and perimeter of the rectangle (this should cofirm the relationships already known)
- Have students explore in their notes the different connections made in today's lesson to material previously covered, new learning that they think was important, and ask themselves 1 or 2 questions they still have rolling around in their head for final classroom conversation.

Extension
- Input the rules/formulas for area and perimeter to have the spreadsheet confirm information provided by students from their investigations

Summary/Synthesis:
- Have students respond to this prompt in writing: "What are the characteristics of rectangles that have a fixed perimeter? Do you think those characteristics will hold if we change the perimeter? How do you think we can test your hypothesis?"

Assessment:
- Students graph paper with calculations/notes

Materials Needed:
- Graph paper
- Spreadsheet
- Rulers (optional)

Final Thoughts:
This kind of exploration is difficult to pull off in one 45-50 minute class period, but gathering data, organizing the data, and having students explore possible connections/relationships is a great start to this lesson. I can imagine this lesson taking two days to pull off, but DO NOT end the first day without having student summarize/synthesize what they learned/experienced today. Just because the lesson isn't fully finished, doesn't mean that students don't need to synthesize their learning. If a class period ends, then we need to help them draw the lesson to a closure so that they have some place to start the next day. For this lesson, I would consider having students predict what they think the relationship between L and W or L and P is so that they get practice with the idea of predicting, come back tomorrow with a place to start the conversation, and have models (from the teacher) for predictions and what you do when they are wrong (it's OK to be wrong as long as you figure out why you were wrong and add that new understanding to your thought processes)

Solving Linear Equations: Vocabulary Development

2009-08-14T11:16:00.000-07:00

Today is day 4 of the challenge and I'm having fun. It's taking a little longer than I want it to but I feel good about the concept. I be taking the weekends off so that I don't take time away from my family, especially since I am taking longer than I wanted to get the posts published. I'm not editing them as well as I like, but it's a good first draft of material and I can come back to the editing process later.

So on to today's lesson. It will be slightly different approach than the ones previously published. I'm going to focus on using an interactive word wall for vocabulary development. Technically this is a classroom routine and not a lesson, so I'm going to add some extra thinking to the template and then develop a lesson, so here goes:
The word wall really works once you get the words on the wall, when students have interactions with the content. I always think of five processes/routines that I want to use with my students over the course of the unit of study/semester:
- students categorize/organize the terms on the WW (the categories change in relation to content, and can be about metacognition- terms we know well/terms we are working on/terms we still don't know)
- put a diagram/graph on the WW and students identify characteristics/components they recognize
- students use the words in a mathematical sentence or make a synthesis of the days learning utilizing terms for the WW (this component may need to be added as students get more experience writing mathematical sentences/summaries, which also means I need to think about how I will develop their mathematical writing skills)
- like I did with the teachers, someone comes to the WW, chooses a word, explains it, someone else comes to the WW and chooses one that connects to the first one chosen, etc.
- students take a word or a couple of words and develops in-depth explanations that uses multiple representations (drill that focuses on creating in-depth understanding. I like to ask students to create an example that uses the term or word)
- Students go to the WW during the lesson and identify words that relate to the days learning which lets everyone stop, make sure they understand the content and can explain the concept

These are just a few ways of interacting with a WW, but I think they get at the heart of the idea.

Standards:
Big Idea: Number Properties and Operations
Students will justify the solution steps in simplifying expressions or solving an equation.
Students will add, subtract, multiply and divide real numbers.
Students will determine the relative position on the number line of real numbers, including very large and very small numbers.
Big Idea: Algebraic Thinking:
Students will write expressions, equations, inequalities and relations in equivalent forms.
Students will use symbolic algebra to represent and explain mathematical relationships.
Students will judge the meaning, utility and reasonableness of the results of symbol manipulations, including those carried out using technology. (Not sure I fully understand this standard, but I believe it means understanding any changes made to an equation or expression.)
Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases.
Students will solve one-variable equations and inequalities using manipulatives, symbols, procedures and graphing, including graphing the solution set on a number line.
Students will solve linear equations and inequalities in one variable

Lesson Description:
Yesterday, we explored solving linear equations using a dynamic applet. In this lesson, I want to explore how I support student understanding of vocabulary as part of teaching the mathematical concepts. It is a day in which students will focus on practicing some procedural fluency and some communication skills.

Accessing Prior Knowledge:
- Using a Pair/Share activity, have students nominate equations that they think were difficult from yesterday's lesson with the focus on being able to describe what they think was difficult about the equations
- Focus the discussion on having students discuss and capture the issues that caused confusion, and how they dealt with those issues. The goal being to develop a process for how to solve a variety of equations using a process of identify the mathematical operation and figure out how to undo or simplify the operation.

New Learning:
- With the discussion of yesterday's equations over, have students go to the word wall and pull terms/words/symbols used in the discussion and place them on the whiteboard beside the item (i.e. put inverse beside the "-1" step in one equation, or coefficient beside the 2 in 2x)
- When time expires or no more terms can be pulled off of the WW have students write down in their double entry organizer the three terms that they are still having trouble identifying or remembering, and create an example to accompany the term
- Students are going to work in small groups to solve a variety of equations. They will work solve the equations in their own section of the poster board for the first fifteen minutes of the activity. they may collaborate if you wish, but I like them to work on their own for a while
- After 15 minutes hand out the answer sheet and have them continue to work through the equations, checking the work they have already done. At this time if they miss any they should work together to correct the equation to make sure that everyone knows how to solve the equation correctly. the goal is not to finish all of the equations but to make sure the equations that are done are done correctly and everyone knows how to solve them.
- After 10-15 more minutes, students change the focus to identifying the equations that were hardest for them to solve. Identifying 3 equations and what was hard about each equation (not because I missed it, but because I had trouble dividing by 2.3 or I didn't simplify the distributive property correctly)
- Students now negotiate the 3 equations that were hardest for the group to solve. I intentionally use 3 equations for 4 people so the group has to work together and analyze rather than just everybody say one.
- Short discussion of the most difficult equations and how people dealt with the problems.
- You now have problems that your students find difficult, how they deal with those equations, posters of good work to hang around the room, and shared thinking about the processes of solving equations

Summary/Synthesis:
- The whole group discussion will act as the summary of the day's learning and if captured on the whiteboard then students should write down the equations, the identifying issue, and the groups way of dealing with that issue which acts as a great study guide (much better than anything I've ever been able to create)
- The posters with student work.
- Exit Slip, have students respond to the following prompt "Create an equation that uses three operations, and has a solution of z = 4" (Another way of creating an equation bank) and then have students swap and identify the first step to take in solving the equation (not actually solving it), again the focus on process

Assessment:
See Above, the poster boards, the exit slips, the discussion, during the activity walk around asking questions, make sure to track the questions and ask everyone at least two questions, group questions can count but I prefer individual.

Materials Needed:
- Poster Board
- Word Wall
- List of or Equation bank

Final Thoughts:
I started the description of this lesson as a focus on the word wall, but it turned into a dialogue lesson, but I still like both aspects of the lesson. Maybe I should count this as two lessons... Nah, but I am going to take the weekend off!

Thanks and I look forward to your thoughts!

