Developing mathematics teachers’ pedagogical content knowledge in lesson study

Abstract

Purpose: This study investigates the development of mathematics teachers' pedagogical content knowledge (PCK) over successive cycles of lesson study. Utilising the framework of Mathematical Knowledge for Teaching (MKT) (Ball, Thames and Phelps, 2008), this research classifies features of PCK as utilised by post-primary mathematics teachers in their planning and reflection conversations in lesson study. The development of these features of PCK is then traced over successive cycles.Design/methodology/approach: Twelve teachers in two Irish post-primary schools participated in this research. Over the course of one academic year, these two groups of teachers completed a number of cycles of lesson study and qualitative data was generated through audio recordings of all lesson study meetings and through individual interviews with participants. Findings: Analysis of teacher dialogue reveals distinct features of Knowledge of Content and Students (KCS) and Knowledge of Content and Teaching (KCT)incorporated by these teachers in their planning and reflection conversations, providing empirical evidence of MKT in lesson study. The occurrence of these features of KCS and KCT in lesson study conversations increased over successive cycles, demonstrating teacher learning.Originality: This research contributes to the literature in expanding the theoretical underpinnings of teacher learning in lesson study. It also provides further empirical evidence of Mathematical Knowledge for Teaching in teacher practice, specifically related to post-primary mathematics teachers.

Improving teaching, developing teachers and teacher educators, and linking theory and practice through lesson study in mathematics: an international perspective

“…With the evidence from various data resources including teacher interviews and teachers' collaborative talk, researchers documented teachers' changes in their mathematics knowledge and skills (e.g., Björk and Pettersson 2015;Dudley 2013;Fernandez 2005;Hunter and Back 2011;Lewis and Perry 2014;Moss et al 2015;Shu and Seshaiyer 2015), pedagogical knowledge (e.g., Cajkler et al 2014;Han and Paine 2010;Lewis et al 2009;, understanding of student learning (e.g., Bocala 2015; Lewis et al 2009;Murata et al 2012), and pedagogical content knowledge (e.g., Dudley 2013; Lewis et al 2009;Shuilleabhain 2015). For example, Moss et al (2015) adopted a Japanese LS enriched by a design experiment to explore the ways of teaching and learning geometry and reasoning in early classrooms.…”

An Investigation into the Preparedness of Teachers to Teach Grade 12 Mathematics: A Case Study

“…A number of studies (Stacey 1988;Vinner 1991;Kieran 1992;Esty 1992;Sfard and Linchevski 1994;Bell 1995;Linchevski and Herscovics 1996;Souviney 1996;Dreyfus 1999;Lithner 2000;Mason 2000;Pyke 2003;Maharaj 2005Maharaj , 2008Brijlall and Maharaj 2014;Shuilleabhain 2015)) have focused on the teaching and learning of school mathematics. Those studies indicated important insights with regard to sources of students' difficulties in mathematics.…”

“…In the case of disposition that he/she has towards mathematics and pedagogy (Mason 2000;Maharaj 2008). (f) It is important for mathematics' teachers to correctly identify students' prior knowledge (Shuilleabhain 2015). This helps teachers to anticipate students' responses and to plan a relevant sequence of learning for their students.…”

“…In terms of APOS, for the concept of the derivative, the mental constructions of those teachers were not adequately developed at the object and schema levels. It could be argued that such teachers who do not have a deep understanding of a concept will be unable to plan and implement sequential lessons (Shuilleabhain 2015) that would lead their learners to a deep understanding of the relevant concept. With regard to the literature review the "style and the nature of questions encountered by students strongly influences the sense that they make of the subject matter" (Mason 2000: 97).…”

Challenging teachers’ ideas about what students need to learn

“…For example, some conclude that social, cultural, and historical perspectives (Skott Krog and Møller, 2017) and feedback derived from theoretical assumptions (Huang and Han, 2015) affect learning in such collaborations. Shuilleabhain (2016) finds that teachers' experiences and their empirical observations and evaluations of research lessons affect teachers' learning. Wood et al (2017) suggest that the key factors are the following: relating varying teaching designs to students' responses, sharing teaching experiences with group members, and overcoming constraints of the syllabus and assessment.…”