kitchen table math, the sequel: cart, horse

Friday, September 3, 2010

cart, horse

from Casting Out Nines:
[I]t’s not clear to me that doing “algebra” is a better idea here than just doing straight-up subtraction.  What’s to be gained by saying “the whole is 8; one part is 3; the other part is ____” versus “What is 8 minus 3?” Again, maybe I’m out of touch, but subtraction is a fundamental skill that algebra builds upon; doing algebra before subtraction seems a little backwards to say the least. A kid who is comfortable with subtraction will be able to do these whole/part problems in a snap by using subtraction. A kid doing these “algebra” problems basically has to invent subtraction in order to do them, or else draw pictures of balloons and start counting. It feels like the curriculum is trying to be intentionally nontraditional here, just for the sake of doing things differently rather than because it works better.


SteveH said...

Everyday Math goes out of its way to be nontraditional. That's a selling point. They claim all sorts of pedagogical reasons, but its all about telling K-6 teachers and administrators what they want to hear.

One of my son's early teachers would show, say, 8 marbles to kids and ask them how many she had. Then she would split them into two hands and ask how many she had in each hand. Next, she would change the number of marbles in each hand and ask again. I don't see anything wrong with this. What is wrong is what comes next. Not much. They think that math is all about some sort conceptual understanding. Why do you need to practice formal subtraction when the kids already understand the concept. Use a calculator.

This might be justifiable for simple things, but it falls apart when you get to advanced topics like fractions and rational experssions. "Drill and Kill". OK, but how do you learn a complex task or subject by avoiding practice. When kids get to pre-algebra and large homework sets that test all corners of their understanding, they fall apart. Schools don't understand that "drill" improves understanding. It's not just a speed issue that can be solved with a calculator. Learning requires hard work and hard work separates kids by ability or willingness to learn and they don't like separating kids. That's why they trust the spiral. It allows them to pretend that the problem doesn't exist.

bky said...

The answer to the question in the second sentence is this: you teach the student that subtraction is how you figure out "the other part" if you know one part. Singapore's number bond diagrams are very useful for making this intuitively clear. This is not algebra, so the calling it "algebra" is slightly pathetic on the part of the curriculum writers.

By the way, on the blog post referred to, the author talked about his daughter's difficulty with terminology, in particular what is meant by the "whole". I have never liked this, especially since I think of "whole" as being essentially an adjective. "Total" is a better word. "The total is 8; one part is 3. What is the other part?"