This is fairly representative of the class’ work. What would your next step be with this class?
Category: High School: Geometry
Do you see the mistake? How would you help this student?
"Find the midpoint of the line segment connecting (2,5) and (2,396)," at the beginning of the unit. Can you predict the top three responses?
— Michael Pershan (@mpershan) April 7, 2014
What would you predict? Here are some twitter responses:
@mpershan Is (0,391) one of them? That seems like a way to get an answer from those two numbers.
— Evelyn Lamb (@evelynjlamb) April 7, 2014
@mpershan (3.5, 199) (2, 200.5) (2, 198)?
— David Wees (@davidwees) April 7, 2014
@mpershan (2,198) is probably one of them. Maybe(1,198). But I am otherwise stumped. Oh! (201.5) maybe?
— Christopher Danielson (@Trianglemancsd) April 7, 2014
@mpershan er…(2, 195.5) as a top answer.
— Christopher Danielson (@Trianglemancsd) April 7, 2014
@mpershan I’ll bet at least one of the top 3 responses includes *two* points.
— Chris Lusto (@Lustomatical) April 7, 2014
—
Here’s your answer key…
First Place:
Second Place:
Third Place
I keep on seeing this in my Geometry classes this year. Tasked with finding the area of a right triangle, kids move toward the hypotenuse even if two of the other sides are given. Then they end up stuck looking for a height that they can’t find.
I’m pretty convinced — based on talking to kids and looking at their work — that this is all about how they see right triangles. These kids must be seeing hypotenuses as bases, and it must feel weird for them to treat the legs as bases. Or maybe instead it’s about the height? Maybe it feels strange to them to use a leg as a height?
Decimals are hard.
What would we even want the student to do here if he’s working in decimal? Like, how do standard multiplication algorithms handle something like a repeating digit?
That’s what I’m getting out of this mistake right now: the deviousness of decimal representation, and the way it can obscure numerical properties.
How about you? What do you make of all this?
1. This is a really cool question.
2. Gregory Taylor says he doesn’t know what the kid was thinking. Thoughts?
Lots to notice here, including the formula that the student is using for the area of a triangle.
Another interesting instance where additive and multiplicative reasoning get entangled when working with similar figures.