Solving Equations with Virtual Applet Support

2009-08-13T13:23:00.000-07:00

Standards:
Big Idea: Number Properties and Operations
Students will justify the solution steps in simplifying expressions or solving an equation.
Students will add, subtract, multiply and divide real numbers.
Students will determine the relative position on the number line of real numbers, including very large and very small numbers.
Big Idea: Algebraic Thinking:
Students will write expressions, equations, inequalities and relations in equivalent forms.
Students will use symbolic algebra to represent and explain mathematical relationships.
Students will judge the meaning, utility and reasonableness of the results of symbol manipulations, including those carried out using technology. (Not sure I fully understand this standard, but I believe it means understanding any changes made to an equation or expression.)
Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases.
Students will solve one-variable equations and inequalities using manipulatives, symbols, procedures and graphing, including graphing the solution set on a number line.
Students will solve linear equations and inequalities in one variable

Lesson Description:
Using dynamic virtual applets, allows students to see what happens when situations are changed, analyze causes and effects, be able to make predictions and test those predictions, and better understand the concepts being studied. The applets themselves don't make those 'things' happen, but if supported instructionally, applets provide opportunities that aren't always available to students. The question that continues to arise, how can teachers support students in learning how to use applets effectively for learning?

This lesson is just a think-aloud in using an applet to solve an equation, making connections between the applet, the symbolic manipulation, and writing connections. Understanding that equations have solutions is not the key to this lesson, but understanding what equivalent means as well as understanding what happens to an equation when you manipulate it and why you do what you do when you manipulate the equation is!

Accessing Prior Knowledge:
- Since we are solving equations I want to make connections to the number line and values for a variable. Have students to create and identify values on the numberline that can be plugged into a given expression and then find the output value for the expression. (i.e. for "x +3", let x = 5 or 3 1/2 or -2)

New Learning:
- Students use some notetaking device to keep track of the teachers thinking, in this example I will utilize the double entry organizer as my tool (so that I can have students capture in the right column the teacher's thinking from the "think-aloud" and their own.
- Pull up the Balance Scale with Negatives applet from the National Library of Virtual Manipulatives
- Enter the equation 2x + 1 = 3x - 1 into the applet, write the equation on the board in the left column of the DOE
- Model the equation on the balance scale, with a comment similar to "When I add x to just one side the scale is no longer balanced, that side of the equation is heavier/lighter because it is on the bottom now."
- Think out loud about what step to make now, "I think I would like to get rid of the units from the right side so I need to figure out how to get rid of the negative one, I could take it away but I don't have one to take away from the other side. So I think I can add one to the right side to make zero and then add one to the other side and that should keep it balanced.
- Add one unit to each side, and observe, "Hey, the equation stayed balanced after I added one to each side!"
- Now, show the manipulation on the board by "+1" to each side of the equation, and observing, "So when I add one to each side that's the same as +1 here and here"
- Observe, "I want to add to the right column of the DOE that it is important to do the same thing to both sides so that the scale or equation stays balanced."
- Continue with this process through solving the entire equation when the equation is simplified observe, "I can tell that the answer is x = 2, but I need to prove that it works another way, so I'm going to plug it in and see if I get a true statement"
- Substitute 2 into the equation and simplify to find that 5 = 5, observe, "when I substitute 2 in for x I get 5 on both sides of the equation which is a true statement." (Setting up the input/output model as well as the check your solution model.)
- Have students then choose one of the equations from the list and go through the process with them providing the thinking, be sure to model how to capture the thinking, ask clarifying questions, insert "hums" or "I wonders" or "What do you want to do now?"
- Students go through the process with another equation from the list in pairs or individually, with a focus on the process of why you make decisions to solve the equation and NOT what the answer to each solution is.

Summary/Synthesis:
- Have students reflect on what different processes in simplifying using the balance scale or the connections between solving the equation symbolically and what each step means in writing/real-life
-As a closing activity have students use the word wall to identify different vocabulary used during the example everyone did together (i.e. equivalent, equation, substitute, solution, variable, addition, subtraction, etc.)

Assessment:
- Reflection sheets
- Worksheet where students solve the last equation modeling, solving symbolically, showed steps in writing, and answered questions about decisions about which steps to do, why, when,

Materials Needed:
- Computer with LCD
- Access to the internet
- List of equations for students to choose from
2x+1=3x-1, 2x-2=x+1, 4+3x=x+2, 5+2x=4x-3, x=2x+4

Final Thoughts: I like this activity because I think using applets is a great tool, because students can create very strong connections between cause/effect issues, create deeper understandings, discuss concepts from an experiential perspective rather than just an abstract rationale. The thing that students don't understand is how to communicate those understandings or to explore with a purpose or that there is a connection between keeping a scale balanced and the mathematical additive equality property. Helping them see the connections, talk about the connections, make the connections the focus (and not the solution) will help them build their skills at observing, asking questions, making their thinking more visible, and help them like/understand math better.

Coach's Corner 08/13/2009

2009-08-12T23:30:00.001-07:00

Idea : Docs for Teachers - Google Docs Help
Google comes up with yet another great way of helping new users (who happen to be teachers) to use their product. Create some templates, package them in one location with some tutorials, and make EASY to use! Yeah for Google.
tags: google, googledocs, education, resources, web2.0, write2learn, write2pub
Main Page - GeoGebraWiki
GeoGebraWiki is a free pool of teaching materials for the dynamic mathematics software GeoGebra. Everyone can contribute and upload materials! All contents of this pool may be used free of charge.
tags: geogebra, math, wiki, interactive, Free, algebra, applet, web2.0

Posted from Diigo. The rest of my favorite links are here.

Data: Measurement: Multi-Age: Fun!

2009-08-12T13:11:00.000-07:00

Standards:
The standards being addressed in this lesson are from the Kentucky Program of Studies, Grade 8 Standards
Big Idea: Data Analysis and Probability- Students will collect, organize, construct, analyze and make inferences from data in a variety of graphical methods (e.g., scatter plots, box-and-whiskers plots).
Students will select an appropriate graph to represent data and justify its use.
Students will determine and interpret clusters, quartiles, gaps and outliers in data.
Students will determine and interpret the mean, median, mode and range of a set of data.
Students will compare sets of data
Big Idea: Measurement- Students will read and use measurement tools

Lesson Description:
The goal of the lesson is to have students measure their heights in either metric or standard, and to compare the data with measurements from another grade for analysis. Data will be either represented via scatter plot or box and whisker plot. Students will analyze the data sets by identifying variables (age, gender, height)

Accessing Prior Knowledge:
Part 1- Have students brainstorm as many ways to organize, sort, display univariate and bivariate data as they can think of
Part 2- Have students discuss the important points to measuring someone’s height accurately and develop a process for measuring heights that will produce accurate and precise data.

New Learning:
- Students will use the process for measuring heights with students from a lower grade in order to gather the heights from both grades in a data set.
- Along with height data students will collect age (or grade), and gender data
- Students will gather data in a spreadsheet
- Students will analyze data looking for patterns relationships and represent the data using a variety of models/representations
- Students will use the data to compare and determine possible relationships
- Students will compare data to determine differences between the various groups
o The analysis may include groups of students working on scatter plots of age vs height,
o univariate analysis by grade/gender/both to compare the measures of central tendency and compare the differences between the groups
o Other comparisons to make??
- Students will choose one comparison of data and write an explanation for the type of analysis they did, why they chose to represent the data this way, what conclusions (or possible conclusions) they can draw from their analysis, next steps if someone wanted to confirm the analysis
Summary/Synthesis:
- Reflection on the process they used to determine the best method for representing the data,
- As well as a reflection on the process of analyzing and comparing data (this component should entail some reflective writing so that students are able to capture the different decisions they made in choosing the graphs they chose, and the decisions they made based on the evidence presented. This will be new to most students and will need continual reinforcement/scaffolding/modeling).

