Plain and Simple: They're Wrong
Darren Kuropatwa,
A Difference,
Apr 30, 2008
OK, while I am sympathetic with Darren Kuropatwa's point, I want to say that the teaching of mathematics is complex and that (therefore) no plain and simple argument is correct. So I would certainly disagree with this study, which says that concrete examples don't help students learn math. Because, as Kuropatwa says, applying math is a matter of pattern recognition, and this needs to be practiced to be learned. But, at the same time, students need to be able to understand formulae without concrete examples. They need to be able to think abstractly. Which in math, at least, means flinging some Xs and Ys around, even if it means blank stares for a bit. Finally, I want to note the irony of a person touting a single 80-person study as evidence for what does or does not work in a math curriculum. Such baseless claims do a disservice to our field in general, and should not be represented in the popular press as 'research'.
Just for the record, there are three major types of inference (not two):
- induction - consisting of an inference from a set or sequence of concrete instances to a generalization about such types of instances;
- deducation - consisting of an inference from a general statement about types of instances, to the nature of a particular instance in that series or set; and
- abduction - also known as 'inference to the best explanation', an inference from a current particular instance to a combination of a generalization and set of particular instances (for example: Robinson Crusoe sees a set of footprints in the sand and concludes, "There's somebody else on the island.")
Just for the record, there are three major types of inference (not two):
- induction - consisting of an inference from a set or sequence of concrete instances to a generalization about such types of instances;
- deducation - consisting of an inference from a general statement about types of instances, to the nature of a particular instance in that series or set; and
- abduction - also known as 'inference to the best explanation', an inference from a current particular instance to a combination of a generalization and set of particular instances (for example: Robinson Crusoe sees a set of footprints in the sand and concludes, "There's somebody else on the island.")
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