Are teachers aware of students' lack of spontaneity in diagram use? Suggestions from a mathematical model-based analysis of teachers' predictions

Abstract

Although many studies have shown that diagrams are effective tools for problem solving, research evidence shows that students do not always use diagrams effectively. One of the most serious problems is their lack of spontaneity in diagram use. However, no previous studies have examined whether teachers are adequately aware of this problem. In this investigation, data were gathered on students' mathematics performance (including their spontaneous use of diagrams) and teachers' predictions of the students' performance. Using a mathematical model (Uesaka & Nakagawa, 2010) to analyze the data, it was found that the parameter representing the accuracy of teachers' prediction was lower for their assessment of spontaneous diagram use compared to other mathematical tasks. This suggests that spontaneity in diagram use is an overlooked aspect in teachers' view of student performance. © 2012 Springer-Verlag.