Assessment: Report on the data analysis, data calculations for finding the measures of central tendency, and displays of the data

Materials Needed:
- Rulers for measuring (tape measures if using something like measuring stations taped to the walls)
- Spreadsheets for capturing data
- Report expectations/guidelines/rubric (not provided here)

Final Thoughts: I like this lesson for several reasons. It has 8th graders measuring with younger students, acting as mentors, showing the students how to measure. Also, the data can be compared in multiple ways and represented in an equally diverse variety of manners. I like to give students choice in representing data. If your students have not used calculators to represent data before that would be an excellent set of lessons to do before this one, so that students can create the calculations and different representations quickly and not get bogged down in actually creating them.

Coach's Corner 08/12/2009

2009-08-11T23:30:00.001-07:00

The Science Teacher's Hub Home - The Science Teacher's Hub
This wiki is a collaborative project for Science teachers to share resources and anecdotes about what has worked and what hasn't in their classroom. Please read at your leisure and join the wiki to post comments and participate in discussions.
tags: science, wiki, web2.0, chemistry, biology
GeoGebra
tags: math, geometry, algebra, calculus, software, web2.0, instruction
NASA - Educators
Anything from NASA will be slick. I'm a little disappointed in the videos about proportion. A 2 minute video and the mathematics is washed over in 13 seconds, and on top of that it's all procedural in nature (cross-multiply) with no explanation as to why it works. Other resources look more promising to me, but hope NASA looks into doing a better job of incorporating more conceptual development/understanding/explanation.
tags: science, nasa, education, math, web2.0, instruction
- The NASA website for educators is the place to start for educational information and lessons on space exploration. - post by misskyleejean

Posted from Diigo. The rest of my favorite links are here.

Measurement: Percent Change

2009-08-11T13:27:00.000-07:00

Standards:
The standards being addressed in this lesson are from the Kentucky Program of Studies, Grade 7 Standards
- Students will extend concepts and application of operations with fractions and decimals to include percents.
- Students will add, subtract, multiply, divide and apply order of operations (including positive whole number exponents) with fractions, decimals and integers to solve real-world problems
- Students will compute percentages
- Students will read and use measurement tools
- Students will determine the length of sides (to the nearest eighth of an inch or nearest centimeter)

Lesson Description:
The goal of the lesson is to have students make a box from a piece of paper; measure the length, width, and height; use a simlar piece of paper to make a box that has one dimension changed by a certain percent; and analyze the changes to the other dimensions.

Accessing Prior Knowledge:
Part 1- Ask students to identify the dimensions of a given object and to talk about how to measure the dimensions using whole group with teacher taking notes on board With Smartboard, add a shape to the board and have students come up and identify the different dimensions, and use the ruler on the smartboard to model measuring to the nearest 1/8 of an inch (7th grade standard)
Part 2- Quickly discuss what 25% percent means and ask students to develop examples of what it means to get 25% bigger using T/P/S

New Learning:
- Have students measure the length and width of the piece of paper they are using and record the information on the recording sheet or spreadsheet
- Students follow directions to build box. simple cut along solid lines, fold along dotted lines; tape flaps to form a box.
- Measure the L, W, H and add measurements to the recording sheet. Students can work in pairs to help speed up the activity or individually if you want/need more data
- Have students calculate what a 50% increase in the height would mean
- At the same time have students predict what the impact on the other dimensions of the box will be, why the impact is what it is, describe what the box will look like as a result of increasing the height by 50% My stated goal in these kinds of interactions is to ask questions that get the students thinking about the connections between the dimensions and using their powers of observation and what they already know to understand that they can predict what happens as a result of their understanding and learn to make those predictions more formally as a result of MATH
- Students now build the second box that has a height increase of 50% and repeat the measurements and recording procedure
- Students analyze the change in the dimensions, record the changes, determine percent change for each dimension, predict/determine why the percent changes are not the same for each dimension

Summary/Synthesis:
- Students respond to the writing prompt "Describe the changes that occurred to the dimensions of the box as a result of increasing the height by 50%, and show using mathematics the changes to one dimension using decimals, percents, or fractions."

Assessment:
- Discussion points captured on Smartboard from opener
- Recording Sheets from each student/pair of students
- Answers from the prompts
- Quick write at the end of class

Materials Needed:
- Box templates (examples are attached here)
- rulers (preferrably english so that students can measure to the nearest 1/8", metric can also be used so that students get experience with decimal computation and metric)
- scissors to cut the box, tape to adhere the tabs to create the boxes

Final Thoughts:
I like the idea of capturing all of the data using a spreadsheet. It allows for continued use of the information and for extension. It would be very easy to save the boxes, revisit this activity measuring using metric and compare the findings (% changes won't be affected, change in dimensions won't be affected, only the numbers being used for calculations will), or extend this to include the calculation of volume (the nice thing about the example boxes is that base ten blocks will fit nicely inside the boxes allowing teachers/students to develop understanding of how the dimensions help create the volume. I've worked very successfully showing the different relationships and letting students have an opportunity to explore those relationships, but that's another lesson). The spreadsheet also allows for the calculation of formulas like average height, average width, average length and the discussion of accuracy/precision when measuring or significant digits (both important science concepts). The spreadsheet can also be used to help develop algebraic reasoning concepts like calculating V based on L, W, H and what the variables are.

Lesson Planning Challenge

2009-08-11T13:11:00.000-07:00

I've been reading about artists that create a piece of art every day for a month (usually January) and have been thinking a lot about using this kind of idea for creating lesson plans. I know it takes time to create lesson plans and since I'm not in the classroom on a daily basis anymore I don't want to lose the ability to create opportunities for students to engage with material in an exciting way. Just going through the excercise of thinking about the content, thinking about a classroom full of students, and thinking through the learning cycle will be a fun way to keep my brain thinking like a teacher.

I know it's not the same a actually being in a classroom, but it is a small step in creating a 'teacher-centered' mindset going into the coming year. I look forward to the challenge and hope that it helps someone else create a classroom that someone else gets something out of it too.

Coach's Corner 08/11/2009

2009-08-10T23:30:00.001-07:00

Teacherly Roles and Technology Integration
Good tutorial/tips site to pay attention to if using technology for education.
tags: web2.0, blog, write2pub, instruction
Math Teaching and Learning Resources
Some interesting applets and well thought out lessons.
tags: math, web2.0, applets
Online LaTeX Equation Editor
Help embedding equations into text on web pages. I haven't been able to get it to work on wikispaces, yet, but it does work with as a gif file there. It's a step in the right direction for creating better use of symbolic representation in web pages.
tags: writing in math, math, web2.0, write2learn, write2pub

Posted from Diigo. The rest of my favorite links are here.

New Every Trails App Testing with My First Road Ride Map

2009-08-10T15:14:00.000-07:00

I came across this app for my iPhone and thought it had some potential as a tool for tracking my workouts. I had no idea!

It's incredibly cool. I love the multiple ways of looking at the map data. Showing the route on the map is cool, showing the geo location is cool, showing the elevation and speed at which you are traveling is cool, but putting it altogether with geotagged photos with a few simple clicks is INCREDIBLE.

Right now, it's just a cool app that lets me track my workouts, walks with my dogs (I would have added photos but we walk at 5:45 and it was too dark to see anything), and my hikes on the farm (I can't wait to add my mountain bike route in Howardstown), but I can envision using this with students. Having students explore the data that allows the app to create the representations would be great fun.

I'm going to play with the files and see what I can come up with. I know they are KML files, but need to look at them to figure out how they are developed. If anyone knows, leave me a comment.

OK, I need your help. Does anyone know how to get access to a KML file on Google Earth/Maps? I want to play with the data base but I don't know how to get access to it, any ideas?

