How Preservice Teachers Interpret and Respond to Student Geometric Errors

Abstract

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a majority of preservice teachers identified the student's errors from conceptual aspects of reflection rather than from procedural aspects. However, when they responded to the student's errors, preservice teachers tried to cope with them by invoking procedural knowledge. This study also revealed the three types of responses and two different forms of address by preservice teachers to student errors; these categories might provide insight into the difficulties arising in communication between students and teachers.

Explanations of prospective middle school mathematics teachers for potential misconceptions on the concept of symmetry

“…This is similar to the findings of the studies by Son & Sinclair (2010), Baki & Kartal (2004). Another important finding of the study indicated that the participants did not use mathematical terminology and jargon in identifying the mistakes of the student.…”

Preservice teachers’ response and feedback type to correct and incorrect student-invented strategies for subtracting whole numbers

“…While some studies reported a strong intersection between teachers' content knowledge (CK) and their ability to evaluate and respond to children's mathematical work (Baumert et al, 2010), others showed that strong CK does not necessarily lead to the development of PSTs' ability to analyze students' strategies (Son & Sinclaire, 2010;Bartell, Webel, Bowen, & Dyson, 2013;Peterson & Leatham, 2010). For example, Bartell et al (2013), in examining the role CK plays in PSTs' ability to recognize children's responses (i.e., specialized content knowledge), reported that CK is not sufficient for supporting PSTs' analyses of children's thinking.…”

Students’ conceptions of reflection: Opportunities for making connections with perpendicular bisector

“…Son and Sinclair (2010) conducted interviews with a group of pre-service teachers (PSTs) to examine how they would evaluate and respond to a student's error on a problem of reflecting a flag across a diagonal line. Over half of the PSTs in the study evaluated the student's work according to the properties of reflection in relation to the perpendicular bisector.…”