What Community College Developmental Mathematics Students Understand about Mathematics
Carnegie Senior Partner Jim Stigler and colleagues Karen B. Givvin and Belinda J. Thompson from the University of California, Los Angeles were commissioned by Carnegie to investigate what community college developmental mathematics students understand about mathematics and how we might help turn around the alarming statistics that show that an enormous number of those students drop out of college because they aren’t successful in math courses. "An assumption we make in this report is that substantive improvements in mathematics learning will not occur unless we can succeed in transforming the way mathematics is taught," the authors write. "In particular, we are interested in exploring the hypothesis that these students who have failed to learn mathematics in a deep and lasting way up to this point might be able to do so if we can convince them, first, that mathematics makes sense, and then provide them with the tools and opportunities to think and reason."
Because the research literature did not cover what mathematical knowledge students have, James Stigler undertook fieldwork to learn more about students’ understanding of basic mathematics, and student perceptions of what they believe it means to do mathematics. This essay, by James W. Stigler, Karen B. Givvin, and Belinda J. Thompson, was published in MathAMATYC Educator, Vol. 1, No. 3. May 2010.
This is an excellent resource that is well written and extremely relevant to adult education mathematics teachers as there is little quality research on adults' understanding of mathematics. The analysis of student errors provided in the resource is very informative and an important indicator of student knowledge. Common student errors described are in the domains of fractions, decimals, percent, or beginning algebra, the same topics that are the focus of most math instruction in ABE or GED classes. By raising adult education math teachers' awareness of these common errors, misconceptions, and misunderstood and misused procedures, they will more likely recognize and address these problems with their learners. Included in the resource are examples that teachers might use as formative assessment items to better understand their learners' reasoning, misconceptions, or gaps in conceptual understanding. This resource could be used as the basis for adult numeracy professional development, whether as part of a presentation, a workshop, or a study circle. Since the majority of instruction that currently takes place in an ABE/GED classroom is one of procedures, this study might serve as a path towards true instructional changes in a program which has not yet begun looking for ways of improving their mathematical instruction.
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