An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey

Reyhan Tekin-Sitrava

doi:10.12973/eu-jer.7.3.513

Abstract

<p style="text-align:justify">The aim of this qualitative case study is to investigate prospective mathematics teachers’ subject matter knowledge of the underlying concepts of standard and nonstandard algorithms used to solve the problems with whole numbers. Twenty three prospective mathematics teachers enrolled in the Elementary Mathematics Education Program of one of the most successful universities in Turkey were the participants of the study. The data was collected through four tasks containing basic algorithms. More specifically, the Ones Task assessed participants’ understanding of the underlying place value concepts of standard algorithms. The Andrew Task and the Doubling Task required participants to conceptualize and interpret nonstandard strategies. In the Division Task, participants were expected to provide in-depth explanation for the difference between multiplication and division and between partitive division and measurement division. The content analysis method was used to analyze the data. The results of the study revealed that more than half of the prospective mathematics teachers had knowledge about the place value of 1 in addition and subtraction, and also multiplication. However, most of the prospective teachers could not explain the underlying principle and the meaning of the nonstandard algorithm in subtraction. Similar to their knowledge on subtraction, prospective teachers’ knowledge on division was limited.</p>

Highlights

In the last few years, there has been an increasing interest in knowledge needed for effective teachi ng
Shulman (1986), one of the pioneers of teachers’ knowledge, i dentified pedagogical content knowl edge (PCK), curricul ar knowledg e (CK) and subject matter knowledge (SM K) as knowledge needed for effective teaching
The purpose of this study was to inves tigate pre-s ervice mathematics teachers’ subject matter knowledge of the underlying concepts of standard and non-s tandard al gorithms used to solve the problems with whole numbers

Summary

Introduction

In the last few years, there has been an increasing interest in knowledge needed for effective teachi ng. Many researchers hav e focus ed on inv estigating the answer to one of the constantly evolving ques tions related to knowledge needed for effective teaching. The central focus of these ques tions is related to the knowl edge needed about a subject which is to be taught and the way of teaching it (Grossman, 1990; Ma, 1999). Shulman (1986), one of the pioneers of teachers’ knowledge, i dentified pedagogical content knowl edge (PCK), curricul ar knowledg e (CK) and subject matter knowledge (SM K) as knowledge needed for effective teaching. Shulman emphasized the importance of SMK by stati ng that “The teacher need und ers tand that something is so; the teacher must further understand why it is so” (p.9)

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Conclusion