What Community College Developmental Mathematics Students Understand about Mathematics, Part 2: The Interviews

In a prior issue of "MathAMATYC Educator," we reported on our efforts to find out what community college developmental mathematics students understand about mathematics (Stigler, Givvin, & Thompson, 2010). Our work painted a distressing picture of students' mathematical knowledge. No matter what kind of mathematical question we asked, students tended to respond with computational procedures, which they often applied inappropriately and incorrectly. Their knowledge of mathematical concepts appeared to be fragile, and weakly connected to their knowledge of procedures. But we also found some reason for hope. First, we found that when students were able to provide conceptual explanations for procedures, they often produced correct answers. Second, though students rarely used reasoning on their own to solve problems, they could reason under the right conditions. (Contains 2 figures.) [For Part 1, see EJ890224.]