Home to park and back! 19 mile loop

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Coach's Corner 08/10/2009

2009-08-09T23:30:00.001-07:00

http://mathdemos.gcsu.edu/mathdemos/physical.html
An interesting collection of activities/demos. Well designed and planned. I like the fact that they have objectives but wish they were standards-based
tags: math, web2.0, applets, iboards

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Coach's Corner 08/09/2009

2009-08-08T23:30:00.001-07:00

Free Stock Image - Sweet pink
Site for free graphics. Option to do a free CC search or open it up to commercial search with a little cost.
tags: no_tag
Pattern Blocks: Exploring Fractions with Shapes
Pattern blocks are great tools for developing conceptual understanding. I hope to continue to see them used in classrooms, but the virtual kind can allow students to share their thinking with other students virtually. I like using screen capture, cut/paste, upload to a wiki, comment on characteristics/size/description of '1'/and sharing with students so that their thikning can be revisited from multiple venues (home, classroom, internet-broader audience).
tags: web2.0, applets, math, Fractions, instruction
- Great website for pattern block puzzles and activities! - post by drewpolly
Guidelines for Educators Using Social Networking Sites - Home - Doug Johnson's Blue Skunk Blog
Important to always think about how to create a safe learning environment. This post is a great analysis of several inputs. Worth reading and a great resource.
tags: socialnetworking, instruction, blogging
Math Publications - Middle School Portal
The Middle School Portal 2: Math and Science Pathways project (MSP2) is a component of the National Science Digital Library (NSDL) that supports middle school educators and youth by offering contextualized, high-quality resources and promotes interactivity, collaboration, and knowledge-sharing among its users.
tags: math, science, web2.0

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Coach's Corner 08/08/2009

2009-08-07T23:30:00.001-07:00

SRTrainingSummer09 / Focus on Inclusion - Annotated
tags: no_tag
- hello - post by jenbrown
- Reading & Writing Quarterly
- - Hi
    - post by juliawilliams
- Focus on Inclusion
- - this word was not misspelled - post by bowski55
- Reading & Writing Quarterly
- ISSN: 1057-3569 print
- Teaching
- Reciprocal
- Ms. Johnson was concerned about the inconsistent performance of several of her students in solving mathematical word problems. A number of her students were one to two grade levels below their grade placement in reading, spoke English as a second language, and had identified reading disabilities
  - many ESL students - post by jisaacs
- Ms Johnson was worried that these students might fail because the state assessment invariably
  - Hi - post by juliawilliams
- Mathematics textbooks and standardized tests contain an increasing number of word problems that students need to be able to solve.
  - I know. good point. - post by mbutler3
  - We all hated word problems...especially if you can't read! - post by croution
- word problems increasingly demand
  greater reading skills (Miller & Mercer, 1997
- wording particularly difficult to understand (Miller & Mercer, 1997; Salend, 2001). Therefore, teaching all

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Coach's Corner 08/07/2009

2009-08-06T23:30:00.001-07:00

Striving Readers Coaches Corner - Focus on Inclusion
tags: no_tag
- Reading & Writing Quarterly
- As students progress in their education, word problems increasingly demand greater reading skills (Miller & Mercer, 1997).
- The four major components of this modified approach are: clarifying, questioning, summarizing, and planning.
How to Make a Voicethread in 60 seconds
Easy to follow tutorial for making a voicethread.
tags: voicethread, web2.0, instruction, dialog
- Description: VoiceThread is an online, interactive album that can
  hold various types of media (images, documents and videos) and allows
  people to make comments in 5 different ways - voice (microphone or
  telephone), text, audio file, or video (webcam). A VoiceThread allows
  group conversations, digital stories, oral histories, commentary, etc.
  to be collected and instantly shared in one place, from anywhere in
  the world. You can embed them into webpages
  (http://voicethread. com/share/ 805/), moderate comments
  (http://voicethread. com/share/ 718/), and more. There is also a
  section called "Ed.VoiceThread" for educators
  (http://ed.voicethre ad.com/) which charges a nominal fee for
  additional content protection and control. All VoiceThread and many
  Ed.VoiceThread pages are completely accessible to anyone. See the
  About pages for a list of tools and links to tutorials. - post by bookminder
- 好音频工具 - post by itspanther
- How do you use Google Earth in the classroom? - post by kwillsonyshs
- Another great VoiceThread from educators around the world discussing the power of the network.
  - post by jutecht
- Worth a listen. A VoiceThread of educators discussing what it means to them to be involved in a global community.
  - post by jutecht
- Herramienta para la publicación y presentación de contenido multimedia, que luego puede ser comentado vía voz y vídeo. Muy útil en el ámbito educativo.
  - post by locative
- An
  awesome blogging tool. A VoiceThread is an online media album that allows
  people to make comments, either audio or text, and share them with anyone they
  wish. A VoiceThread allows an entire group’s story to be told and collected in
  one place. “Creating VoiceThreads will always be free for educators and the
  students that fill their classrooms. This includes publishing them on the web,
  and sharing them with the child’s friends and family. It’s really important to
  us that there are no barriers; no cost to fully participate, no software to buy
  or download, and no contracts to manage.”
  
  - post by bigfellow
- Upload photos and then record audio explaining them. Check out the "What's a VoiceThread anyway?" for an introduction. This could have some interesting applications working with primary sources; rather than writing text, you could record audio. Free for educators and students.
  - post by christyinsdesign
- Free for educators. Has excellent info on how to get started with it. Even has a classroom section.
  - post by msstern
- This program allows you to upload pictures and then talk about them like a presentation. Powerful...need to play with this more.
  - post by jutecht
Data, Probability and Statistics
tags: iwb, data, math, interactive

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Coach's Corner 08/06/2009

2009-08-05T23:30:00.001-07:00

TI Physics
TI activities are generally excellent and a great source of engaging, literate, standards based activities.
tags: ti, instruction, technology, physics, science
Mini-Movies for Your SmartBoard
increasing the engagement of activities when using the IWB
tags: iwb, web2.0, instruction

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Coach's Corner 08/05/2009

2009-08-04T23:30:00.001-07:00

Trends in International Mathematics and Science Study (TIMSS) - Overview
tags: math, assessment, research, instruction
- Trends in International Mathematics and Science Study (TIMSS, formerly known as the Third International Mathematics and Science Study) provides reliable and timely data on the mathematics and science achievement of U.S. students compared to that of stu... - post by cpudawg2k

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Coach's Corner 08/04/2009

2009-08-03T23:30:00.001-07:00

Reflections of a High School Math Teacher: Finding the Regression Curve of a Sin Graph in Precalculus Class
I like Dave's blog for several reasons. He gives his students voice, he uses technology well, and he seems to find some interesting activities for his students. This post is right up my alley; he uses data that is relevent to his students, has them do some basic analysis and then in explore other data and compare/analyze the data with the original (relevant) data!
tags: math, write2learn, dialog, algebra

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Coach's Corner 08/01/2009

2009-07-31T23:30:00.001-07:00

Thoughts on ‘literacy across the curriculum’ from my students « Birds fly, fish swim
Interesting blog from Steve Shann. This post on literacy across the curriculum is worth reading from some post-grad students exploring the topic.
tags: literacy, instruction, write2pub
25 Must-Have Firefox Extensions for e-Learners
Drag & Drop.io 2.0.1: Store and share pictures, videos, audio, documents and more without an account, registration or email address. Sharing is private.
tags: web2.0

