The writing of explanations and justifications in mathematics : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education, Massey University

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Massey University
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This study reports on the writing of explanations and justifications in mathematics. A variety of approaches including a document analysis, teacher survey, students' responses to problem solving tasks, and student interviews were used to examine the complexities and interpretations of writing explanations and justifications in mathematics. The study involved six teachers and 36 Year 11 students from a provincial co-educational secondary school; 14 of the students were interviewed. An analysis of the Year 11 national mathematics examination, School Certificate, revealed a significant increase in emphasis on the writing of explanations; from 2.7% of the total marks in 1992, to 16% of the total marks in 1997. It was not until 1997 that students were specifically asked to write justifications. In this study students experienced some difficulties writing explanations and had concerns about whether their explanations were satisfactory; a variety of modes of representation were used by students. Most students surveyed were unable to write justifications; they lacked knowledge and confidence in justifying their solutions. The teachers believed that the writing of explanations and justifications was an important process but expressed a number of concerns. These concerns were the class time needed, and the lack of resources and professional development. Both students and teachers were concerned about not knowing what makes a quality response. The writing of explanations and justification should be a valued and regular part of the mathematics programme so that students are able to develop and evaluate mathematical arguments and proofs and effectively communicate their findings to others. The study suggests that students and teachers need to work together in negotiating an understanding of what is meant by an explanation, and a justification, and what makes a quality response.
Mathematics, Secondary school mathematics, Problem solving, School Certificate Examination (N.Z.), Secondary school maths, New Zealand