Unpacking Mathematics Pedagogical Content Knowledge for Elementary Number Theory: The Case of Arithmetic Word Problems

Wing Yee Lo

doi:10.3390/math8101750

Abstract

“Number” is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader’s mathematical misconception, but most of them were unable to precisely indicate the third grader’s error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers’ MPCK in teaching arithmetic word problems.

Highlights

The core of primary mathematics is the understanding of number concepts and operations.Problem solving and daily life applications as part of mathematics teaching and learning in primary schools are highlighted in reform mathematics curricula across countries [1]
Primary students in Hong Kong can struggle with mathematics word problems even if they maintain an outstanding performance in Trends in InternationalMathematics and Science Study (TIMSS) [5,6]
Question 1a shown in Table 1 aimed to determine the extent of pre-service teachers’ mathematics pedagogical content knowledge (MPCK) in teaching a class of third graders

Summary

Introduction

The core of primary mathematics is the understanding of number concepts and operations. Problem solving and daily life applications as part of mathematics teaching and learning in primary schools are highlighted in reform mathematics curricula across countries [1]. In reviewing the research literature on initial teacher preparation, there has been a longstanding interest in pre-service primary teachers’ knowledge of elementary number theory [3,4]. Far too little attention has been paid to their pedagogical knowledge for teaching arithmetic word problems primary students always demonstrated difficulty in solving multi-step word problems involving whole numbers in international assessments, for example, the Trends in International. Primary students in Hong Kong can struggle with mathematics word problems even if they maintain an outstanding performance in TIMSS [5,6]

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