Using errors in math instruction
Many teachers are reluctant to use errors in teaching math because they're concerned that students will duplicate the errors rather than learn from them, says a recent study in The Journal of Educational Research.
But an Israeli study of 115 9th-grade boys and girls found that students who diagnosed errors as part of math learning performed better in a 9-item assessment of misconceptions and misinterpretations of graph representations and linear functions than controls and students using other metacognitive approaches. The students attended 4 math classes at a junior high in Israel.
"On the basis of the present findings and other research conclusions, we call for a metacognitive culture, in which making errors is acceptable and students are encouraged to (a) self-question and analyze errors, (b) make corrections, and (c) formulate an action plan on how they have learned and understood the material and how they will remember this information," the authors write.
The study also looked at another metacognitive approach to math learning, improvement via self-questioning. In this approach, students regulate learning by using self-questioning to understand the problem, make connections between previous knowledge and new knowledge and using appropriate strategies for solving the problem.
Students using self-questioning outperformed students using diagnosis of errors (DIA) in problem-solving skills and metacognitive strategy use, the researchers report. Students who used a combination of skills did even better when compared to controls and students using either approach alone.
"The present findings extend to other research studies that have indicated metacognition is teachable and that students who are exposed to multilevel metacognitive approaches may be able to use metacognitive processes more often than students exposed to single metacognitive approaches," the researchers write.
"Using Errors as Springboards for Enhancing Mathematical Reasoning With Three Metacognitive Approaches," by Bracha Kramarski and Sarit Zoldan, The Journal of Educational Research, November/December 2008, pp 137-151.
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