When Memory Fails: Community College Developmental Math Students' Deference to Memory Over Meaning

• In Event: 75.031 - Deepening Our Understanding of Student Mathematics Knowledge in Community Colleges

Abstract

More and more students are attending community colleges and the majority of entering students place into “developmental” mathematics courses (e.g., Adelman, 1985; Bailey et al., 2010). Sadder still is that most of these students never complete the sequence, making developmental mathematics a primary barrier to completion of a post-secondary degree.

Students’ placement comes as the result of their poor performance on tests (e.g., Accuplacer, Compass, MDTP) that emphasize knowledge of procedures. They are designed to assess what students are able to do, but not what students understand about fundamental mathematical concepts. If these students are the product of American K-12 education, their poor performance comes in spite of having spent years in math classes that emphasized procedures (Stigler & Hiebert, 1999; Hiebert et al., 2003). For these students, what should have been appropriate preparation for the test was sorely inadequate.

Our aim was to gather information about what students actually understand about the mathematics that underlie the topics they've been taught, including their understanding of the reasons for using known procedures. We also sought, specifically, evidence that students used reasoning in answering mathematical questions. If students had some degree of conceptual understanding and were able to draw on it, it would suggest an alternative instructional approach with potential to help this group.

We conducted interviews with thirty students (15 female, 15 male) enrolled in developmental mathematics courses at a community college in the greater Los Angeles area. Students ranged in age from 17 to 51 (M = 21.6, SD = 6.5). Eleven were Hispanic, nine were white, four were African-American, and six were of mixed ethnicity. For ten students, English was not the primary language spoken at home. Interviews ranged in length from 54 to 128 minutes (M = 75.6, SD = 14.2). The interview assessed students’ understanding of key math concepts, from arithmetic through pre-algebra. For each line of questioning we anticipated possible responses and created structured follow-ups. Each of the mathematical questions concluded with prompts that pressed for reasoning.

The interviews confirmed students' inclination to approach problems procedurally. They did so even when we deliberately asked questions for which executing a procedure was not necessary. And, they reported that doing math was about executing procedures. However, we found also that it was often possible to coax students into reasoning. Furthermore, students often arrived at correct solutions through reasoning when they were unable to do so through procedures.

The goal of much of developmental math education appears to be to get students to try harder to remember the rules, procedures, and notations they’ve repeatedly been taught. Given high failure rates in developmental math classes, this approach does not seem to be working. Our interviews suggest that these students might experience success if we reawaken their disposition to figure things out and re-socialize them to believe that this is a critical element of what it means to do mathematics.

Authors

• Karen B. Givvin, University of California - Los Angeles

• Belinda Thompson, University of California - Los Angeles