A value-based approach to promoting excellence in mathematics education
- Authors: Austin, Pamela Winifred
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa , Active learning -- South Africa , Effective teaching -- South Africa , Self-efficacy
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: vital:9482 , http://hdl.handle.net/10948/1656 , Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa , Active learning -- South Africa , Effective teaching -- South Africa , Self-efficacy
- Description: This research study has emerged as a result of my concern regarding the apparent low self-efficacy amongst initial teacher education students in my mathematics education classes. It also reflects a reported renewed interest in values, and the promotion of excellence in education. The effects of a values-based approach to mathematics education towards improving students’ self-efficacy and promoting excellence have been investigated, grounded within my ontology of excellence in mathematics education, which incorporates the values of respect, fairness, accountability, honesty and compassion. An inquiry-based teaching and learning approach formed the framework within which the study took place. Notions of ‘new scholarship’, premised on the view that teaching is about engagement in participatory learning, and the development of communities of creative students, provided the theoretical framework. Both quantitative and qualitative data gathering methods were used. Data-collection tools included affective-disposition statements, interviews, journal entries, as well as a video recording of a mathematics education lesson. The quantitative and qualitative data generated suggest improved levels of self-efficacy amongst the students who participated in the study. The data also suggest that a valuesbased approach to teaching can be used as an effective approach by mathematics teachers – and mathematics teacher educators – for the purpose of promoting the pursuit of excellence. As teacher education worldwide is currently characterised by a lack of vitality in teacher preparation (Grossman, 2008), the findings of this study should provide insights for teacher educators, teachers and policy makers who wish to promote mathematics self-efficacy, excellence and facilitate enhanced vitality within the teaching profession.
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- Date Issued: 2010
The identification of criteria to be utilised in mathematical diagnostic tests
- Authors: Wagner-Welsh, Shirley Joy
- Date: 2008
- Subjects: Educational tests and measurements -- South Africa -- Port Elizabeth , Mathematical ability -- Testing , Ability -- Testing , Guidance test battery for secondary pupils , Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: vital:10501 , http://hdl.handle.net/10948/708 , Educational tests and measurements -- South Africa -- Port Elizabeth , Mathematical ability -- Testing , Ability -- Testing , Guidance test battery for secondary pupils , Mathematics -- Study and teaching -- South Africa
- Description: School-related mistakes and low pass rates have led this researcher to perceive that some students are not adequately prepared for Mathematics 1. To address the problem of under-preparedness overseas universities use placement or diagnostic tests. Diagnostic testing identifies areas of weakness and provides information to guide the development of appropriate remedial support. This researcher embarked on a study to identify the sub-domains (criteria) that should be included in a diagnostic Mathematics test battery at the NMMU. An analysis of first-year curricula was undertaken to determine the required Mathematical pre-knowledge and skills entry-level students should have. Thereafter, the required pre-knowledge and skills were reflected against the standard grade school syllabi. From this it was determined that the school learners should acquire the necessary pre-knowledge and skills for university success as part of the school syllabus. However, in reality this is not the case as the researcher and other Mathematics lecturers identified a number of basic errors that incoming students make. This suggests that they have not developed all the required knowledge and skills. Furthermore, their performance in the matriculation examinations does not provide an adequate measure of the requisite Mathematical pre-knowledge and skills necessary for success at university-level Mathematics. No suitable existing diagnostic Mathematics test could be found. By utilizing both an action research as well as a test development methodology, the researcher thus proceeded to delineate the sub-domains that should be included in a diagnostic Mathematics test battery. Thereafter, test specifications were developed for two pilot tests and items were developed or sourced. The constructed response item-type was chosen for the pilot tests as it was argued that this item-type was more useful to use in a diagnostic test than a multiple-choice item format, for example. The pilot test battery, which consisted of a pilot Arithmetic and Algebra and Calculus tests, was administered to a sample of first-year students at the NMMU in 2004 and their performance in Mathematics at the end of the first year was tracked. Tests were scored holistically and analytically to provide a rich source of information. Thereafter, the test results were analysed to obtain evidence on the content validity of the pilot tests, including the item difficulty values and the item-total correlations; to determine the predictive validity of performance on the pilot tests with respect to final first-year Mathematics marks; and their reliability was determined using the Cronbach’s Alpha statistic. These findings suggest that appropriate sub-domains (criteria) were delineated and the items appropriately covered these sub-domains (i.e. the content validity of the pilot tests is acceptable). Furthermore, the predictive validity of the pilot ix tests was found to be acceptable in that significant correlations were found between the pilot tests and performance in first-year Mathematics. Finally, the pilot tests were found to be reliable. Based on the results, suggestions are made regarding how to refine the diagnostic test battery and the research related to it. The final diagnostic Mathematics test battery holds much potential to be able to assist in the early identification of at-risk students who can be timeously placed in developmentally appropriate Mathematics modules or provided with appropriate remedial intervention.
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- Date Issued: 2008