Expertise in Mathematics Instruction: Advancing Research and Practice from an International Perspective

Abstract

This chapter draws on data and findings from several video studies to describe the quality of mathematics teaching in Switzerland. The focus is on features of instructional practice and quality as core components of classroom behavior that reflect the teacher's expertise in creating optimal learning opportunities. The didactic triangle is used as the basis for describing the profile of expertise in Swiss mathematics instruction in terms of three interdependent dimensions of instructional quality. A core element of this pofile can be identified in Swiss mathematics teachers' particular strengths in the culture of communication, support and relationships. Findings also paint a generally positive picture of the culture of teaching, learning and understanding (e.g., methods and choreography of teaching) in Swiss mathematics classrooms. However, the culture of objectives, materials and tasks proves to be rather average in international comparison in several respects (level of mathematical content, characteristics of the problems set and the way they are worked on in lessons). In particular, there seems to be room for improvement in the specific context of the didactics of mathematics (e.g., the level of cognitive and mathematical challenge) Abstract This chapter draws on data and findings from several video studies to describe the quality of mathematics teaching in Switzerland. The focus is on features of instructional practice and quality as core components of classroom behavior that reflect the teacher's expertise in creating optimal learning opportunities. The didactic triangle is used as the basis for describing the profile of expertise in Swiss mathematics instruction in terms of three interdependent dimensions of instructional quality. A core element of this profile can be identified in Swiss mathematics teachers' particular strengths in the culture of communication, support and relationships. Findings also paint a generally positive picture of the culture of teaching, learning and understanding (e.g., methods and choreography of teaching) in Swiss mathematics classrooms. However, the culture of objectives, materials and tasks proves to be rather average in international comparison in several respects (level of mathematical content, characteristics of the problems set and the way they are worked on in lessons). In particular, there seems to be room for improvement in the specific context of the didactics of mathematics (e.g., the level of cognitive and mathematical challenge).

Developing a deeper understanding of mathematics teaching expertise: an examination of three Chinese mathematics teachers’ resource systems as windows into their work and expertise

“…More recently, possibly triggered by the success of Chinese Shanghai students in studies such as PISA and TIMSS (OECD, 2010), much attention has been given to studying mathematics teachers in mainland China and Shanghai (e.g., Li & Huang, 2008), and one of the particular areas of interest is the nature of their expertise in mathematics teaching (e.g., Ma, 1999). However, at a more general level there is insufficient knowledge of the nature of teacher expertise in mathematics education (e.g., Li & Kaiser, 2011), and hardly any relating such expertise to teachers' resources and how they work with these resources in their daily practice. We define teachers' resources as the curriculum/text, material and personal resources that teachers use and develop in their daily practice, in and for their teaching.…”

Improving teacher expertise through master teacher work stations: a case study

“…Although understanding the nature of mathematics teacher expertise remains a challenging question (Li & Kaiser, 2011), existing studies confirm that knowledge and its structure are key aspects of expertise, in general (Chi, 2011), and Chinese teachers' expertise in mathematics instruction, in particular (Li, Huang, & Yang, 2011). Thus, it is not surprising that Mr. Zheng's training has been effective in improving teachers' expertise.…”

“…Thus, we did not aim to explore all possible aspects of teacher expertise and relevant changes for those teacher participants when working with the master teacher's work station. Instead, by building upon existing studies on expertise in mathematics instruction (Li & Kaiser, 2011), we focused on those teacher participants' knowledge development in mathematics and pedagogy, and their performance in instructional design that combines the use of their knowledge in mathematics and pedagogy.…”

Chinese and American Elementary Mathematics Teachers’ Between Desk Instruction

“…Teachers are key factors to classroom instruction and have an important impact on student"s learning (Borko, 2016;Hiebert & Morris, 2012;Li & Kaiser, 2011;Sun & Hanna, 2013;Wagner, 2007). Ball, Lubienski, and Mewborn (2001) claimed that "What teachers and students are able to do together with mathematics in classrooms is at the heart of mathematics education" (p. 433).…”