
RE: Teaching Dev Mathematics Conceptually: practical ideas
Posted:
Feb 20, 2009 12:15 PM



George wrote something that caught my eye; that is, "Some we agree on: right is positive, left is negative on a number line." In the last year and a half, I am having more and more students who do not understand that on a graph the numbers increase in size from left to right. And I'm speaking of students who've had either college algebra or intermediate algebra before this statistics class.
Any thoughts on how so many students are missing such a fundamental idea?
________________________________ From: ownermathedcc@mathforum.org [mailto:ownermathedcc@mathforum.org] On Behalf Of George Alexander Sent: Friday, February 20, 2009 9:38 AM To: Alain Schremmer Cc: mathedcc@mathforum.org Subject: Re: Teaching Dev Mathematics Conceptually: practical ideas
Why is it necessary that we teach and learn mathematics in the same order that concepts were developed historically? Why can't we start with integers as our base number system and build consistent and meaningful ways to add, subtract and multiply integers? I don't see why we need to continue giving the natural numbers such a special place in the mathematical universe.
It seems to me that if our students are entering with some understanding of integers, then we should build on that knowledge rather than moving backwards to a world with no negatives first. Everyone has experience with both positive and negative numbers by adulthood (commonly through the checkbook). I would prefer to meet my students on some common ground and build concepts from there. I see no need to reconstruct basic math from it's chronological human history, which is more an accident of discovery than necessity.
So every number has a sign, positive or negative. This sign label is a matter of perspective. Some we agree on: right is positive, left is negative on a number line. Or temperatures are positive above 0 degrees and negative below 0 degrees. But the banker's positive (interest payment on a loan) is my negative.
For calculation strings, we simply have a list of signed numbers to combine. Any + or  sign applies to the value to its right. No sign is assumed to mean positive. We combine terms here. Adding and subtracting operations are only a means to balancing the checkbook.
6  10 + 8  15 means we combine positive numbers 6 and 8 with negative numbers 10 and 15. The balance is 11.
Any other operations (including groupings, exponents, multiplication, etc in the order of operations) need to be simplified before combining any terms.
 George Alexander Mathematics Instructor Madison Area Technical College 3550 Anderson St Madison, WI 53704 6082466187 On Thu, Feb 19, 2009 at 9:54 AM, Alain Schremmer <schremmer.alain@gmail.com<mailto:schremmer.alain@gmail.com>> wrote:
On Feb 18, 2009, at 8:14 PM, Jonathan Groves wrote: At one point, according to what I've seen there was a movement to try to use different symbols to mean "the opposite" and "minus." It didn't catch on, obviously. In one case, the opposite was higher on the line and smaller than the minus. I cannot reproduce it on the keyboard.
I had checked with Wikipedia's article "Plus and Minus Signs," and the article says the programming language APL still uses small, raised hypens as negative signs. I remember seeing these in some textbooks a while back; my sixth grade math book was the first book I remember seeing negative numbers in, and the book used these special negative signs. I still use them sometimes in handwritten work but only when I subtract a negative or add a negative so that I don't have to use parentheses.
Absolutely! Unfortunately it works only if one's handwriting is neat and mine is far from neat. But I do write 5  7 without, seemingly any mishap.
Regards schremmer
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