Enhancing Mathematics Teachers’ Knowledge of Students’ Thinking From Assessing and Analyzing Misconceptions in Homework

Abstract

This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth-eighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of students' thinking. By engaging in the inquiry process of the 4 steps of identifying errors, analyzing reasons for the errors, designing approaches for correction, and taking action for correction, the teachers made obvious progress in their knowledge of students' thinking, understood the difficulties and challenges their students had in learning mathematics, and enhanced their pedagogical content knowledge.

A Study on Sixth Grade Students’ Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume

“…Another reason related to the chain of errors on spatial measurement might be due to ineffective monitoring and assessment process of student learning. An & Wu's (2012) study revealed that analyzing errors in homework improves teachers' understanding of students' thinking as well as the strengths and weaknesses of instruction. In this respect, paying explicit attention to monitor students' learning process and to analyze how and why they make errors can help to overcome the construction of the error chain in spatial measurement.…”

A Qualitative Study on the Development of Pre-service Teachers’ Mathematical Knowledge for Teaching in a History-based Course

“…Many studies have posited the importance of profound mathematical content knowledge in mathematics teachers' knowledge. (An & Wu, 2012). Before the 1970s, it was believed that the more a teacher knew about his subject matter (SMK), the more effective he would be as a teacher (Begle, 1979).…”

Developing Pre-Service Teachers’ Noticing of Students’ Understanding of the Derivative Concept

“…The teachers' decisions are based on how the teacher notices the students' understanding. In this context, designing approaches based on error identification, analysing the reasons why these errors occur and designing approaches to correct and implement them helps teachers to understand the difficulties and challenges faced by their students (An & Wu, 2012;Biza, Nardi & Zhachariades, 2007).…”

“…In this context, we have seen an emphasis on the need for teachers to base their teaching decisions on their students' learning characteristics of mathematical content (Franke & Kazemi, 2001). This has raised a number of questions about the way in which teachers notice the signs of students' understanding (An & Wu, 2012;Fernandez, Llinares & Valls, 2012;Magiera, van den Kieboom & Moyer, 2013) and about the development of this skill (Bartell, Webel, Bowen & Dyson, 2013;Fernández, Llinares & Valls, 2013;Wilson, Mojica & Confrey, 2013;Spitzer, Phelps, Beyers, Johnson & Sieminski, 2011). These research studies support the idea that teachers must know how students understand mathematical topics in order to make appropriate teaching decisions.…”