8P29 Week 5 Post

This week the focus was on integers. Integers aren’t too bad once you learn the rules. The trick is to understand the logic behind the rules, otherwise they become harder to remember and you can mix them up depending on what operation you’re completing (for example, thinking two negatives make a positive when you’re subtracting, rather than multiplying or dividing integers). But once students understand the rules, it becomes simple computation, something students would have been doing for years already.

I may have mentioned this before, but I have to say that Marian Small’s book Making Math Meaningful is a tremendous resource for pre-service teachers. Everything in the book is laid out clearly and there are plenty of class activity ideas within each chapter. If you’re a pre- or in-service teacher looking to improve their skills teaching math concepts, go out and buy this book, you won’t regret it.  Small’s chapter on integers is no exception to the rule. She suggests a fun card game called Integro to help students practice adding and subtracting integers. Have an Integro tournament in your class to see who will reign supreme as Imperator Integro (that’s a working title for the winner of the tournament, message me if you think of a cool one).

Making Math Meaningful by Marian Small p. 327

It’s easier to teach if you can get students to connect the concepts to something in the “real world”. Small suggests temperature, altitude, and sea level, but I think the real world example I like the best is debt. One, it’s good in general to teach students that debt is an awful hole that makes you think you have money, but really you don’t, and two, you can apply the debt situation to any of the operations. Here’s a quick example:

If I’m broke and I borrow 5 from Tony and 3 from Pauly, how much total debt do I have?

(-5) + (-3) = (-8)

Here you can see adding together two negatives puts you deeper in the hole, because I start at 0 and now I owe money I don’t have. Now let’s say I have a windfall:

Tony, in his magnanimity, has forgiven my debt, but Pauly still wants me to deliver. However, Silvio also gave me $4 birthday money as a gift. Now what’s my total debt?

(-8) – (-5) + (+4) = (+1)

See, I paid back Pauly, because he was starting to scare me a little (his eyes get all buggy when he’s angry), which makes me debt free, and also not broke anymore (thanks Silvio!). Putting it in a story like this makes it make a lot more sense than trying to memorize a set of rules. Add in some manipulatives and a number line (number line is key), and your lesson would hit a lot of bases.

What this is teaching me about teaching math is that there’s a lot more to students learning rules than them just learning the rules to certain concepts. Without the “why” there is very little retention, or common mistakes and mix-ups can occur. The “why” doesn’t have to be tremendously complex, but without context math is meaningless punching in figures like computers, and we aren't trying to make students into automatons, but autonomous, curious, problem-solving individuals.