I know that there are people who do not love their fellow man, and I hate people like that!
Tom Lehrer (1928 – )
This is the first in a planned ongoing series of posts where I try to figure out what problem(s) people have with math. Here’s the drill:
1. I search on the phrase “hate math”
2. I pick the top result (assuming it’s not this blog or one that I’ve picked before).
3. I present their argument and try (if I can) to answer it.
So today’s top link is an article from USA Today News from 07/09/12, written by Patrick Welsh (a high school teacher in Alexandria, VA) entitled “Column: Why Our Kids Hate Math”
Here is his primary argument:
“I worry that we’re pushing many kids to grasp math at higher levels before they are ready. When they struggle, they begin to dread math, and eventually we lose thousands of students who could be the scientists and engineers of tomorrow. If we held back and took more time to ground them in the basics, we could turn them on to math.”
Further down, he makes a second claim:
“In fact, for the majority of jobs, math is not included in the top five qualities that employers seek in their workers.”
I feel this second point requires a larger discussion, so I’ll take it up in a separate post. For now, let’s just address the initial claim that kids are being pushed into math too early. The basis of this argument is that eighth-graders can’t handle the abstraction of subjects like algebra. His colleague Sally Miller represents this view pretty eloquently in the same article:
‘Miller, like every math teacher I talked to, says schools are pushing too many middle-school kids into algebra. “Many of the concepts in algebra are abstract,” Miller says, “and if children are not developmentally ready to deal with abstraction, you can turn them off to math forever. Even the best students who can pull off A’s in eighth-grade algebra by just memorizing eventually end up realizing they did not really learn it.”’
I do agree that math requires abstract thinking but I have two issues with this statement. First, though I’m not a psychologist, Piaget’s work on cognitive development indicates that once they reach the age of twelve children are capable of grasping abstract concepts. Unless they’re starting children in school at a different age then when I was a kid, eighth-graders should be thirteen or fourteen. Now I’m not ignoring the differences between individual children but in theory they should be able to manage algebra by the eighth grade.
My second issue is that she points out the problem in her statement without realizing it. We introduce students to math by way of arithmetic. Granted, arithmetic is the foundational toolkit for mathematics but it’s also a topic that doesn’t play to our strengths as humans. Thus we have students memorizing multiplication tables and lists of rules, properties, theorems and lemmas just so they can get through the class. Arithmetic as currently presented is as intellectually stimulating as clerical work. (No offense to clerks who love their jobs.)
So it’s no surprise that, without having had any practice dealing with abstraction, students tackle algebra using the same tools that they developed for arithmetic — memorization, memorization, memorization. (And the answers to the odd numbered problems are in the back of the book, kids!)
Humans are pattern seekers. Millions of years of evolution have developed this ability in us to a high degree. The proto-hominid who couldn’t tell whether that flicker of light and shadow in the bushes was predator or prey (and figure it out pretty damn quickly) didn’t survive to breed. Mathematics is about deriving patterns from the universe around us so it fits beautifully with our native skill-set. Numbers are our palette and arithmetic gives us our brushes, knives and canvas.
Mathematics should be a delight but instead it’s this source of terror and doubt and the problem starts with the way we teach arithmetic.