Math Mistakes

Your finest complex number mistakes, please!

Post author By mpershan
Post date February 15, 2014
5 Comments on Your finest complex number mistakes, please!

Help, if you don’t mind!

I’d like to flesh out our collection of complex numbers mistakes. If you’re teaching this topic in the next few months, could you send me some pictures of mistakes? I’m looking for all sorts of mistakes — either common or uncommon errors.

In the meantime, would you take a second and comment about a complex numbers mistake that you’re used to seeing from your students?

When you’re done with that, check out some of the new mistakes that I just posted…

Going 4325 mph, or how do you help kids check their problems for reasonableness?
Integrating by parts, and a reflection on working through unfamiliar subject areas through mistakes.
A fascinating fraction addition mistake.
A time-telling puzzle. (We’ve got the answer, but I’m withholding it.)
Decimals are hard.
So are fractions and negative numbers.

Thanks for all the great mistakes and comments lately, guys. Keep up the great work!

Negative numbers and fractions

Post author By mpershan
Post date February 15, 2014
5 Comments on Negative numbers and fractions

Would this student also say that 1/2 is equal to 2?

Decimals Geometric Measurement and Dimension Surface Area and Volume

A decimal mistake

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?

Measurement & Data

Time-telling puzzle

Today a student wrote ten past six on an analogue clock as 6:40.

She then wrote 25 past nine as 10:10

Ed sends this, along with the answer. Can you figure out what this kid was doing?

(Telling time is in CCSS. Huh, didn’t know that.)

Fractions Number & Operations -- Fractions

3/7 = 10/14 and 1/2 = 3/14

Post author By mpershan
Post date February 15, 2014
6 Comments on 3/7 = 10/14 and 1/2 = 3/14

Nathan sends along a really lovely fraction mistake.

If I’ve got this right, the kid added 3 and 7 to get the numerator, and added 1 and 2 to get the numerator? This is a way of thinking about fractions that’s new to me. Can anyone offer a better theory or some helpful context for this kids’ thinking?

Integration

Integrating by parts

I’ve never taught Calculus, and I find myself struggling with this mistake…

…in a good way. Here’s what’s want through my head:

Oh, God, integration.
How would I solve it? Is there any way that I can avoid integrating by parts? (Yeah: transform the numerator to (x-1)+1.)
Oh, shoot, how do you integrate by parts anyway? It’s vdu – uduvuvvvvvuuu or whaaaaa???
[Googles integration by parts]
[Solves it using integration by parts]
Good Lord I don’t like integrating by parts.
What did this kid do wrong?
It looks like they ended up with a square root instead of a square?
That makes sense. People often make association mistakes when they’re working on a problem where they have to keep in mind a bunch of moving parts.

I think that working through math mistakes like this one would be a great way to prepare for a new course.

(Hey! Someone should start collecting and organizing these so that they’re available to new teachers…)

Feedback Rates Ratios & Proportional Relationships

4325 mph

Decimals are hard!

“Kid should’ve realized that her answer needs to be smaller.”

How do you help kids monitor themselves in this way? Do you monitor yourself in this way when you’re doing math?

(Thanks, Ruth, for the submission!)

Site Business

A bunch of new mistakes for you to check out

Post author By mpershan
Post date February 6, 2014

Hey everybody! It’s so nice of you to visit here.

I recently posted a bunch of mistakes, and I know how easy it is to get slogged down in the internet, but I think that you’ll like these. So go check out…

… a mini-essay I wrote about some 3rd Grade Exponent mistakes.

… a student who thinks that ln(5)-ln(4)=ln.

… some very non-standard fraction notation that my 4th Graders started using.

… all of the answers my kids gave to Andrew Stadel’s Black Box lesson.

… a meditation on the spoken of language of fractions, inspired by a kid who calls three quarters “a third.”

… a confusion a Geometry student of mine had about “scale factor.”

Also, from other people’s classrooms, we’ve got…

… a problem with equivalent fractions in algebra. Or, does squaring the top and the bottom of a fraction not do the trick?

… a division mistake, and what’s going on with it anyway? (I thought it was a calculator mistake.)

… a mysterious claim made from a sort of geometric scatterplot question that I’ve never seen before.

Come comment and join the fun!

logarithms Seeing Structure in Expressions