What does it take to ask students a question like this?
A poker face? A bit of malice? Nitsa Movshovits-Hadar argues [pdf] that it requires only the ability to trick yourself into forgetting that you know every triangle has the same interior angle sum. “Suppose we do not know it,” she writes, which is easier said than done.
The premise of her article is that “… all school theorems, except possibly a very small number of them, possess a built-in surprise, and that by exploiting this surprise potential their learning can become an exciting experience of intellectual enterprise to the students.”
This is such a delightful paper — extremely readable and eminently practical. Without knowing me, Movshovits-Hadar took several lessons that I love, but which seemed to me totally disparate, and showed me how they connect, and how to replicate them. I’m pretty sure I was grinning like an idiot the whole way through this piece.
[via Danny Brown]
@rawrdimus i.e. think less like a math teacher who knows how to write a circle equation
— Dan Anderson (@dandersod) June 10, 2016
Not easy for math teachers to do!
@ddmeyer I did a similar thing with my Year 9 students and the trig ratios!!! Heaps of fun and surprise!
— David Ross Lang (@Davidinho_78) June 12, 2016
What if you asked two questions: which triangle has the longest perimeter and which triangle has the largest angle sum? It might clarify what can change in a triangle and what cannot. Also it hides the surprise better. If you teach via surprise consistently, kids start looking for the punchline.
Elementary may actually have an advantage here! We play these games all the time. Some favorites:
Draw me a two-sided quadrilateral
Draw me a triangle with three right angles (or three obtuse angles)
(We have a manipulative that consist of little plastic sticks that snap together to build things)–Build me a triangle with the red stick (6″), the purple stick (1″) and the green stick (2″ )
Once the whole class is convinced they can’t you can get at why and then writing a rule for it. There is nothing an 8 year old likes better than proving the teacher wrong.
Theorems and formulae in textbooks should be marked with a “spoiler alert”.