William Atkins
Friday, 25 April 2008 21:13
Science -
Health
Page 1 of 3
Researchers from Ohio State University find that when students learn math with concrete examples (story problems) it is difficult for them to apply it to other real-world situations. They suggest first using abstract symbols (such as x, y, and z) to learn and understand math concepts.
The article “
The Advantage of Abstract Examples in Learning Math” appears in the Friday, April 25, 2008 issue of the journal
Science (volume 320, number 5875, pages 454-455).
Lead author of the study is American research scientist Jennifer A. Kaminski (Center for Cognitive Science at Ohio State University. She is joined in the study by Vladimir M. Sloutsky (Center for Cognitive Science) and Andrew F. Heckler (Department of Physics), all associated with the Ohio State University in Columbus, Ohio, U.S.A.
Kaminski stated,
“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.” [New York Times: “
Study Suggests Math Teachers Scrap Balls and Slices"]
Specifically, the Kaminski team performed a randomized, controlled experiment involving four separate examples on U.S. undergraduate students to test their hypothesis. Each example involved simple mathematical concepts that were applied under different conditions.
The math concepts involved such properties as associativity (the order of the operations (such as with parentheses) does not change the result as long as the sequence of the operands (such as “+”) is not changed: (a + b) + c = a + (b + c) = d, or specifically: (4 + 5) + 2 = 4 + (5 + 2) = 11).
In each example, the students learned math principles with generic symbols (a, b, c, etc.) while others were taught using concrete examples (blue train, green airplane, and yellow car).
For instance, students taught with concrete examples were asked about number of slices, tennis balls, measuring cups, and other such real-life objects.
However, other students were taught the same math principles but were taught solely with abstract symbols.
After learning a particular math concept, the students were given a multiple-choice test to show whether they mastered the principle or not. The researchers found that, generally, the students learned the math concept well using either the abstract method or the concrete method.
However, later the researchers re-tested the students using a different concrete example. This example was told to them as a children’s game from another country.
Please read the second page for results of the four examples.