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Coach's Corner 07/30/2009

2009-07-29T23:30:00.001-07:00

SpringerLink - Journal Article
discussions of significantmathematical content. This tension in teaching was not easily resolved;throughout the school year
tags: discourse, math, sherin
JSTOR: Cognition and Instruction, Vol. 21, No. 2 (2003), pp. 175-207
tags: discourse, math, knuth
JSTOR: Journal for Research in Mathematics Education, Vol. 25, No. 6 (Dec., 1994), pp. 608-636
tags: discourse, math
Talking mathematics in school ... - Google Books
tags: discourse, math
SpringerLink - Journal Article
discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics
tags: discourse, math
Glogster - Poster Yourself - Annotated
Easy way to create mashups of video, audio, graphics, and text, and publish for sharing.
tags: web2.0, poster, write2learn, write2pub
- Just heard about this site from Deb T. Could be a good one for our Web 2.0, Part 2 class in April. - post by chrislonge
- e sure to use the EDU version, to allow for private glogs and safe place for kids - post by datruss
- Hi Lauren,Thank you very much for posting this link. It´s really a "killer application" for language teachers. It´s a great tool for task-based language learning. I think it is a very easy and powerful way to publish task-outcomes in a 2.0 wayRegards,Victoria - post by acastrillejo
- very cool application! - post by possbeth
- - make flash posters on the fly
    - post by branzburg
Stellarium
Stellarium is a free open source planetarium for your computer. It shows a realistic sky in 3D, just like what you see with the naked eye, binoculars or a telescope.
tags: astronomy, science, dialog, instruction, iboards
- Gratis programvare som viser stjernehimmelen - post by werlien

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Coach's Corner 07/29/2009

2009-07-28T23:30:00.001-07:00

Practices to Support Collaborative Discussion
tags: no_tag
- pg 258 "In collaborative discussions, the teacher's comments direct students not only to understand what others are saying, but also to respond to, extend, or connect to those ideas. For example, the teacher can ask, "Does anyone want to build on what sally just said?"...However, the teacher can encourage students to work directly with one another's ideas and can take steps to foster such interactions."
  
  pg 258-9 "To get students to listen to, comprehend, and extend other's ideas, teachers must ask them to do this consistently and not only in a whole-class format. For example, during a group work, the teacher can actively support collaborative discussions by engagin all students at the table in the conversation...the teacher responded only to "group questions" or called on specific students to ask the question to make sure that everyone was in agreement with the necessity for a question and what the topic should be.
Aspects of Pedagogy for Discussion
tags: no_tag
- pg 258 "We capture differences in these kinds of discussions by talking about three key aspects of pedagogy: positing students for discussion, managing wrong answers, and connecting and linking across ideas."
  
  Annecdotal evidence from observation and analysis of lesson film.
Types of discourse
tags: no_tag
- pg 257 "We focus on two kinds of classroom discussions: sharing discussions and collaborative discussions. In sharing discussions, students share their answers and teachers value their contributions... In collaborative discussions, students also share their ideas, but in addition, the build on the thinking of their classmates' responses, take up classmates' ideas, and work with these ideas explicitly to extend the line of thinking that emanates. "
Discourse, Teaching, and Learning
tags: no_tag
- pg 88 "Questions such as the following might orient this work.
  * What is the communicative history of a particular activity structure (e.g.,
  science talk) in a given classroom?
  * How is disciplinary knowledge interactionally accomplished through
  discourse within this activity structure?
  * What do individual children discursively contribute to this collective
  activity, and how do their contributions change over time?
  * How do the voices of individual children, reflective in part of community
  membership, intermingle over the course of the construction of classroom
  discourse?"
Discourse, Teaching, and Learning
tags: no_tag
- pg 76 "When Michaels asked her why she didn't explain her solution processes in the first place, Elizabeth responded", I didn't understand your question" (Michaels & O'Connor, 1990, p. 16)."
  
  Teachers must scaffold/support metacognitive questions so that students become aware of their thinking patterns. Students do not automatically understand how to express their thinking verbally or in written form so teachers must, "Embed Communities of Discourse"in their instruction.
Discourse, Teaching, and learning
tags: no_tag
- jjpg 72 "Classroom Discourses and Educational Reform
  Educators working across disciplinary domains have begun to recognize that educational reform requires addressing traditiona classroom discursive practices. Inquiry learning, for instance, cannot occur as long as teachers and students communicate largely in ways reflective of direct instruction, where the teacher and the classroom texts hold the key to knowledge in the form of the "right" answer. Many educational reform efforts that have made discourse a centerpiece of reform have done so from a sociocognitive or sociocultural theoretical framework. Examples of such efforts from three academic discipline areas-reading and language arts, science, and mathematics illustrate how research on discourse has played a key role in attempts at improving classroom teaching and learning."
  
  Discourse must change if instruction is to change.
  Key component of sociocognitive framework is that students communicate with each other around the construction of understanding/content.
Discourse, TEaching, and Learning
tags: no_tag
- "In my own work on narrative discourse and classrooml earning( see Hicks, 1993), I have argued that narrative discourses should be examined in light of the speech activities in which participants are engaged. In this sense, narrative can be explored as a family of discourse genres in which children and teachers construct extended oral
  or written texts that order, describe, explain, or emplot events, both real and fictional."
  pg 70 "Studies of children's language use and classroom learning have suggested a
  relationship between such extended talk about events and children's successful
  participation in school tasks(Snow, in press). In large part, such studies have
  connected children's narrative performances with their literacy learning. Since
  oral narrative genres represent extended discourse in which the speaker constructs
  a text as opposed to a single utterance, studies of children's oral
  narratives have been viewed as a possible "window" onto their classroom
  literacy learning. Such work has often been focused on sociolinguistic differences
  in the narratives constructed by children from differing communities.
  Recall that Heath's ethnographic study of communities' ways with words
  revealed important differences in narrative socialization. In subsequent studies
  of children's classroom narratives, Michaels (1981) found cultural differences
  that supported Heath's work. The Sharing Time narratives of Black children
  were rooted more in an "oral" discourse style, where events were connected
  through linguistic devices like repetition, such as one might find in poetry.
  The SharingT ime narratives of White children tended to be more essayist
  or "literate"in nature, in that a single topic was chosen and events connected
  to the topic were related in a sequential manner. Researchers like Sarah
  Michaels have concludedt hat differing forms of narrative discourse may
  provide children with differential access to literacy. As Scollon and Scollon
  (1981) note in a chapter titled "The L iterate T wo Year Old," preschool children
  in many middle-class families may be literate long before they are able to
  read and write."
  
  Implications for dealing with different student populations and needs to address different cultural learning styles.
Discourse, Teaching, and learning
tags: no_tag
- Classroom Genres of Discourse:
  Triadic
  pg 69 Monologic form of talk. A child in a mathematics classroom may be asked to elaborate on how she arrived at her answer to a problem... The speaker is given the floor for a much longer period of time. The "rules of the game"-the participant frameworks that define social roles and obligations-have shifted somewhat so that the speaker no longer expects an immediate response.
  pg 70 Narrative discourses, oral and written texts representative of a series of connected events, may be another overarching discourse genre in the classroom, one with many variations in both form and function...Two examples that come to mind are (a) Morning Circle (or First Circle) and Sharing Time, where children construct narratives of personal experience (Dorr-Bremme1, 992;Kantor, Green, Bradley, & Lin, 1992; Michaels, 1981), and (b) Journal Writing, where children
  typically write journal entries grounded in fictional or personally experienced events (Dyson, 1989, 1993; Hicks & Kanevsky, 1992)."
  pg 70 "In my own work on narrative discourse and classrooml earning( see Hicks, 1993), I have argued that narrative discourses should be examined in light of the speech activities in which participants are engaged. In this sense, narrative can be explored as a family of discourse genres in which children and teachers construct extended oral or written texts that order, describe, explain, or employ events, both real and fictional."
  
