January 15th, 2013 by Dan Meyer
a/k/a Dave Major Rides Again
It turned out to be productive and fun arguing over who among the four contestants in this video did the best job drawing a square. Video served us well. It gave us something to look at, argue about, and abstract. But video is still a static medium in many ways. The pictures are moving but it doesn't edit well. It doesn't personalize. It doesn't reflect the learner in any way.
So Dave Majors and I partnered up again to kick around an idea of what this task would look like in code, in a web browser, and came up with better best squares.
He's written a post describing some of his technical innovations. I'm going to use this space to point out our pedagogical innovations.
- The most obvious difference here is that instead of watching four people attempt to draw a square, you get to attempt to draw a square yourself.
- That quadrilateral then follows you throughout the text. Rather than using a generic example to illustrate a mathematical concept, we use the example you created. We talk about its perimeter. We talk about its area. The diagrams in the margins change. The text in the textbook changes.
- You see your classmates' quadrilaterals and make an intuitive ranking of their square-ness. When we formalize the concept of square-ness later, we'll refer back to our initial rankings. Ideally, the mathematics will validate the student's intuition and vice versa.
- You can revise and skip most questions. We're deviating here from our last experiment where each question had to be completed before you could move on. In a print textbook, you can always flip forward and see what's next or move onto a new task if you don't want to complete the current one. So you can leave an answer blank. You can go back and revise your answers. The textbook doesn't judge you. It doesn't say, "You're wrong." It reports your response (or non-response) to your teacher and lets your teacher make the pedagogical judgement there.
- The teacher's edition is so useful. I asked Dave to let me see all responses disaggregated a) by student and b) by question. I want to click on Mike's name and see all his progress throughout this unit — everything he drew, everything he wrote. Then I want to click on each question and see every response. Dave went above and beyond here. You see every student response but you also see the revision history on those responses. You can trace the student's thinking. You can also flag student responses to show the class. I'm such a fan of Dave's work here.
- Don't like our definition of "best square" as being the ratio of areas? Submit your own. The system will accept your formula, send it to the teacher, and then use it to rank the entire class' quadrilaterals.
Dave and I both agreed this problem is a little too obscure and weird to justify all the effort we put into it. But critique the digital pedagogies rather than the task itself. These pedagogies can transfer to other, better tasks. Critique this definition of personalized learning.
Previously. Dave Major Shows You The Future Of Math Textbooks.
2013 Mar 27. A UK teenager codes the algorithm for judging the best circle. Be sure to stick around for the part where the cat judges you.