Browsing by Author "Bicknell, Brenda Anne"

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    Multiple perspectives on the education of mathematically gifted and talented students : a dissertation presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Education at Massey University, Palmerston North, New Zealand
    (Massey University, 2009) Bicknell, Brenda Anne
    This study examines multiple perspectives on the education of a group of fifteen Year 6 and Year 8 students identified as mathematically gifted and talented. The students’ mathematical experiences, both past and present are examined using evidence from school policy documents; student, teacher, and parent interviews; questionnaires; and classroom observations. The purpose of this case study was to seek understandings about awareness of the characteristics of mathematically gifted and talented students, the identification of and educational provisions for mathematically gifted and talented students, parental involvement, and school transfer. The group of fifteen students consisted of ten Year 6 students who transferred from primary school to a new school for Year 7, and five Year 8 students who moved to secondary schools for Year 9. These students had been identified by their school and teachers as gifted and talented in mathematics. This predominantly qualitative study is underpinned by an interpretive paradigm and influenced by a sociocultural philosophy of learning and teaching. The literature review presents the dilemmas, similarities, and differences that prevail in the field of gifted education. A more specific focus is given to the education of mathematically gifted students to highlight gaps in the field. This two-year study tracking a group of students provides a cohesive approach to understanding the educational provisions for students identified as mathematically gifted and talented in the New Zealand setting. The multiple case studies included interviews, questionnaires, documents, and observations. The research findings show that there is not a comprehensive understanding by schools and teachers about the characteristics of mathematically gifted students. Despite the documentation of a range of identification processes in school policies, a multiple method approach is not practised in many schools. Provision of appropriate programmes is variable and determined by factors such as school organization, identification, teacher knowledge and expertise, and resources. Parents play a key role in their children’s mathematics education as motivators, resource providers, monitors, mathematics content advisers, and mathematical learning advisers. Schools, teachers, parents, and peers all contribute to the success of a student’s transfer from one phase of schooling to another; they support a student’s social and emotional well being and influence curriculum continuity in mathematics. This study provides insights into the various determinants of the development of mathematical talent. For New Zealand schools and teachers, it provides evidence that understanding the characteristics of mathematical giftedness is important and that identification processes must reflect this understanding. Provisions must be well considered and evaluated; the role of parents should be understood and valued; and home-school communications strengthened. Together, all stakeholders share a critical role in the education of mathematically gifted and talented students.
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    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
    (Massey University, 1998) Bicknell, Brenda Anne
    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.