# My Math Education Blog

"There is no one way"

## Sunday, October 23, 2011

### Escape! meeting notes 1 -- tools, backward design

Last Saturday, I attended an Escape from the Textbook! meeting. As always, it was stimulating. Here are some notes.

Carlos Cabana talked about the special role of tools in a student-centered pedagogy. Used properly, they allow us to reverse questions and get at big ideas. This is in contrast to the shallow use of tools which unfortunately dominates the mainstream use of electronic tools: "do this, do that, what do you notice?". The latter robs students of the opportunity to develop their own ideas, and in any case is not very effective. These ideas were familiar to me, as I have written much on this topic. (See for example "For a Tool-Rich Pedagogy" on my Web site.)

But Carlos takes this a step further: when designing a course, he thinks first about these things:
• what are the big ideas?
• how will the students will be working? (groups, Socratic discussion, etc.)
• what tools are available to do this work?
• what curricular resources are available?
He counterposes this to the currently fashionable idea of backward design. (Well, it's fashionable at my school, anyway.) In backward design, you think about your learning goals, design appropriate assessments, and then design the unit backwards from there: what do students need to do to be able to do this well? Carlos warns that starting with this approach can lead to narrowing of the curriculum, and atomizing it. For example, if we want algebra students to be able to solve linear equations, we work our way back to solving simpler and simpler equations as scaffolding, leading to mind-numbing problems like "solve for x: x+9=12", which requires no algebra. Moreover, in the process, we can easily forget to involve students in activities that might throw light on what solving an equation even means, with the result that  many Algebra 1 alums can solve an equation, but have no idea what they have accomplished. ("I have to get x alone, right?")

This of course does not mean that there is no place for backward design, just that it should not be the only model we use to frame our curriculum, or the dominant one. Carlos suggests it should come into the conversation after a discussion of the initial questions listed above, not before.

Another point he made was that connections between algebra and geometry are one way to bring the conversation back to big ideas. Absolutely! This is to a large extent what I've tried to do with the Lab Gear, the geoboard, and function diagrams -- tools that by their very nature make those connections.

More notes from the meeting: Part 2 | Part 3

--Henri