Tuesday, November 26, 2013

First Idea; Best Idea...

...and the Worst Idea

Creating a Culture of Questions was, by far, the most popular post on this blog until someone somewhere starting linking to the post on Exponent Rules.

I think a natural follow up to the Culture piece would be with regards to establishing a classroom culture where feedback is given and accepted.

The First Idea is the Best Idea and the Worst Idea

The first time students hear this, I usually get, "Gosh, that's mean."

But we discuss how the first person who puts forth an idea holds the best idea as there is nothing to which we can compare it.  But using the same logic, this idea should be the worst.  This assumes the flow of ideas that should follow.

I think this encourages two important things:

1.  "If I go first, it doesn't matter that my idea isn't fully formed."  This student has established a floor on which each other student can stand and/or build.

2.  "I can take someone's idea and help them make it better."  The real work is done by the first follower.  This student chips away at any imperfections and helps the first student refine her idea.  Subsequent students then follow suit.

What's this look like?

Yesterday, we trying to determine the equation between the points below and students wanted the y-intercept.

Students were using what they knew about slope to find other points and had to wrestle with the fact this particular line doesn't have a lattice point for a y-intercept.  Once we were finished, I asked students to write down any questions they had.

Student 1:  "I have a comment."

"Ok, what is it?"

Student 1: "No matter which points we choose, the slope simplifies to the same thing."

"Can you turn your observation into a question?"

Student 1: "Will that happen all the time?"

Now here is where it happens.

"I can misunderstand [Student 1]'s question, can we make this more precise?"

Student 2: "Will the slopes always simplify to the same thing?"

Student 3: "Will the slopes between two points always simplify to the same thing?"

"Are we only using two points?"

Student 4: "Will the slopes between three points always simplify to the same thing?"

Student 5:  "Will the slopes between any two pairs of points always simplify to the same thing?"

Student 6: "Are the slopes between any two pairs of points always equal?"

"Are we really talking about any 4 points here?"

Student 7: "Are the slopes between any two pairs of points on a line always equal?"


Ben Morris said...

I like this. I can introduce it when using estimation180 as my warm-up. It's soooo hard to get them to feel comfortable throwing things out there. And I catch myself saying "don't just guess" all of the time. I need to do a better job of differentiating between when it's good (read: okay) to guess and when it's not.


David Cox said...

I kind of see guessing as part of the precision continuum. We want to avoid random guessing, of course. But, a continuum that goes something like:

Gut Guess -> Guess with Reason -> Precise Method

is always welcome. I think it's my job to take the gut guesses and help the student funnel his reason towards precision.

Unknown said...

Your article about the First idea Best idea is really good article. You have include so many helpful points in your article. I must follow those points. I appreciated your work. You have done such a good job. Keep it up.
Fun Math Worksheets