visitor tracking

If your children have trouble with integers, they’re not alone!

Posted by
November 26, 2007

A recent instant scratch lottery game had to be withdrawn in Britain because too many people couldn’t figure it out. Winning this winter-themed game depended on scratching a card to reveal temperatures lower than a given reference temperature. From Good Math, Bad Math : Pathetic Innumeracy – this time from Great Britain:

So many people didn’t know that below zero, larger numbers are lower and thus colder, that the lottery had to withdraw the game!

To quote one of the “victims”:

On one of my cards it said I had to find temperatures lower than -8. The numbers I uncovered were -6 and -7 so I thought I had won, and so did the woman in the shop. But when she scanned the card the machine said I hadn’t.

I phoned Camelot and they fobbed me off with some story that -6 is higher – not lower – than -8 but I’m not having it.

Of course, much of the dispute was over the use of the word “lower” and one would hope that using the word “colder” wouldn’t have caused such a problem. This just shows that even when our minds know the application of a mathematical concept, for example that -10 degrees is colder than -8 degrees, we may still get the math wrong. This is why so many people think “word problems” are difficult: because sometimes the math we instinctively use in everyday life doesn’t register in our brains as being math.

Other applications of integers you can work into your math teaching at home:

Here’s a cute website with some online integer games and challenges. And, my booklet explaining operations with integers is freely available from my Teachers Pay Teachers website.

disturbing, homeschooling, mathematics

Did you enjoy this post? Why not leave a comment below and continue the conversation, or subscribe to my feed and get articles like this delivered automatically to your feed reader. If this is your first visit, please be sure to check out "starter kit" of articles. Then, click on the pages, posts or categories on the right that interest you for much more information about home school university admissions in Ontario and Canada.

Comments

What is so hard about integers!!!!!!!!!!!! I need help for my project!!!!!!!!!! on misconceptions with integers!!!!!!!!!!!!

Comment by julieta on October 19, 2008 @ 4:41 pm

Julieta, here are a few things that students typically find difficult about integers:

1. MAGNITUDE (size) of numbers: 8 is a larger “size” than 3. +8 is bigger number (ie. more positive) than +3, but -8 is smaller (ie. less positive) than -3. Students have a difficult time realizing that when we call a number “bigger”, we mean “more positive” not “larger magnitude.”

If students don’t learn integers in a sensible way, it can be REALLY difficult to separate the SIGN of the number from the MAGNITUDE of the number. 8 is bigger than 3, right, so isn’t -8 bigger than -3? Well, it’s MORE NEGATIVE, but it’s actually a SMALLER quantity.

2. Multiplying and Dividing with integers: Why do two negatives make a positive? Can YOU explain it? Do you think a 12 year old can? Aren’t we taught that “two wrongs don’t make a right?” Why is -3 times -5 equal to +15? Because it’s not an intuitive process, students are forced to memorize RULES, and they memorize them often incorrectly because they don’t understand them. For example, students learn that “two negatives make a positive” which is true for multiplication (neg times neg = pos) but not for addition/subtraction (neg + neg = neg)

3. Most teachers don’t really understand it themselves: Here in Ontario, students will encounter negative numbers in Gr. 7, middle school. Middle school teachers need almost no background in mathematics themselves. (If they do have a background, they TEND to go into high school teaching, not middle school. Not 100%, but most of the time.) So, these teachers rely on suspect methods THEMSELVES for teaching/answering these kinds of problems. But, not every child learns in the same way, and some of the “rules” that these teachers make up are either wildly inefficient (or wrong, as I’ve seen way too many times) and the children never have a fighting chance. Mathematicians and college educators are still arguing to this day about how to teach “negative numbers” and what they really mean… if the experts can’t agree, why are we relying on the “grasping at straws” techniques of middle school teachers?

4. Zero messes kids up. It sits in between the positives and negatives, and for some reason, kids want to ignore it on the number line.

That’s just a start…. good luck with your research!

Comment by Sarah Rainsberger on October 19, 2008 @ 5:09 pm
Leave a comment

(required)

(required)