The Concept of Integer Addition

7th graders don’t get it. It’s pretty sad. Now I did not say addition and subtraction because they are the same thing. Subtraction is just the addition of a negative.

Anyway, onto a recap of the classes I observed this Friday. The teacher who’s classes I’m observing had to go to a workshop, so I got to see how the substitute (a retired math teacher) handled things. The normal teacher left his classes a few review sheets that involved addition and subtraction of positive and negative numbers… also known as integers. The sub went over how to do addition and subtraction and went over the problems in sets of 5-10. The first sheet was on addition, the second on subtraction. This is what they were told to do for addition:

If the signs of the numbers are the same, add the numbers and keep the signs

If the signs of the numbers are different, subtract and keep the sign of the larger number

This is what you’re supposed to do, none of the 8th graders had problems but some of the 7th graders were confused. I tried to relate negative numbers to the concept of owing someone money when helping out a few students, but they totally didn’t get the concept of owing money. It wasn’t until later that I realized they were too young to really get that when people lend you money you need to pay them back, and that I should have explained this concept to them with the use of a number line.

Instead of explaining -5 +3 by saying, if you owe someone five dollars, and then you get three dollars and give that back to them, how much do you still owe them, I should have drawn a number line. I would have said that first we move 5 away from 0 in the negative direction, then we move 3 forward. Or I could have said we dig a 5ft deep hole, then we fill it in 3ft, how deep is it now? The concept of owing money isn’t easy to visualize, but the concept of digging a hole is. Why couldn’t I have thought of that sooner.

I ended up caving in and just teaching them how to use the rules properly. Then when it came to the subtraction sheet they were told something we’ve all heard:

Keep, change, change

Meaning if we have, -5 – -2 it can be rewritten as -5 + 2, or if we have 4 – 6 it can be rewritten as 4 + – 6. Basically they’re changing it into addition, but none of the kids can see that it’s the same thing. I also would have been able to similarly explained how this worked using a number line or the idea of digging a hole, but I came up with the idea too late. I will remember to use that idea when I student teach/teach though. Once again I just caved in to teaching them how to use the rules.

It’s pretty sad that they couldn’t see that -5 + 10 and 10 – 5 were the same thing. I was happy that I got one girl to see it. It pratically blew her mind.

I think the solution to this problem would be elementary school teachers teaching addition with a number line and 3d cubes, instead of just 3d cubes. You can’t have negative 3d objects…. they should also be teaching negative numbers in elementary school if they aren’t. If you just give kids rules you’re only giving them shit to memorize, not teaching them how to understand anything. If you give a kid an understanding of a concept, they’ll always know how to do the problem.

In other news I saw two boys get into a fight! The sub told me in this school the kids are pretty good in that the class will break up the fight rather than join in on the fight like they do in crap schools. She also told me if you can break up two boys they’ll chill out, but you can never turn your back on two girls fighting or you’ll end up with a chair in your back. That was some pretty useful advice that makes a lot of sense.

My apologies for those of you who didn’t understand this post… though if you don’t it’s pretty sad. Assuming you’ve graduated high school. I’d be more than happy to explain these concepts to you in a variety of ways if you’re confused!!!

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4 Responses so far »

  1. 1

    Scott Pool said,

    I don’t remember ever having much problems understanding the concept of negative numbers myself, though I guess that’s because I understood the concept of owing someone money >>.

    But yeah that’s a good idea teaching them using the digging the hole method, it’s easy to visualize and the ground level makes a good 0. Arrgh if only I could have thought up drawing instructions to the kids in the ESL class who couldn’t speak english. Oh well, if I ever have to go back down there again to help her with the Rosetta Stone kids I’ll remember that!

    • 2

      improperintegirl said,

      But even so, concepts build on each other. You have kids that don’t understand algebra because they don’t get the concepts of arithmetic. And then you have kids that don’t get calculus because they don’t understand the concepts of algebra and trig… I feel like schools aren’t giving kids the best foundations they can have.

  2. 3

    I remember the number line! That thing was my friend, even in high school when we had to do graphs & greater than/equal to quadrant things.

    From what I remember, my teachers taught me integers I used that keep change change rule a lot.

    Then, in high school I started liking math A LOT, and I got way better at comprehending it.

    Here I am in college, and it seems math has broken up with me & I am not as efficient at it as I used to be it seems 😥 Though the integer rules still stay with me in my Bio calculations 🙂

    • 4

      improperintegirl said,

      I had the keep change change rule also 😄
      I’m sure you could still do well in math, but that it was hard for you to keep up while focusing on other things at the same time. If you ever run into jokes based on calculus or anything beyond that, I would be happy to explain it. I see you as having the potential of understanding it because you at least know “some” calculus… If I tried to explain the jokes to a high school student they probably wouldn’t get them.


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