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    The relationship between spatial ability and mathematical ability : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Psychology at Massey University
    (Massey University, 1996) Flynn, Peter M
    The purpose of this study was to examine the relationship between spatial ability and general mathematical ability. Many researchers have assumed that a positive correlational relationship exists between mathematics and spatial ability. However, a review of the literature shows that the relationship is not as simple as thought, partly because there is disagreement among researchers on a definition of spatial ability. In the present study general mathematical ability was indexed by the Progressive Achievement Test: Mathematics. A group of 50 high ability and a group of 50 low ability children completed five tests relating to spatial ability from the Kit of factor Related Cognitive Tests. Results from a discriminant function analysis supported the hypothesis that a positive correlational relationship exists between spatial ability and general mathematical ability. This result is important because it provides new evidence to support the argument that there is a relationship between spatial ability and general mathematical ability. The potential for spatial ability tasks to aid in the understanding of mathematics is discussed. However, it is argued that there is a need for greater refinement of the spatial ability construct before more research using it as a factor is conducted.
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    E-asTTle as a catalyst for change : a thesis presented in partial fulfilment of the requirements for the degree of Masters in Education - Teaching and Learning at Massey University, Palmerston North, New Zealand
    (Massey University, 2016) Carnegie-Harding, Susan
    This thesis studies the introduction and use of the formative assessment tool e-asTTle (Assessment for Teaching and Learning) in a low decile, high Māori school and the impact it has on teacher practice and student achievement. The project’s aim was to identify if teachers, through using the data from the tool, moved to an evidence based teaching model which supported increased student achievement in reading and mathematics. Identifying a major shift in teaching practice and corresponding rise in student success would support the assertion unpinning the study, that e-asTTle is a catalyst for change. The data for this study was gathered during the first quarter of the school year. Teachers of Year 7, 8 and 9 students volunteered to complete a confidential online survey. The focus of the survey was to identify previous and current assessment practices, changes to practice and prompted teachers to reflect on the usefulness of data in supporting their teaching practice. Beginning of the year and mid-year student assessment score data in reading and mathematics was gathered and compared to identify shifts in achievement of each year group. These shifts were then compared to e-asTTle nationally expected shifts to identify the level of progress. The results suggest that the introduction of the e-asTTle tool into the school supported teachers to change to formative assessment, evidence-based teaching practice. This change had a positive effect on student achievement with accelerated progress occurring in reading and mathematics. However, the results also identified a much lower level of progress for Year 7 students, which is consistent with trends identified in national research data on the transitioning of students between primary and secondary schools. Based on this data a recommendation was made to study the transitioning of students between the local primary schools and the study school, and the impact it may be having on learning and achievement, particularly in mathematics. Should the results of the study support it, a programme could be put into place that met identified student needs and supported their successful integration into the school. Although evidence of accelerated progress met the study’s brief, the continued low level of achievement of the students in reading compared not just to all schools but to other decile one, high Māori roll schools, is a concern that needs to be addressed.
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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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    A clinical study of the mathematical incompetence of some university students : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Education at Massey University
    (Massey University, 1982) Knight, Gordon Henry
    The objectives of the study are to contribute to the clear identification and understanding of the factors which lie behind the severe mathematical difficulties experienced by some otherwise able university students. A careful description of the phenomenon, which might lead to an explanation, is dependant on an understanding of the cognitive processes of the individuals concerned. Consequently a research method and theoretical perspective were chosen which would enable a study of these processes to be made as they were used in solving mathematical problems. The method was based on the Piagetian clinical interview and the theoretical background was essentially that of Skemp's (1979) model of intelligent behaviour. The principal advantages of this model were its structural rather than global features and the close relationship implied between the cognitive and affective determinants of behaviour. Twenty six subjects were interviewed having a wide range of mathematical abilities and interest. Each subject was presented with the same sequence of tasks taken from the primary-secondary school arithmetic-algebra syllabus. The responses were probed in an unstructured manner. The analysis of the interview data had two stages. Firstly, in order to provide an overview, a formal coding was undertaken in which the response to each item was classified according to the level of understanding indicated. The resulting data was analysed initially in an entirely descriptive manner and then was subjected to Latent Response Analysis. Following this statistical analysis a closer clinical analysis was made using a multiple-coding approach to build up a mosaic of evidence concerning the conceptual structures used by the subjects. The principal conclusions of the study relate firstly to the vital importance of the availability of appropriate initial frameworks for the successful handling of mathematics. It is argued that the absence of such frameworks, or schema, interpreted in the light of Skemp's theory, explains both the affective reaction of subjects having difficulty with mathematics, and the development of intelligent behaviour within one form of knowledge but not in another. Secondly, the evidence of the study indicated that it was unlikely that the difficulties which the students were having with mathematics were due either to the abstract nature of the concepts involved or to the logical nature of the subject matter. Thirdly, the topic of fractions emerged clearly as the most likely source of real difficulty. It is suggested that generations of curriculum designers have seriously underestimated the difficulties associated with learning in this area. Finally attention is drawn to the necessity for teachers to constantly monitor the development of the cognitive structures of their students and to be sensitive to signals in the affective domain which might indicate developing problems in the cognitive area. In this way the vicious interaction of cognitive and affective reactions to mathematics, which is the most distressing feature of the problem, might be avoided.