A case study of a pre-service mathematics education course to grow and develop proficient teaching in mathematics in the intermediate phase
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
- Full Text:
- Date Issued: 2014
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
- Full Text:
- Date Issued: 2014
Integrating information and communications technology (ICT) into teaching and learning: the case of mathematics, science and technology education in one higher education institution
- Authors: Addam, Billey Bright Kwadwo
- Date: 2014
- Subjects: Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: vital:16224 , http://hdl.handle.net/10353/d1019736 , Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Description: This study explores the integration of Information and Communication Technologies (ICT) into teaching and learning within one Higher Education institution. The main question driving the study was: How is ICT integrated in the teaching and learning of mathematics, science and technology education (MSTE) in a Bachelor of Education programme? This is a case study of lecturers and students in Mathematics, Science and Technology Education. It makes use of questionnaires, interviews, field notes and document analyses to collect data. MSTE lecturers and students were assumed to be well versed in ICT usage and, therefore, well placed to assess its integration into teaching and learning. There were five main findings: First, that Mathematics, Science and Technology Education lecturers showed some ambivalence in their ontological and epistemological orientation to using ICT. Some leaned towards the instruction paradigm and used ICT as a tool for the transmission of knowledge; others leaned towards the learning paradigm, showing an awareness of the need to elicit discovery through ICT. Secondly, that lecturers’ understanding of ICT integration was oriented towards teaching and learning from technologies rather than with technologies. Thirdly, that processes of ‘pedagogical evolution’ were taking place, in terms of which there was a gradual but perceptible shift in the teaching and learning practice of both students and lecturers. Fourthly, there was no evidence to show that lecturers used ICT to promote innovative and creative teaching; in fact, students appeared to be more creative in using ICT resources, than lecturers. Fifthly, and finally, lecturers did not assign ICT-based tasks that promote conceptual understanding. They assigned tasks that asked students to extract and reproduce information from computers, without demonstrating understanding. When used in this way, ICT can, in fact, be de-skilling. From these findings, it can be concluded that ICT integration cannot be understood without exploring the ontological and epistemological orientations, as well as the theoretical orientations, at play in the teaching and learning situation. It is on the basis of these that people, that is, lecturers and students, make use of, ICTs to achieve desired goals. It is therefore recommended that, for the improvement of integration, there should be a greater emphasis on developing and sharing pedagogical expertise concerning ICT use in teaching and learning. It is recommended that a country-wide research survey should be undertaken, based on probability sampling and focussing on pedagogical issues in ICT integration in teaching and learning.
- Full Text:
- Date Issued: 2014
- Authors: Addam, Billey Bright Kwadwo
- Date: 2014
- Subjects: Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: vital:16224 , http://hdl.handle.net/10353/d1019736 , Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Description: This study explores the integration of Information and Communication Technologies (ICT) into teaching and learning within one Higher Education institution. The main question driving the study was: How is ICT integrated in the teaching and learning of mathematics, science and technology education (MSTE) in a Bachelor of Education programme? This is a case study of lecturers and students in Mathematics, Science and Technology Education. It makes use of questionnaires, interviews, field notes and document analyses to collect data. MSTE lecturers and students were assumed to be well versed in ICT usage and, therefore, well placed to assess its integration into teaching and learning. There were five main findings: First, that Mathematics, Science and Technology Education lecturers showed some ambivalence in their ontological and epistemological orientation to using ICT. Some leaned towards the instruction paradigm and used ICT as a tool for the transmission of knowledge; others leaned towards the learning paradigm, showing an awareness of the need to elicit discovery through ICT. Secondly, that lecturers’ understanding of ICT integration was oriented towards teaching and learning from technologies rather than with technologies. Thirdly, that processes of ‘pedagogical evolution’ were taking place, in terms of which there was a gradual but perceptible shift in the teaching and learning practice of both students and lecturers. Fourthly, there was no evidence to show that lecturers used ICT to promote innovative and creative teaching; in fact, students appeared to be more creative in using ICT resources, than lecturers. Fifthly, and finally, lecturers did not assign ICT-based tasks that promote conceptual understanding. They assigned tasks that asked students to extract and reproduce information from computers, without demonstrating understanding. When used in this way, ICT can, in fact, be de-skilling. From these findings, it can be concluded that ICT integration cannot be understood without exploring the ontological and epistemological orientations, as well as the theoretical orientations, at play in the teaching and learning situation. It is on the basis of these that people, that is, lecturers and students, make use of, ICTs to achieve desired goals. It is therefore recommended that, for the improvement of integration, there should be a greater emphasis on developing and sharing pedagogical expertise concerning ICT use in teaching and learning. It is recommended that a country-wide research survey should be undertaken, based on probability sampling and focussing on pedagogical issues in ICT integration in teaching and learning.
- Full Text:
- Date Issued: 2014
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.
- Full Text:
- Date Issued: 2010
- 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.
