@dcox21 @cheesemonkeysf I love the 'see if you can wreak' it mentality. It's not something ppl naturally do and so important
— Ashli (@Mythagon) April 5, 2014
The fact that you are supposed to wreck your own conjecture. Your conjecture isn't something you're supposed to protect from your peers and your teacher as though it were an extension of your ego. It's supposed to get wrecked. That's okay! In fact, you're supposed to wreck it.
Kirsten (1st Period):
It's easier said than done.
We've grown accustomed to math that does the following:
1. Teacher asks question
2. Student answers question
3. Teacher evaluates answer while student moves on about her day
Hypothesis wrecking requires a different model -- one that asks students to take a look in the mirror and give constant self-evaluation. It also depends on problems that lend themselves to establishing this mindset. These aren't always easy to find, though. I've found that the problems with a really simple prompt tend to work best. Here is a list of problems I've used:
1. The Diagonal Problem
2. Pick's Theorem
3. Doodle Math
4. The Locker Problem
5. The Handshake Problem
6. Tilted Squares (or Pythagorean Theorem disguised)
I don't actually use this lesson, but I liked how the "tilt" of the square was defined as x/y which makes data gathering quite nice.
7. How many ways?
8. Pile Pattern Problems
a. Fawn's Visual Patterns
b. GeoGebra Book we're working on
9. Avery's Edges, Vertices, and Faces
10. The Painted Cube
11. Math Without Words
12. Add the numbers 1 to n.
Maybe this is off topic, but it's on my mind recently and somewhat related. This is an example of something that looks like it has no pattern, but then suddenly one emerges from nowhere:
I love this idea. I have already began to think of ways that I might challenge teachers to design lessons with this concept embedded.
I had no idea what this was, but I don't think it's off topic at all, CalcDave.
This is really interesting. I think it takes a lot for a student to want to wreck his/her own hypothesis, but if the hypothesis withstands the attempts at wreckage then it is much stronger than it was before. It's definitely unnatural, as you said, but also extremely useful.
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