The nature and development of middle school mathematics teachers’ knowledge

Abstract

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers' knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers' confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.

Explaining Student Achievement: the Influence of Teachers’ Pedagogical Content Knowledge in Statistics

“…For example, Author3 (2001) developed a profile instrument to measure teachers' knowledge on each of Shulman's dimensions in relation to the teaching of data and chance. This instrument was later broadened for the teaching of middle school mathematics more generally (Beswick, Author1, & Author3, 2011;Author3 et al, 2011).…”

Exploring the complexities of describing foundation phase teachers’ professional knowledge base

“…This is in line with the local work of Graven (2004) on teachers' learning in in-service courses, where she found confidence to be a key factor. Moreover, the issue of increased confidence in teaching mathematics aligns with the findings of research conducted by Beswick and colleagues in Australia (Beswick et al 2011). They explored not just teachers' knowledge of content and PCK, but also their personal confidence about their own numeracy knowledge and their teaching, as well as their beliefs about the use of materials.…”

“…To some extent, it is in the nature of a written questionnaire or test that it cannot generate a more in-depth understanding of teachers' knowledge, thinking, beliefs and practices, but we still felt that we could do better in capturing such issues. Therefore, we redesigned the test, and the new version of the instrument contains questions inspired by Beswick et al's (2011) instrument (which is not in the public sphere, but was kindly shared by Beswick) on confidence, personal numeracy in context and beliefs about teaching, all requiring the teachers to indicate agreement/ disagreement on a continuous scale. We retained some of the questions from the original test that aimed to interrogate teachers' PCK, and added extra ones to reflect the consideration of explaining and exemplifying.…”

“…A different challenge comes from the work of Beswick and colleagues, who also developed an instrument for large-scale studies of teachers' mathematical knowledge for teaching (Beswick, Callingham & Watson 2011). Their instrument was an extension of the LMT one, as they included teachers' confidence and beliefs.…”

“…The questions served to indicate how comfortable the teachers were with numeracy and literacy, and were selected and adapted from Beswick's instrument (Beswick et al 2011).…”