Contrast that with a model I’m more familiar with, where the teacher acts as the arbiter while engaging one student at a time in verbal ping-pong (aka initiate-respond-evaluate, on repeat).

In the former model, the notebooks are a place where ideas become arguments and are workshopped and refined throughout the lesson. In the latter, there’s a lot of improv, and it’s easier for students to avoid rigorous thinking.

In other words, I think Dan’s on to something here! And it’s unquestionably true that the pedagogical shift requires a related curricular shift. Excited to see how these ideas develop.

]]>Another thing I like about “list of things” is that it’s transferrable. I could use it when teaching transcendental equations. I could use it in geometry. I could use it when connecting graphical and algebraic representations of equations. Really, it’s brilliant.

]]>It doesn’t have to be complete, and it may include extra attributes.

Students can compare lists and share things they liked, and things they questioned about each other’s lists. Then you can ask a student to share their list with the class.

They can then refine (second draft) their own list to cut out things they think are ‘extra’ and add things they think are necessary. Counter-examples might pop-up…controversies!

Now try this with Isosceles Triangle, or Trapezoid, or Isosceles Trapezoid.

I like that a LIST OF THINGS can be written as a draft, can be adjusted and refined easily (cut, add or change) for future drafts. Old drafts can be seen in new drafts. An editor’s work on a script.

How does the LIST OF THINGS work for the other questions?

Q3) Write a list of things you know about the answer to 5-2x=10.

A student might write:

x does not equal 2, I tried it.

x does not equal 0.

the answer won’t be positive.

I think it’s negative.

Future drafts may include:

I think x is a decimal?

x=-3 is close

As always, a very thoughtful post and tremendously thoughtful comments.

Thank you for sharing Dan.

Thanks! I agree! A more general question would more effective for students to formulate the math concept before they finalize what the math concept means to them.

]]>That’s true. This was still huge though! Probably one of the top 3 pieces of advice I’d give to my younger self.

Just in case you ask me, here’s my current top 3:

1) Use tasks with more than one solution method.

2) Pick which groups/students present initial attempts at a solution methods (and in what order) rather than asking them to volunteer (this works best in conjunction with the next one).

3) Talk about the importance of rough draft thinking and the revision process in absolutely EVERY part of life–including math class. We are not expecting a finished piece of work, we are asking for your starting ideas on the problem.

Surprisingly, there wasn’t a lot I needed to change other than the language we used in the classroom. I asked students to present their ideas as rough drafts. Over and over again we normed the idea that having the correct answer was not expected in your initial thoughts on a topic anywhere in school–not even in math. We just needed a 1st draft to start our revision process as a class. Together, as as class, we were going to revise the idea but we had to have a place to start. I used the same tasks as last year. However, this year the courage to make mistakes in front of the class started happening in August rather than in November. That’s huge. That’s the power of language.

Here’s the blog post:

http://www.andrewbusch.us/home/no-hands-up-and-rough-draft-thinking-trying-to-level-up-my-formative-assessment-game