Teacher noticing of student thinking: an analysis of a teacher's interpretation of mathematics problem solving

• Author: A. Cavalcante/E. Polotskaia/A. Savard/O. Fellus
• Position: Paper presented at the International Conference 'Contemporary Perspectives in Psychology, Education and Social Work/McGill University, Canada/Université du Québec en Outaouais, Canada/McGill University, Canada/University of Ottawa, Canada
• Pages: 9-18

Bulletin of the Transilvania University of Braşo v

Series VII: Social Sciences • Law • Vol. 12(61) No. 1 – 2019

https://doi.org/10.31926/but.ssl.2019.12.61.1.1.

TEACHER NOTICING OF STUDENT THINKING:

AN ANALYSIS OF A TEACHER’S

INTERPRETATION OF MATHEMATICS

PROBLEM SOLVING1

A. CAVALCANTE2 E. POLOTSKAIA3

A. SAVARD4 O. FELLUS5

Abstract: One area of particular difficulty in mathematics learning is the

transition from arithmetic to algebra. In this paper, we report on results

from a project whose goal was to produce mathematical tasks and

strategies to support the development of holistic relational thinking in

problem solving among middle school students. Based on a teacher’s written

journals, we focus on her noticing of student work while solving problems

provided in our project. Our results show that the teacher would benefit

from paying closer attention to students who generally succeed in

mathematical problem solving, and from strengthening her ability to

interpret a wider range of possible representations, especially those that do

not conform to the representation usually used.

Keywords: teacher noticing, mathematics problem solving, relational

thinking, algebra.

1. Introduction

One area of particular difficulty in mathematics learning is the transition from

arithmetic to algebra. In elementary school, problems are solved using arithmetic, i.e.,

concrete numbers and operations on them; in secondary school, however, the y are

solved using algebra, i.e., equations, inequalities, functions, knowledge of structures and

relationships (Cai & Knuth, 2011; Kieran, 1989; Schmidt & Bednarz, 2002). Within the

arithmetic-algebra transition, problems become mathematically more complex.

Students, who have not developed more sophisticated arithmetic strategies and

1 Paper presented at the Internationa l Conference “Contemporary Perspecti ves in Psychology, Educatio n

and Social Work” – 3rd edition (COPES 2019), Constanța, 24-26 May 2019

2 McGill University, Canada. Contact: alexandre.cavalcante@mail.mcgill.ca

3 Université du Québec en Outaouais, C anada.

4 McGill University, Canada.

5 University of Ottawa, Canada.