
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 25, 2013 12:57 PM



On Nov 25, 2013, at 12:07 PM, Wayne Bishop <wbishop@exchange.calstatela.edu> wrote:
> I got kind of behind on my email including this thread but Pam is right here, Bob. This approach, combined with competent arithmetic through ordinary fractions of course, is the best algebra readiness I've ever seen. As I mentioned, if it's been done well, by the more complicated problems of 6th grade, it's really time to drop it in deference to symbolic algebra but it IS a general approach with everything in place for genuine "algebraic thinking" as opposed to the nonsense that gets advertised as such (mathematically insupportable pattern recognition, for example).
Well, then all those top schools are wrong and math is just a gimmick done with pictures and crayons.
And by the way, what exactly is the "approach" you are are speaking to? There were two...
Mine  Use bar diagrams to develop the student's ability to see the *expression* in a word problem. Note, nowhere do I say symbolic. In fact, like you, I do not support algebra at this point unless the students have generalized (gotten quite good at) extracting the expression (the math) out of word problems.
Pam's  Use bar diagrams with coloring and gimmicks to make kids (and their parents) think they good at math.
Let me try to explain it another way. You are familiar with logic puzzles where you are given a list of people and a set of clues that establish relationships between these people. I believe they are called logic grid puzzles. They can be solved in two ways, by deduction or by making a grid and checking off boxes.
Which "approach" would you prefer?
I did not have an issue with bar diagrams, I had an issue with using them as a gimmick that doesn't support the teaching of mathematics, the goal of which is to progressively build the level of sophistication in one's thinking. In math in particular, but in many other things in general.
We at least agree that they should be dropped at some point, because isn't that the point of using manipulatives, to not use them? But you can't drop them if you use them as a gimmick like Pam did. What is the student to do? All of a sudden figure out that there is an expression in the word problem?
Bob Hansen

