Academic journal article Educational Technology & Society

Improving Pupils' Mathematical Communication Abilities through Computer-Supported Reciprocal Peer Tutoring

Academic journal article Educational Technology & Society

Improving Pupils' Mathematical Communication Abilities through Computer-Supported Reciprocal Peer Tutoring

Article excerpt

Introduction

Mathematical communication, a fundamental mathematics educational objective that involves cognitive and social activities (Baroody & Ginsburg, 1990), is used to engage students in communicative situations for increasing learning interaction with others to obtain mutual mathematical ideas (Silver & Smith, 1996), share mathematical thoughts, develop mathematical concepts and strategies, and reflect on their current mathematical understanding (Whitin & Whitin, 2000; Cooke & Buchholz, 2005). Mathematical communication abilities also include expressing mathematical thought by using mathematical language clearly, precisely, and succinctly (National Council of Teachers of Mathematics, 2000); understanding others' mathematical equations and concepts (Lin & Lee, 2004; Lin, Shann, & Lin, 2008); and evaluating others' mathematical concepts by, for example, asking meaningful questions and explaining the reasons for others' incorrect mathematical thought (Lin & Lee, 2004).

Various means of fostering mathematical communication abilities have been proposed. For example, Baroody and Ginsburg (1990) suggested that students should communicate mathematical ideas through representing, listening, discussing, reading, and writing. Cobb, Boufi, McClain, and Whitenack (1997) also claimed that students' mathematical discourse in classrooms can support their conceptual development, while Shimizu and Lambdin (1997) revealed that students who write about the thinking process of their solutions can organize complex thoughts and evaluate their own opinions. Similarly, Steele and Arth (1998) argued that reflecting on how to solve a problem by writing their solutions can facilitate students to explain their thinking process more clearly, thereby benefitting themselves in learning mathematics and learning to communicate mathematically by constructing mathematical artifacts as well as developing and evaluating mathematical arguments (National Council of Teachers of Mathematics, 2000). Similarly, students can adopt written mathematical communication by using text, figures, tables, pictures, diagrams, or mathematical symbols to provide critical evidence of their mathematics ideas and concepts (Mooney, Hansen, Ferrie, Fox, & Wrathmell, 2012; Whitin & Whitin, 2000). Additionally, students can learn mathematics by observing, interacting with, and manipulating physical objects and the representations of objects and concepts (Sedig, 2008). Besides, students may support their claims by describing and recognizing patterns, generalizing rules, and using various types of representations (Moschkovich, 2012). These studies have demonstrated various methods for expressing or explaining mathematical ideas by writing or creating mathematical materials. The content of mathematical communication can be treated as an artifact of reflection, refinement, discussion, and modification. Therefore, mathematical communication ability should be fostered in students by simultaneously training their oral expression and various mathematical representations for explaining their understanding of mathematical ideas and strategies concretely as well as sharing their work with one another (Dacey & Eston, 2002).

To improve students' mathematical communication ability, several studies have shown the potential of using computers. For instance, Koedinger, Anderson, Hadley, and Mark (1997) built Practical Algebra Tutor (PAT) system to engage students in investigating real-world problems and using algebraic tools to generate multiple representations (tables, graphs, and symbols) for solving algebra problems and communicating results. Stahl (2009) designed a Virtual Math Team (VMT) system for students' exploring and discussing mathematical topics with peers for improving the quality of mathematical conception through online mathematical text-based chatting. Furthermore, Tsuei (2012) adopted G-Math, a synchronous peer-tutoring system, for pupils to discuss mathematical word problem solving via a sharing mechanism, which takes advantage of the availability of students' works to communication and obtain mutual perspectives. …

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