Should math be applied?
By Murray Bourne, 01 May 2008
In a recent New York Times article, Study Suggests Math Teachers Scrap Balls and Slices, Kenneth Chang says:
...many educators in recent years have incorporated more and more examples from the real world to teach abstract concepts. The idea is that making math more relevant makes it easier to learn.
He goes on to report that researchers at Ohio State University have conducted research that purport to refute that claim:
An experiment by the researchers suggests that it might be better to let the apples, oranges and locomotives stay in the real world and, in the classroom, to focus on abstract equations.
Better? Better for whom? In what sense better? For the learning of algebra only? And what good is that for most of the population?
Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State is quoted as saying:
“The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning. It was really just that, a belief.”
Chang then writes that the researchers "performed a randomized, controlled experiment" which he says is "relatively rare in education research". Really?
I started to lose it with this article when I got to the next bit:
Though the experiment tested college students, the researchers suggested that their findings might also be true for math education in elementary through high school.
There is a big difference between the abstraction skills of college students and those of elementary students. Haven’t these people heard of Piaget's developmental levels? (The final sentence from that resource says "Abstract reasoning is simply not universal." Indeed, many adults do not even reach Piaget's formal operations stage. Most elementary students are at concrete operations stage. Get that - concrete operations.)
Back to this questionable experiment:
In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container.
Those who learned it abstractly did better than those who had experience with the concrete examples.
There could be so many other things going on here. If an elementary teacher just gets students to play with blocks, the students are unlikely to progress very far mathematically. If there is a proper design to the lesson and the students are given opportunities to make the appropriate connections, then there is a better chance that abstract thought could be triggered.
In the experiment, it is quite possible the students randomly combined liquids with no notion of why. No wonder they had trouble learning anything from it.
Another key consideration that is missing in this research is that the human brain will only remember things that have meaning and emotional significance. The whole idea of including "real life examples" is so that students will connect those experiences with the algebra (or process, or graph, or whatever) that is currently being studied.
In fact, one of the main reasons that the majority of the population (well, it always seems like the majority) don't like math and believe that it has no use in the real world is precisely because they have never seen how it is used in the real world.
Enough from me on this awful article. Go have a read and tell me what you think.
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