Teacher Knowledge and Learning In-situ - Issue 3 - Abstract and key findings on Grade 4 long division

Oct 15, 2026

The study explores and enhances experienced school mathematics teachers’ knowledge of students’ thinking as it manifests in practice. Data were collected through classroom observation records, teacher interviews, and weekly teacher-researcher meetings in the school. The paper examines mathematical challenges for a primary teacher unpacking the division algorithm in a Grade 4 setting. The findings illustrate how focusing on in-situ mathematical knowledge can shift teachers’ well-formed beliefs and support broader understanding of teaching demands during educational reform.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages21

Reading Time53 min

AccessFree to download

Abstract

Introduction

Specialized teacher knowledge and its critiques

Implications for professional development design

Case study focus and reported change

Australian Journal of Teacher Education | Volume 43 | Issue 3 | Article 1 | | --- | --- | | 2018
Teacher Knowledge and Learning In-situ: A Case Study of the Long Division Algorithm
Shikha Takker
Homi Bhabha Centre for Science Education, TIFR, India, [shikha4268@gmail.com](shikha4268@gmail.com)
K. Subramaniam
Homi Bhabha Centre for Science Education, TIFR, India, [subra@hbcse.tifr.res.in](subra@hbcse.tifr.res.in) | | Recommended Citation Takker, S., & Subramaniam, K. (2018). Teacher Knowledge and Learning In-situ: A Case Study of the Long Division Algorithm. Australian Journal of Teacher Education, 43 (3). Retrieved from [http://ro.ecu.edu.au/ajte/vol43/iss3/1](http://ro.ecu.edu.au/ajte/vol43/iss3/1) This Journal Article is posted at Research Online. [http://ro.ecu.edu.au/ajte/vol43/iss3/1](http://ro.ecu.edu.au/ajte/vol43/iss3/1) Australian Journal of Teacher Education Teacher Knowledge and Learning In-situ: A Case Study of the Long Division Algorithm Shikha Takker K. Subramaniam Homi Bhabha Centre for Science Education, TIFR, Mumbai, India Abstract: The aim of the study reported in this paper was to explore and enhance experienced school mathematics teachers’knowledge of students’thinking, as it is manifested in practice. Data were collected from records of classroom observations, interviews with participating teachers, and weekly teacher-researcher meetings organized in the school. In this paper, we discuss the mathematical challenges faced by a primary school teacher as she attempts to unpack the structure of the division algorithm, while teaching in a Grade 4 classroom. Through this case study, we exemplify how a focus on mathematical knowledge for teaching ‘in situ’helped in triggering a change in the teacher’s well-formed knowledge and beliefs about the teaching and learning of the division algorithm, and related students’ capabilities. We argue that in the context of educational reform, an analysis of knowledge demands placed on the teacher helps in understanding and supporting teachers’work. Key words: learning in situ, long division algorithm, mathematical knowledge for teaching, professional development, students’ mathematics, teacher challenges. Introduction The claim that teachers need specialized knowledge in order to teach school subjects effectively, has had a widespread influence on education research as well as on the design of interventions in teacher development (Edwards, Gilroy & Hartley, 2005) . Sustained efforts have been made by researchers to develop characterizations of specialized teacher knowledge that remain close to the actual work of teaching (Petrou & Goulding, 2011) . The design of teacher education curricula or professional development interventions is founded on a conception that individual teacher’s knowledge of mathematics teaching impacts their practice. Curricular reform efforts in India, as in the other countries across the world, have called for changes in teaching practice, which place new demands on teachers’knowledge required for teaching (NCTE, 2009; ARC, 1990; Tatoo et al., 2012) . There is a need to identify both the form and the content of teacher knowledge that is most likely to translate into changed classroom practice. Existing frameworks of teacher knowledge attempt to identify its components, especially those components that are missing from typical trajectories laid out by formal teacher preparation programmes (Ball, Thames & Phelps, 2008) . Teacher knowledge is characterized by focusing on the teacher and the knowledge that the teacher brings to the classroom. Such frameworks have been criticized for at least two reasons. First, the existing frameworks view teacher knowledge as static (Hodgen, 2011) . Hodgen argues,“teacher Vol 43, 3, March 2018 1 Australian Journal of Teacher Education knowledge is embedded in the practices of teaching and any attempt to describe this knowledge abstractly is

FAQs

What is the purpose of the study?

To explore and enhance experienced school mathematics teachers’ knowledge of students’ thinking as it is manifested in practice.

How is data collected for the case study?

Through records of classroom observations, interviews with participating teachers, and weekly teacher-researcher meetings organized in the school.

What classroom context does the paper analyze?

A Grade 4 classroom where a primary school teacher attempts to unpack the structure of the long division algorithm while teaching.

Oct 15, 2026

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