Category: Calculus

Sum of an Infinite Series

We chatted on twitter about this question for a bit. What predictions can you make about the predictions that were made? Click through to check your answers!

It's #mathmistake time! What percent of kids got this right? What was the most common wrong answer? Percent on that? pic.twitter.com/lNbaDxUeXx

— Michael Pershan (@mpershan) August 18, 2014

Here are the results from the 59 students who answered this question on an exam:

How would you give feedback to the students who wrote “infinity”?

Imagine that you were to give feedback to the students who wrote “-3/7.” What feedback would you give?

Derivatives logarithms

The Derivatives of e^x and ln(x)

Post author By mpershan
Post date June 10, 2014
5 Comments on The Derivatives of e^x and ln(x)

What you need to know is that the student work is the stuff typed in red, and that this came on a take-home quiz:

Why does this student think that ln(e) = x^1. Or did I get that wrong? Are there ideas that “feel similar” that he’s confusing, or is it something else?

(Thanks Taylor!)

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…)

Derivatives

Derivative of a Constant

Sandra reflects:

“It’s really not an ERROR in the ANSWER, just an ERROR in thinking that they have to do any work at all to get the answer. Perhaps an over-achiever?”

What say you all, Calculus people?

Thanks to Sandra for the submission!

Limits

Negative Infinity

What’s the fastest way that you could help this student?

Thanks to Tina for the submission! Go check out her very exciting new and remarkable collaboration with some dude, Productive Struggle.

Feedback Tangent Lines

Lines Tangent to a Point

What does the student know? What doesn’t the student know yet?

Calculus Rates of change

Rate of change of a volume of a growing sphere

Post author By mpershan
Post date August 29, 2012
6 Comments on Rate of change of a volume of a growing sphere

There were two parts to this calculus problem, and both parts are below. Time to sharpen your Calc skills, folks:

Calculus pros: what’s going on here? Where did the student go right? Where did she go wrong? How would you help?

Conditional Probability and the Rules of Probability Expressions and Equations Limits

I’m sitting on a bunch of Khan Academy questions from users that I marked as very interesting. I never posted them, and I feel a little cheap giving them all their own posts. So I figured I’d just dump the whole lot on you all. These questions reveal interesting things about the way these students are thinking. If you think that you’ve got something interesting to add, either on the diagnosis or prescription side of things, dig into the comments below.

The first is a nice probability puzzler. How did this student get 3/8?