  Different forms of discourse in the classroom. Focus on discourse (especially in younger students) that is not fully content related. A major difference is that the context of the learning for younger students is more closely tied to the general understandings at the secondary level discourse can move to more content 'heavy'/specific, but it should be noted that discourse/learning is still a social construct and context is still critical. A scaffolded approach must be made, processes identified, routines developed, long-term focus on helping students understand content related/specific discourse that is less connected to personal/fiction constructs.
Discourse, Teaching, and Learning
tags: no_tag
Discourse, Teaching, and Learnign
tags: no_tag
- pg 67
  "the IRE/IRF sequence has come to be associated with broader teaching practices or philosophies, such as the direct instruction of skills or the elicitation of so-called known-information questions, questions where the teacher is seeking the "right answer." The IRE sequence has, for some educational researchers, come to be associated with a "skill and drill" mode of instruction, and reform efforts have therefore made such modes of communication one of their primary targets of change."
  
  Further evidence of lower-level discourse expectations.
Discourse, Teaching, and Learning
tags: no_tag
- pg 66
  "IRE/IRFT: he Unmarked Case?
  Across the literature on classroom discourse, certainly the most robust
  form of talk documented has been that of the Initiation-Response-Evaluation
  (Cazden, 1988; Mehan,1 979) or Initiation-Response-Follow-up (Sinclair &
  Coulthard, 1975; Wells, 1993) sequence. This genre has come to be viewed
  as what linguists call the unmarked case; it constitutes somewhat of a norm.
  Perhaps the robustness of the IRE/IRF sequence across classroom settings
  can be related back to the example of mother-child interaction shown in
  Example 4 (lower-level, fill in the blank/rote memory kind of response) . There, as the more capable adult in that example assumed an instructional role, she provided conversational slots so that the child could successfully participate in joint book reading. The provision of such slots or openings for learners may be a means through which caretakers, and teachers, provide access to discourses and forms of knowledge beyond the child's independent means.
  The IRE/IRF organization of classroom lessons has been documented
  largely for group discussion activities in which the teacher asks a question,
  a child (or a group of children) responds, and the teacher follows through
  with a comment, often evaluative in nature. The following example from
  Courtney Cazden's own teaching illustrates the typical triadic structure of
  classroom lessons. In this example, the teacher has been eliciting children's
  birthplaces as a means of helping them learn about geography, distance, and
  family origins. One student, Prenda, has been called on to identify her birthplace
  and then to find it on a map."
  
  Confirms my experiences in the classroom that teachers rely on very low level, one word responses from students as the majority of interactions.
Discourse, Teaching, and Learning
tags: no_tag
- pg 62
  "This concludes my discussion of theoretical perspectives on discourse and
  learning. I might summarize this section by stressing that discourse is an
  inherently social construct that mediates, indeed partly constitutes, the teaching
  and learning that take place in classrooms. Through meaningful classroom
  activity, children appropriate the discourses that situationally define "what
  counts" as knowing within disciplines. In the following section, I turn to
  current research on classroom discourse. I explore prominent classroom
  genres, such as the Initiation-Response-Evaluation/Initiation-Response-Follow-
  up instructional sequence; efforts at educational reform tied to discourse;
  the "embeddedness" of classroom discourses in community-based discourses;
  and the heterogeneous discourses that are woven into one text or turn of talk.
  Each of these topics is elaborated through reference to work of current
  researchers in the field. Because of the breadth of this field, I cannot hope
  to cover all of the research that would fall under a given topic. Rather, I
  provide exemplars that will, I hope, enrich readers' understanding of the
  research topics currently being addressed within the field of classroom
  discourse."
  
  Nice synopsis of the discourse conversation so far.
Discourse, Teaching, and Learning
tags: no_tag
- pg 59
  "How do teachers teach and children learn these more formal academic
  discourses? There have been some efforts to incorporate the explicit teaching
  of academic genres into literacy instruction (see Reid, 1987, for a discussion of
  the controversy surrounding "genre instruction"). However, a sociocognitive
  perspective on discourse would suggest that children learn academic discourses
  through their repeated participation in meaningful social activity (Rogoff, 1990). Classroom teachers set the stage for this learning process by providing the discursive" slots"t hat enablen ovice learnerst o participatein disciplinaryp ractices.T his can occur withing roupd iscussionsi n which the teachero rchestratesc lassroom discourse (NCTM, 1991, p. 35), or it can occur in small group or one-on-one conferences."
  
  Difficult to teach the content literacies in generic form as the learning is social and must be connected to the learning before it is internalized. Further evidence/necessity that discouse must be established/developed/supported in the content area.
Discourse, Teaching, and Learning
tags: no_tag
- pg 58
  "Literacy is generally thought of as the ability to read and write. However,
  some theorists have extended the meaning of literacy to encompass more
  than just the ability to read and write. Full literacy, according to some, entails
  mastery of secondary or formal institutional, often academic discourses (Gee,
  1989). These secondary discourses typically involve ways of describing,
  explaining, and questioning that are dissimilar to "ordinary" conversation."
  
  Great rationale for the inclusion of dialog in our conversations of literacy and nice description that content literacy is more that conversation and contains skills/concepts/components that need to be taught/supported/developed.
  
  Implications for teachers: scaffolding/gradual release/experiences that include multimodal forms of communication ...
Discourse, Teaching, and Learning
tags: no_tag
- pg 58
  "Similarly, some theorists would suggest that "learning science" is a process that is framed by discourse genres, forms of activity, and ways of establishing semantic
  links among events, objects, and persons (see Lemke, 1988, 1990; Rosebery,
  Warren,& Conant, 1992). Other researchers have explored similar issues
  with respect to mathematics instruction (Ball, 1991, 1993; Bill, Leer, Reams,
  1992; Hiebert & Wearne, 1993; Lampert, 1990; Spanos, Rhodes, Corasaniti
  Dale, & Crandall, 1988)."
  
  Connections between interactions in math and science classes are closely related.
  Also, several references to consider:
  Ball, D. (1991, November). What's all this talk about "discourse"? Arithmetic Teacher; pp. 44-48.
  Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93, 373-397.
  Lampert, M. (1990). When the problem is not the question and the solution is not
  the answer: Mathematical knowing and teaching. American Educational Research
  Journal, 27, 29-63
Discourse, Learning, and Teaching
tags: no_tag
- pg 55
  "and teacher and student interactions in classroom settings have drawn upon sociocognitive theory to explain how children learn in what Vygotsky termed the
  "zone of proximal development" (Vygotsky, 1978; see also Rogoff & Wertsch,
  1984). A central metaphor that has emerged from this work is that of scaffolding
  (Wood, Bruner, & Ross, 1976)."
  