- Full Text:
- Date Issued: 2010
Searching for common ground: developing mathematical reasoning through dialogue
- Authors: Webb, Marie Lynette
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: vital:9493 , http://hdl.handle.net/10948/1132 , Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Description: In the majority of the schools in the Eastern Cape, South Africa, teaching and learning takes place in the second language, English, of both teachers and learners. The purpose of this research was to elicit the perceptions of teachers in multilingual mathematics classes about language issues that they encounter and to ascertain whether they could experientially learn the theory of dialogic teaching through an intervention in order to introduce dialogue in practice in their classes. The effect of the intervention on teacher practices was qualitatively observed and the effect of the teacher practices on learner reasoning competence, numeracy competence and English language competence was quantitatively tested by using validated pre- and post-tests. The study follows a mixed method concurrent triangulation design with both quantitative and qualitative results. Two cohorts of students/teachers studying for qualifications at Nelson Mandela Metropolitan University centres throughout the Eastern Cape expressed their opinions about language challenges and solutions through questionnaires, reflective writing and poetry. A cohort of BEd Honours (Mathematics and Science) students experienced a semester long intervention on the theory and practice of dialogic teaching, particularly exploratory talk, and were tasked to introduce the practice into their multilingual mathematics classes in the form of reported action research. The next phase of the study focussed on the practices of three teachers and their grade seven multilingual mathematics learners who were observed and tested over a period of nine months. The following year the observations and testing were repeated with one teacher and his grade seven learners to ascertain whether the intervention would result in similar findings. iv The results enhance the validity of the Vygotskian claim concerning the relationship between language use, social interaction and reasoning development. In classes where there was evidence of dialogic practices the learners collaborated in groups using code-switching and their main language. Their reasoning, numeracy and English skills test scores improved statistically significantly. Teachers were able to give voice to their deep-felt emotions through poetry. They felt that the devaluing of isiXhosa had resulted in the loss of learners’ main language literacy competencies and consequent loss of cultural capital; however they considered it necessary to develop English competence in the learners, even if it was at the expense of developing mathematical competence. The introduction of exploratory talk in their home languages served the dual purpose of promoting the value of isiXhosa in an academic environment as well as enhancing mathematical reasoning. It appears that when teachers focus on developing language as a tool for reasoning, significant improvements in learners’ problem solving competences occur. When the language used is the main language of both teachers and learners both mathematical understanding and cultural identity are enhanced. The study concludes with a suggestion for a model for future interventions to train teachers to introduce dialogic practices in multilingual mathematics classes.
- Full Text:
- Date Issued: 2010
- Authors: Webb, Marie Lynette
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: vital:9493 , http://hdl.handle.net/10948/1132 , Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Description: In the majority of the schools in the Eastern Cape, South Africa, teaching and learning takes place in the second language, English, of both teachers and learners. The purpose of this research was to elicit the perceptions of teachers in multilingual mathematics classes about language issues that they encounter and to ascertain whether they could experientially learn the theory of dialogic teaching through an intervention in order to introduce dialogue in practice in their classes. The effect of the intervention on teacher practices was qualitatively observed and the effect of the teacher practices on learner reasoning competence, numeracy competence and English language competence was quantitatively tested by using validated pre- and post-tests. The study follows a mixed method concurrent triangulation design with both quantitative and qualitative results. Two cohorts of students/teachers studying for qualifications at Nelson Mandela Metropolitan University centres throughout the Eastern Cape expressed their opinions about language challenges and solutions through questionnaires, reflective writing and poetry. A cohort of BEd Honours (Mathematics and Science) students experienced a semester long intervention on the theory and practice of dialogic teaching, particularly exploratory talk, and were tasked to introduce the practice into their multilingual mathematics classes in the form of reported action research. The next phase of the study focussed on the practices of three teachers and their grade seven multilingual mathematics learners who were observed and tested over a period of nine months. The following year the observations and testing were repeated with one teacher and his grade seven learners to ascertain whether the intervention would result in similar findings. iv The results enhance the validity of the Vygotskian claim concerning the relationship between language use, social interaction and reasoning development. In classes where there was evidence of dialogic practices the learners collaborated in groups using code-switching and their main language. Their reasoning, numeracy and English skills test scores improved statistically significantly. Teachers were able to give voice to their deep-felt emotions through poetry. They felt that the devaluing of isiXhosa had resulted in the loss of learners’ main language literacy competencies and consequent loss of cultural capital; however they considered it necessary to develop English competence in the learners, even if it was at the expense of developing mathematical competence. The introduction of exploratory talk in their home languages served the dual purpose of promoting the value of isiXhosa in an academic environment as well as enhancing mathematical reasoning. It appears that when teachers focus on developing language as a tool for reasoning, significant improvements in learners’ problem solving competences occur. When the language used is the main language of both teachers and learners both mathematical understanding and cultural identity are enhanced. The study concludes with a suggestion for a model for future interventions to train teachers to introduce dialogic practices in multilingual mathematics classes.
- Full Text:
- 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.
- Full Text:
- Date Issued: 2008
- 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.
- Full Text:
- Date Issued: 2008
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