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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.
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    The gifted and talented in New Zealand secondary schools : an overview of procedures and practices in mathematics : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies (Mathematics) at Massey University
    (Massey University, 2000) Winsley, Jan Adrienne
    A large nation-wide survey was carried out to collect data on the extent and nature of programs currently offered to gifted and talented mathematicians in New Zealand secondary schools. Quantitative data was collected on the identification of gifted and talented mathematics students, school-wide policy on the gifted and talented, ability grouping, acceleration and enrichment as well as demographic factors associated with the research variables. Open questionnaire responses by Heads of Mathematics Departments indicated strong interest in the educational provisions for the gifted and talented. A semi-structured interview was also used with three secondary schools in order to expand upon the issues that had arisen from the postal surveys. It appears that the situation of the gifted and talented in New Zealand secondary schools is still unsatisfactory. Only 60% of respondents reported having identified gifted and talented students within their school, 32% of respondent schools had a written policy on the gifted and talented, just over a third of respondent schools had no forms of ability grouping and just under a half of the respondent schools did not have an acceleration program. The Development Band Certificate was used in 45% of respondent schools. The research raises concerns about the lack of well conceived, continuous programs in mathematics available to gifted and talented students in New Zealand secondary schools.
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    Acceleration in mathematics : students' perspectives : a thesis presented in partial fulfilment of the requirements for the degree of Masters of Educational Studies (Mathematics) at Massey University
    (Massey University, 2000) Rawlins, Peter Leslie Charles
    This study examines accelerate programmes in mathematics within New Zealand secondary schools from the participant students point of view. Focus group interviews and questionnaires were used to gather information from students about their acceleration experiences in four state secondary schools. An analysis of the data gathered reveals that for many students, the opportunity to study one or more Bursary subjects earlier than their age cohort is seen as a motivational factor for participation in acceleration programmes. This opportunity allows them to either broaden their subject base at the Bursary level, or to repeat a subject and try and improve on their marks, perhaps securing a Scholarship. Not all students have long-term goals, however and many students appreciate the immediate challenge of working one year ahead of their normal age cohort. Contrary to fears identified by educational practitioners, this research does not support the commonly held belief that students who are accelerated will suffer from undue stress that may hinder their social and emotional development. Participants perceive that inclusion in the acceleration programme has not affected their friendship base and they report being comfortable being in classes with older students. Students perceive that they have a normal adolescent social and emotional development. Coupled with these findings is the fact that, almost without exception, participants felt that participation in an acceleration programme had been beneficial to their learning needs. No significant problems with compacting the curriculum or gaps in knowledge were identified by the majority of students in the research sample. Overall, this study demonstrates students' endorsement of acceleration programmes. Acceleration is perceived as a viable and valuable tool for meeting the educational needs of gifted and talented students within New Zealand secondary schools. It should be remembered, however, that acceleration is not the only tool available and schools are urged to develop individual, cohesive and flexible programmes to meet the needs of this very varied group.
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    Process mnemonics and mathematics learning disabilities : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Psychology, Massey University, Palmerston North, New Zealand
    (Massey University, 1996) Manalo, Emmanuel; Manalo, Emmanuel
    This study investigated the effects of process mnemonic instruction on the computational skills performance of 13- to 14-year-old students with mathematics learning disabilities (LD). Two experiments were carried out. In Experiment 1, 29 students with mathematics LD were assigned to either a process mnemonic instruction group, a demonstration-imitation instruction group (which served as a comparison instruction group), a study skills group (which served as a placebo instruction group), or a no instruction group. Those in the process mnemonic and the demonstration-imitation groups were provided with instructions in computational skills. The present author acted as instructor. Assessments of performance were undertaken at pre-instruction, immediate post-instruction, 1 week later, and 6 to 8 weeks later. The results showed that those in the process mnemonic group made significant improvements following the instructions provided. During the earlier stages of post-instruction, the magnitude of improvements they made were generally equivalent to that made by students in the demonstration-imitation group. However, in the longer term, the improvements made by the students in the process mnemonic group maintained better. No significant changes in performance were observed in the study skills and no instruction groups. In Experiment 2, 28 students with mathematics LD were assigned to groups similar to those in Experiment 1, but without the study skills group. Two research assistants acted as instructors to control for any possible unintentional bias, and to investigate the effectiveness of the process mnemonic method when used by other instructors. Assessments of performance were undertaken at pre-instruction, immediate post-instruction, 1 week later, 4 weeks later, and 8 weeks later. The results obtained were similar to those in Experiment 1. Furthermore, the students in the process mnemonic group generally made greater performance improvements compared to those in the demonstration-imitation group. No significant changes in performance were observed in the no instruction group. Areas focused on in the discussion include the possible reasons why the process mnemonic method of instruction proved to be effective, the method's potential applications in mathematics LD remedial instruction, and the implications of the findings about the mathematics LD condition.