  Important for classroom practice to recognize the necessity of scaffolding and creating experiences that push students development but don't move too quickly for students to garner experience/cognitive benefit.
Discourse, learning, and Teaching
tags: no_tag
- pg 53
  "Discourses, some of which may be conflicting
  identities for them. For instance, my own working-class roots can be in
  conflict with the Discourses that I must assume for the purpose of being
  an academic; similarily, academic Discourses may be in conflict with the
  Discourses that are associated with my being a woman (Ellsworth, 1989;
  Hollingsworth1, 994).
  It is important to add that academic discourses also embody such ideologies;
  they are also Discourses. Thus, learning to "talk science" or "talk math"
  involves more than just learning a set of linguistic forms; it also involves
  learning beliefs and values (Lampert, 1990; Lemke, 1990; Yackel et al.,
  1990). Gee (1989, 1990) and Lemke (1990) both point out that the ideologies
  embodied in such academic discourses maybe in conflict with some children's
  home and community discourses. Minimally, these academic discourses may
  be unfamiliar to children who have not experienced at home what Scollon
  and Scollon (1981) term essayist literacy."
  Important to understand that discourse is not separated from environment, culture, experience.
Discourse, Learning, and Teaching
tags: no_tag
- Toward an operational definition of discourse from the cognitive perspective: "For reasons that will become more clear as this review progresses, the term discourse implies communication that is socially situated and that sustains social "positionings": relations between participants in face-to-face interaction or between author and reader in written texts."
  
  "The term discourse implies a dialectic of both linguistic form and social
  communicative practices. One can talk of discourse in terms of oral and
  writtent exts that can be examined after the fact and socially situated practices
  that are constructed in moment-to-moment interaction ( Fairclough, 1992;
  Gee, Michaels, & O'Connor, 1992). Thus, use of the term discourse implies
  a decision about how classroom communicationis to be theoretically positioned
  in research on teaching and learning"
JSTOR: Review of Research in Education, Vol. 21 (1995 - 1996), pp. 49-95
Discourse, Learning, and TeachingDeborah Hicks
tags: discourse, dialog, math

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Coach's Corner 07/28/2009

2009-07-27T23:30:00.001-07:00

Dilemmas of Discourse-Oriented Teaching in One Middle School Mathematics Classroom.
tags: discourse, math, dialog
Dilemmas
tags: no_tag
- pg 2
  "...core recommendations of the reform movement are carried out: students use visual models and manipulatives; they work together in groups; they are expected to focus on the process of doing mathematics rather than on just obtaining an answer; they are expected to discuss their understadnings and to communicate their findings; they work on open-ended problems that often require more than 1 class period to solve; and they are asked to make conjectures, to justify their thinking, to assess their knowledge, and to take a degree of responsibility for their learning. In short, many of the visible elements of reform are present in this classroom and provide a comparatively rich environment for learning mathematics."
  Nice description of components of a reform oriented classroom, but more specifically the processes that are critical to developing a focus on dialog in the classroom. In a middle school setting, but nothing prohibits this approach in the secondary setting.
  Finally, not strong research, much self-report and qualitative in nature, but can still access the processes/strategies/focus/routines
Discourse in Mathematics Classroom Research
Research gathered from studeis around discourse in mathematics. Working document
tags: discourse, dialog, math, secondary
JSTOR: Educational Researcher, Vol. 23, No. 7 (Oct., 1994), p. 4
tags: no_tag
Communicating Math 7
tags: no_tag
- References for further research:
  Manouchehri, A., & Enderson, M. C. (1999). Promoting mathematical discourse: Learning from classroom examples.
  
  Mathematics Teaching in the Middle School, 4 , 216–222.
  Langer, J. A. (2001). Beating the odds: Teaching middle and high school students to read and write well.
  
  American Educational Research Journal, 38 , 837–880.
  Pugalee, D. K. (1999). Constructing a model of mathematical literacy.
  
  The Clearing House, 73 (1), 19–22.
Communicating Math 6
tags: no_tag
- pg 16
  "Our knowledge function analysis of participants’ discourse indicates a gap in linguistic functions characteristic of teacher talk, as compared with student talk—with student talk reflecting lower-level knowledge structures, even in the presence of teacher’s discourse that illustrated varied, higher-level knowledge structures. These results suggest that the features of teacher discourse do not automatically transfer to student discourse through class discussion. Yet, when students were put in the position of “teaching,” they did demonstrate the construction of higher-level knowledge structures that were present in teacher discourse."
  Focus for results is to create opportunities for students to speak to students using the language of the teacher, the teacher to model but not expect that to do much unless coupled with student speaking opportunities.
  pg 16
  "The study suggests that instructional design in math education would be best served by systematically integrating math thinking and math talking at all levels of knowledge structures. Also, since conceptual understanding and procedural knowledge (representing the classification and principles knowledge structures) are the very foundation of mathematical reasoning, instructional design plans would benefit from a widening of the range of discourse functions to especially include those associated with higher-level knowledge structures. Teaching strategies should promote such discourse by students. To achieve this goal, teachers need to play the role of both a mathematician and a mentor—to do math but also to “talk” math as a way to model for students the way they should talk math."
  Further rationale for study/project
Communicating Math 5
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- pg 13
  "For instance, right after the instance in Vignette 9 (when Ms G tried to push students to articulate principles but did not follow through), two more equations were written on the chalkboard. This time, the students were asked to work as individuals, and the class was absolutely silent. When students were placed in a position to talk as a “teacher,” though, students did display higher-level knowledge structures. This transformation of student talk was evident in Vignette 6. Perhaps placing students in a teacher role helped them think more intensively in terms of their classroom audience, and therefore move towards..."
  pg 14
  "...higher-level knowledge structures in their discourse. (What does the audience need to know beyond the sequence of steps? How can I connect the steps to the principles? How can I help them connect what they don’t know with what they do know?). Perhaps allowing students to speak from a teacher’s role in a peer-to-peer..."
  p 15
  "...context provides them with an opportunity to reflect on their knowledge structures. “Think aloud” protocols, in which students are asked to articulate their knowledge in an explicit fashion, have been shown to help students develop metacognition, which is so crucial to math learning (Davey, 1983)."
Communicating Math 4
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- pg 9
  "The following examples show how student discourse was limited in expressing higherlevel knowledge structures when conceptual understanding was the goal of the lesson. Specifically, our analysis suggests that the classification knowledge structure occurred frequently, as illustrated in Vignettes 4 and 5, but such discourse was usually produced in an elaborated fashion by the teacher only, while student discourse expressing theory aspect structures was limited, if it existed at all.
  Though these data revealed that student talk was limited in expressing higher-level knowledge structures, we did find some examples of student discourse that
  
  demonstrated higher-level knowledge structures. These theoretic aspects of knowledge structures occurred in student discourse primarily when students acted as teachers themselves, as illustrated in Vignette 6
  Reinforces the need for students to speak to each other, not the teacher speaking for them or to them.
Communicating Math 3
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- In the field of communication in education, there have been numerous studies of oral discourse in the classroom (see Rubin, 2002).
  Rubin, D. L. (2002). Binocular vision for communication education. Communication Education, 51, 412–419.
  Many focus on “talk as learning” in the contexts of English, language arts and social studies (e.g., Nystrand, 1997; Nystrand, Gamorean, & Carbonaro, 1998). These studies have clearly identified connections between knowledge construction, communication, and students’ learning(e.g., Comstock, Rowell, & Bowers, 1995; Langer, 2001). Within the field of mathematics education, the role of communication in mathematics learning has also been extensively explored.While available studies suggest communication is one of the key processes in building understanding (Hiebert et al., 1997; MacGregor & Price, 1999; Manouchehri & Enderson, 1999; Monroe, 1996; Warfiel, 2003), most seem to focus on communication as a means to achieve the goal of acquisition of math content (e.g., Borasi, Siegel, & Fonzi, 1998) and not as an objective in itself. Additionally, most of the studies focus on elementary math settings and do not fully explore secondary mathematics classrooms.
  Most of the study in the field has been at the elementary level, indicating a need for more study at the secondary level.
Communicating Math 2
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- The language socialization concept provides useful insight into the relationship between the learning of math content and the acquisition of math language. Thus, following Ochs, we propose an activity model as follows:
  
