The Effect of the Use of Calculators to Teach Below Average Students

Abstract

This article focuses on three key factors that a survey of literature indicated impact the teaching and learning of mathematics with calculators: access to calculators, the place of calculators in the mathematics curriculum, and the connection between calculators and pedagogical practice. Access to calculators is associated with student achievement gains and a wide array of problem-solving approaches. The research suggests students' achievement is positively affected when they use curricula designed with calculators as a primary tool. Studies of teachers' use and privileging of calculators illustrate the impact professionals have on students' mathematical knowledge and calculator expertise. Implications of these research findings for pre-service and in-service teacher education are summarized.

Calculators were first introduced in 1985 and within a few years mathematics educators began to study the role and impact of this tool on the teaching and learning enterprise. The field has amassed a significant body of research on students' performance and learning with calculators and a small, now growing, body of research on teachers' use and knowledge of calculators. An analysis of research studies published in peer-reviewed journals over the past 2 decades suggested a framework for summarizing the findings and implications of this research. Three themes emerged that cut across the existing literature: access to calculators, the place of calculators in mathematics curricula, and the connection between calculators and pedagogical practice.

This article addresses what this literature suggests about teaching and learning mathematics with calculators, as well as the implications of these research findings for pre-service and in-service teacher education.

Table of Contents

Chapter 1: Introduction5

Background5

Problem Statement8

Chapter 2: Literature Review10

Chapter 3: Methodology21

Chapter 4: Discussion and Analysis27

The methods30

Quickness and other benefits35

Tables of values39

Chapter 5: Conclusion41

References47

Chapter 1: Introduction

Background

Traditionally, mathematics has been taught as a collection of rules and procedures that make computations more efficient. Thus, it comes as little surprise that in a context where the focus of mathematical activity is computation access to tools that can perform many of these computations has historically been restricted. The studies discussed in this section illustrate how teachers' beliefs and knowledge influence access to graphing calculators and how, in turn, this access influences students' mathematical performance.

The students' approaches to calculation on their calculators partly reflected Artigue's (1996) findings on efficient use of full computer algebra systems. Quickness and ease were pursued (a) in numerical calculation, (b) through selection of algebraic solutions in preference to graphical solutions and vice versa, and (c) involved coordination of numerical, graphical and algebraic work. The social means to quickness, in the main, comprised debate, direction by the teacher, and use of a view screen with students' calculators attached.

Potential points of interest in the paper, for the reader, will be students' use of tables, graphs, and commands on the calculator; the ways the use changed over time; the transportation of information between different platforms of the calculator; and the nature of activity when the view-screen was used. The paper follows others on open-ended questioning by the teacher (Davis and Forster, 2003) and the ...