Knowing about not knowing: A cognitive view of mathematics anxiety.

摘要

In order to close the gap that exists between the research areas of mathematics anxiety and mathematics learning, this study examined cognitive, metacognitive, and affective aspects of mathematics anxiety as well as students' mathematics performance and competence. One hundred and five grade 9 students, 51 males and 54 females, from two high schools in the same school board provided data on current and past final grades and anxiety measures, both general and specific to mathematics anxiety. A subset of 40 students was selected based on either high or low mathematics anxiety, and verbal protocols were collected while they solved six mathematical problems. Students ranked themselves and teachers ranked their students on how confident they felt about solving each problem. Two sets of marks were assigned to students' performance, one based on their written work only and the other one also taking into account knowledge evidenced from their verbalizations. As predicted, the more mathematics-anxious students showed greater awareness of their mathematical knowledge or the lack thereof, making significantly more coded statements for four out of the six variables that implied greater awareness. High-anxious students were less likely to consider continuing their mathematical education. Teachers overestimated their students' performance, while students underestimated their knowledge level, but more closely estimated the mark they would receive on a test regardless of anxiety level. Given that mathematics-anxious students seem aware of their lack of knowledge, any treatment of mathematics anxiety needs to include teaching not only mathematical knowledge, but also skills such as monitoring and reflecting about application of such knowledge to the solution process.