  language of/
  
  language of/
  language of/
  
  for mathematics (movement back and forth) classroom activity (movement back and forth) sociomathematical knowledge
Communicating Math
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- The National Communication Association promotes the role of communication as a vehicle for “creating meaning, influencing thought, and making decisions” (National Communication Association, 1998). Consistent with that view, the National Council of Teachers of Mathematics in their Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) make communication an important objective in the teaching and learning of mathematics by including the following communication standard: “Instructional programs from prekindergarten through grade 12 should enable all students to organize and consolidate their mathematical thinking through communication, and communicate their mathematical thinking coherently and clearly to peers, teachers, and others . . .” (p. 348).
  Rationale for the importance of discourse in the mathematics classroom.
Communicating Mathematically: Comparison of Knowledge Structures in Teacher and Student Discourse in a Secondary Math Classroom - Communication Education
tags: discourse, math, dialog
O'Hallaran- Ambiguity of verbal expression
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- Student quote "and ``r'' equals ten on tan of theta take tan of alpha" for "r = 10/(tan theta - tan alpha)"
  A similar situation is demonstrated in the second example where the grammar of mathematical symbolism allows for ellipsis of the Operative process of multiplication together with brackets to indicate the grouping of nuclear configurations. When verbalized, however, there is ambiguity to the meaning of this linguistic statement.
  EDITORIAL: Allowing students to use imprecise language and using imprecise language ourselves contributes to this laxity of understanding.
o'Hallaran 6
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- Figure 3 embedded on hybridalgebra.wikispaces.com- ohallaran_figure_3
  "For example, the mathematical definitions and properties that have been assumed in the consequential relations in Fig. 5 include the definition of the tangent ratio1(lines 1 and 2), the Multiplication Property of Equality2 (lines 4, 6, 11), the definition of the Multiplicative Inverse3 (lines 4, 6, 11), the Addition Property of Equality4 (lines 5 and 9), the Definition of Subtraction 5 (lines 5 and 9), the Equality Property6 (lines 8 and 13) and the Distributive Property of Multiplication Over Addition 7 (line 10)."
O'Hallaran 5
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- "Structural condensation, whereby meaning is encoded in the most economical way possible, is achieved through devices such as:
  1. a specific rule of order for Operative processes (brackets, indices, multiplication/division and addition/subtraction)
  2. the possibility of alternate orderings through use of different forms of brackets
  3. ellipsis of the Operative process of multiplication
  4. exploitation of the resources of spatial graphology
  5. conventionalized symbolic forms"
  
  "For example, in the case of s(t) = ÿ16t^2 + 80t, the condensatory devices that have been employed include the rule of order so that multiplication, ÿ x 16 x t x t and 80 x t, occurs before addition of these two terms, ellipsis of the multiplication sign in -ÿ16t^2 and 80t, and use of spatial graphology so that t^2 means t x t. Other strategies involve the use of standard functional notation; for example, s(t) to mean the value of the function s at t."
  Great example of the meaning incurred in a simple function written symbolically!
O'Hallaran 4
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- "the impact of the multisemiotic nature of mathematics on classroom discourse to three main areas: first, the nature of the lexicogrammar of mathematical symbolism and its effect on the surrounding verbal discourse; secondly, some general features of mathematical pedagogical discourse arising from the multisemiotic nature of its makeup; and, thirdly, the shifts in meaning that result with movements between codes."
O'Hallaran 2
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- "For example, Burgmeier, Boisen, and Larsen (1990, p. 83) give the mathematical description s(t) = ÿ16t 2 + 80t for the height of an arrow shot vertically into the air, where t is the time in seconds. In this mathematical symbolic description, the complete pattern of the relationship between time and height of the arrow is encoded."
  The information that is presented in an equation or symbolic representation is/can be ver complete. That ability to present information in the computer era is getting stronger as diagrams and graphical representations become more dynamic.
  "In this respect, the visual display is not only limited in functionality, but also graphs and diagrams are usually only partial descriptions of the complete description encoded in the mathematical symbolic statements. In addition, there exists a possible misuse of diagrams, although Shin (1994) maintains that each of the above claims do not entirely warrant the lower status accorded to mathematical visual display. With the power of computers to dynamically display visual images, however, the status of this semiotic appears to be rapidly increasing."
O'Hallaran 3
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- Thus, the analysis of ``mathematical language'' must undertaken within the context of which it occurs; that is, in relation to its codeployment with mathematical symbolism and visual display. The analysis of the language of mathematics classrooms must necessarily be incomplete unless the contributions and interaction of the symbolism and visual display are taken into account."
  Reinforcing the multiple representation and having students work fluently with each form as well as work with back and forth with each form.
O'Hallaran
tags: no_tag
- "Mathematics is multisemiotic because the linguistic, visual and symbolic semiotic systems differentially contribute to the meaning of the text."
  Multiple Representations, again.

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Coach's Corner 07/26/2009

2009-07-25T23:30:00.001-07:00

India becomes R&D hot spot as high-tech firms cut costs | Technology | Reuters
"Staffed with about 60 full-time researchers, many of them Indians with PhDs from top universities in the United States, the center is at the cutting edge of Microsoft's R&D. It covers seven areas of research including mobility and cryptography."For now, the US is still the center of tech education. How long will people continue to come to the US for education? How can we change the tide of American students not choosing/being prepared for engineering/leadership
tags: instruction
280 Slides
280Slides is an online presenation tool. I played with it and created a quick presenation with embedded video really quickly. Just another PP tool for those who don't have access to Microsoft or want to do their presentations online.
tags: web2.0, powerpoint, presentations, write2learn, write2pub
Australia Publishes CC Info Pack - Creative Commons
Through its Copyright Advisory Group, the Australian Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA) has published a Creative Commons information pack online, a bundle of eight documents that distills the basics of CC licensing and the philosophy behind it. This pack is a great resource for educators and students, and we encourage you to use it in your schools by adapting it however you like. Read more: http://creativecommons.org/weblog/entry/13982#ixzz0MJNj0MUM Under Creative Commons License: Attribution
tags: creativecommons, copyright, publish
discourse in mathematics - Google Scholar
three characteristics of an alternative discourse of mathematics education are proposed. These are: that the learners make the mathematics; that mathematics involves thinking about problems; and that difference and individuality should be respected.
tags: discourse, math
9 Advanced Twitter Tips | Tech N’ Marketing
Great set of tips for using Twitter more effectively. I really like #3, because it's all about interaction in my opinion. If working with teachers on backchannel conversations/routines, then these tips should help the teachers understand how to support the process more effectively. Thanks Clif for sharing!
tags: twitter, socialnetworking, write2learn
sumadd
Having students start understanding number properties early is a significant aspect of developing algebraic reasoning. I really like that this game allows students to 'play'/explore different number combinations. I can even see using this game with older (3-5th) students to have them explore different characteristics of the problems, i.e. 3 + 4 = 7 the larger number goes at the end, 3 and 4 can be switched and still get 7 to introduce number properties in a concrete experiential way.
tags: math, smartboard, iwb, addition

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Coach's Corner 07/25/2009

2009-07-24T23:30:00.001-07:00

The eyeballing game
Great activity for having students develop their skills at estimating. Potential for developing their understanding of error analysis/estimating/measurement. Easy to play, and allows comparison to other players or comparison to their own plays.
tags: math, geometry, game, estimation
bodmas blog » Blog Archive » Accuracy (Google Earth and sundials)
tags: no_tag

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