Comments on: If your children have trouble with integers, they’re not alone! http://www.rainsberger.ca/blog/2007/11/26/if-your-children-have-trouble-with-integers-theyre-not-alone/ periodic downpours of information about Ontario Homeschool University Admissions Mon, 14 Nov 2011 22:25:15 +0000 hourly 1 http://wordpress.org/?v=3.2.1 By: Sarah Rainsberger http://www.rainsberger.ca/blog/2007/11/26/if-your-children-have-trouble-with-integers-theyre-not-alone/comment-page-1/#comment-11652 Sarah Rainsberger Sun, 19 Oct 2008 22:09:58 +0000 http://www.rainsberger.ca/blog/2007/11/26/if-your-children-have-trouble-with-integers-theyre-not-alone/#comment-11652 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! 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!

]]> By: julieta http://www.rainsberger.ca/blog/2007/11/26/if-your-children-have-trouble-with-integers-theyre-not-alone/comment-page-1/#comment-11650 julieta Sun, 19 Oct 2008 21:41:09 +0000 http://www.rainsberger.ca/blog/2007/11/26/if-your-children-have-trouble-with-integers-theyre-not-alone/#comment-11650 What is so hard about integers!!!!!!!!!!!! I need help for my project!!!!!!!!!! on misconceptions with integers!!!!!!!!!!!! What is so hard about integers!!!!!!!!!!!! I need help for my project!!!!!!!!!! on misconceptions with integers!!!!!!!!!!!!

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