Show Your Work

Teachers love to force students to show their work. It’s not only a way to see if the student actually knows what they’re doing; it’s also a way to see exactly what a student doesn’t know. A wrong answer tells nothing about what the student knows or doesn’t know. Partial credit is usually the incentive for students to show their work – but you shouldn’t force students to show everything if the reaction is negative because you don’t want to have your students feel annoyed by you. As a teacher, you need to motivate, inspire, encourage, and enlighten. If you focus on the wrong parts of math, you’ll lose your students.

With that said, here’s a fun comic to remind us to lighten up sometimes. Don’t forget to use PEMDAS to get the correct answer!


Everybody Steals

While people have tried to pinpoint exactly who discovered what in mathematics, it’s impossible to truly give credit for certain discoveries. For example, we don’t know who the first person was that came up with the idea of zero. Even if we did it wouldn’t matter because there were people separated by great distances that developed mathematics separately from one another. It’s not fair to give credit to only those that worked on mathematics in a certain part of the world (although that’s what has happened anyway).

Confusing the history even more is the fact that mathematicians often accused each other of stealing their ideas, while other mathematicians did in fact steal others’ ideas (either from peers or their students). We don’t know for sure sometimes who did what because there can be conflicting accounts. It seems to have been fairly commonplace at the time.

I like this from Abstruse Goose – which came with the quote, “Good mathematicians copy; great mathematicians steal”:

It may seem harsh, but it’s not entirely incorrect in its assumption that Pythagoras stole the work of his students. It’s a commonly held belief that he in fact did do this – whether or not he murdered them is an entirely different account.

It also reminds me of a project called The Mathematics Genealogy Project that maps mathematicians’ relations to other mathematicians. For example, if you know someone who got their Ph.D. in mathematics, you can type in their name and see their advisor. Then you can click on the advisor’s name and see that person’s advisor. You can keep clicking and see who their “related to,” mathematically.

Mathy FoxTrot

Since Borders is going out of business, I had to use a gift card I had so I purchased Bill Amend’s themed FoxTrot collection:

In general, this is a pretty amazing little collection. I highly recommend it to those that are especially fond of math, science, and/or computer programming. As you can see in the above photo, I took my new gift to myself outside and decided to share some particularly mathy gems in one of the least-tech ways possible, by taking pictures of them. Please excuse the quality, I just don’t have a scanner. Enjoy.

Why You Can’t Divide By Zero

There are two ways to think about division.

1. You can divide a certain number of things into groups of a certain size. For example, 6 ÷ 3 can be thought of as: 6 things divided into groups of size 3. The answer of course is two, so you have two groups, 3 things in each group.2. You can divide a certain number of things into a certain number of groups. For example, 6 ÷ 3 can be thought of as: 6 things divided into 3 groups. The answer two refers to how many things are in each group.

Now let’s use this to think about dividing by zero.

1. Can you divide a certain number of things into groups of size zero? Let’s use the example 5 ÷ 0.

2. Can you divide a certain number of things into zero number of groups? Use the example 5 ÷ 0 above.

This is why the calculator screams “ERROR” when you try to divide by zero.

Get Them All Across the River

Below is a somewhat popular logic puzzle that I presented to my class to change the routine up a bit. I was able to utilize an interactive whiteboard with this so that the animals and cabbage could be dragged around to check solution methods. After immediately pointing out that the cabbage was not proportional, they really got into it and were able to solve it quite quickly.

Here’s the Dilbert comic that reminded me of this challenge:

Sometimes It’s Too Much

I had to stop myself from doing this to my students yesterday. Sometimes I have to remind myself that the things I think are awesome about math are going to be overwhelming for them. I like to think that they are starting to enjoy math a little bit and I would hate to ruin that.


The title of this illustration from xkcd is both awesome and inappropriate so I leave it to you to find it yourself if you so choose.

There are a few I would change (only slightly) but for the most part I agree with their representation of these fruits’ tastiness and difficultly to eat. I also agree with their method of representation 🙂

I know where Larry David would place apricots on this chart…

Curb Your Enthusiasm – Ep.61: Clip – Larry on… Apricots