218 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.In this study the effects ... more 218 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.In this study the effects of a computer-integrated learning milieu on the levels of understanding novel mathematical concepts were investigated. Secondary questions investigated were the effects of this learning experience on attitudes toward mathematics and computer use in education. The Solomon-Four Group design was used with two classes of preservice elementary teachers in regularly assigned classes in a college of education in a developing population. The one class studied an instructional unit on transformation geometry in a learning environment consisting of manipulatives and computer software which allows the investigation and exploration of transformation geometry concepts. The other class studied the unit using only traditional geometry tools.Six hypotheses were investigated to discover whether significant group differences were achieved in levels of understanding reflections, rotations, and translations, confidence in learning mathematics, attitude toward success in mathematics, and attitude toward computer use in education as a result of studying transformation geometry concepts in a Logo-enriched environment.Half the participants in each group were randomly selected to receive the pretest. No significant pretest group differences were reported. Posttest scores were analyzed using a 2 by 2 analysis of variance technique in which the pretest was considered as another treatment coordinate. Significant group differences were reported for levels of understanding rotations, levels of understanding translations, and confidence in learning mathematics. These results led to the conclusion that integrating computer software which allows the exploration and investigation of mathematical concepts with manipulatives may be a useful activity to enhance students' comprehension of mathematical concepts.A replication of the study, with a different model of levels of understanding, to further validate the results, is recommended. In addition to this, recommendations include teaching-experiment type research to investigate misconceptions and the processes involved in moving from level to level; and a longitudinal study on the effects of experiences of the nature of the study on the teaching methods prospective teachers eventually employ in their classes.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2020
Mathematical literacy is generally viewed as embedded in mathematical modelling and the applicati... more Mathematical literacy is generally viewed as embedded in mathematical modelling and the applications of mathematics. It is therefore not unreasonable to expect that the development of mathematical modelling competencies should be accorded priority in mathematical literacy. In South Africa, mathematical literacy is examined through a nationally set examination at the end of 12 years of schooling. Schemes of marking of five consecutive examinations for mathematical literacy were analysed to ascertain the prioritisation of mathematical modelling competencies in these examinations. It was found that more than 80% of marks were awarded to mathematical calculations and that the formulation of a problem statement and the validation of a model did not appear in any of the schemes of marking. The implications of these results are discussed.
International Reflections on the Netherlands Didactics of Mathematics, 2019
The project Realistic Mathematics Education in South Africa (REMESA) was introduced in South Afri... more The project Realistic Mathematics Education in South Africa (REMESA) was introduced in South Africa during a period when curriculum changes were introduced to fit the educational ideals of the ‘new’ South Africa. In this project, modules based on Realistic Mathematics Education were developed by a team comprising staff from the Freudenthal Institute and the Mathematics Education sector of the University of the Western Cape. The modules were implemented in classrooms. In our chapter, we reflect upon the appropriation by practicing teachers of two modules. Teachers viewed the module Vision Geometry with scepticism whilst the module Global Graphs was more readily accepted. The appropriation was thus differential. In current school mathematics policy documents and learning materials, the major ideas of the module Vision Geometry are virtually invisible. The ideas from the module Global Graphs are more visible. This can be ascribed to the prominence of graphical representations in South ...
... of “a participating citizen in a developing democracy [who has] a critical stance with regard... more ... of “a participating citizen in a developing democracy [who has] a critical stance with regard to mathematical arguments presented in the media and other ... It does allow for reflection on issues of a political nature but remains at an awareness and conscientization level. ...
South African Journal of Childhood Education, 2016
et al., 2016, 'Searching for research results to inform the design of an initial professional tea... more et al., 2016, 'Searching for research results to inform the design of an initial professional teacher education programme for the foundation phase: A systematic review', South African Journal of Childhood Education 6(1), a285.
A comparison between the contexts grade 8 to 10 urban and peri-urban learner's context preference... more A comparison between the contexts grade 8 to 10 urban and peri-urban learner's context preferences for Mathematical Literacy. The study explored the comparison of grade 8 to 10 urban and peri-urban learners' contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas; least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners. iv DECLARATION I declare that A comparison of grade8 to 10 urban and peri-urban learners' context preferences for mathematical literacy is my work, that it has not been submitted before for any degree or examination in any other university, and that all the sources I have used or quoted have been indicated and acknowledge as complete references.
When one studies the above table one would be able to reflect on how to teach mathematics better ... more When one studies the above table one would be able to reflect on how to teach mathematics better to grade 7 learners so that they enhance their mathematics performance. The decline in grade 9 mathematics performances might emanate from the teaching strategies applied in the phase and lower grades. Another rationale for this study is to provide a turn-around strategy in teaching mathematics so that learners understand and master the subject. One assumes that it is every teacher's wish to improve learners' performance in his or her subject by the end of the year. In this research project learners were encouraged to understand integers. Learners were also provided with an improved introduction of integers through using temperature model as a basic means of understanding integers. Another indirectly motivating factor of this study comes from South African learners' poor performance in large scale national and international studies such as TIMSS and the Southern and Eastern Africa Consortium for Monitoring Educational Quality (SACMEQ), (Department of Education (DoE), 2005; Mothibeli, 2005). The aim of this study was to investigate how grade 7 learners deal with the introductory constructs of integers when they are introduced through a temperature model. How do grade 7 learners deal with the introductory constructs of integers when they are introduced to it through a temperature model? Key terms of this study and their definitions The grade 7 curriculum and assessment policy statement (CAPS) document (Department of Basic Education, 2011, p.16) requires learners to be able to compare, order and recognise integers as skills that should be attained before adding and subtracting integers. Recognising and using commutative and associative properties of addition and multiplication for integers is regarded as a primary skill.
International Perspectives on the Teaching and Learning of Mathematical Modelling
The chapter concerns prescriptive mathematical modelling and the development of critical competen... more The chapter concerns prescriptive mathematical modelling and the development of critical competence. The potential of such modelling examples to promote critical discussions about the role of mathematical models in society is argued. A study is presented in which Norwegian and South African prospective teachers critically discuss a task dealing with a mathematical model, the Body Mass Index. The question posed in this chapter focuses on critical issues that come to the fore during the discussions. Four themes were identified, connected to several limitations of the model and to possible alternative models. The themes are discussed in relation to prior research on critical discussions of mathematical models in society and teacher education.
International Perspectives on the Teaching and Learning of Mathematical Modelling
The extra-mathematical domains that feature prominently for mathematical modelling and the applic... more The extra-mathematical domains that feature prominently for mathematical modelling and the applications of mathematics in ICTMA deliberations are the physical, biological, economic, environmental, social and engineering sciences. This chapter focuses on the deployment of mathematics in domains other than these dominant ones. Sources such as novels, stories, monographs, journalistic-like commentaries on mathematics, anecdotal accounts on mathematics by ordinary people and so forth were mined to ascertain the uses mathematics is put to in such sources. The uses are classified as backgrounding storylines through encryption and decryption; depictions of cleverness, dissent/avoidance and madness; rendering political commentary; and entertainment through humour. It is suggested that students should be afforded opportunities to put mathematics to use in a similar manner.
This study reports on an intervention that emanated from a concern a mathematics teacher had abou... more This study reports on an intervention that emanated from a concern a mathematics teacher had about the unsatisfactory performance of grade 12 learners in the school-based mid-year examination. The intervention was based on distributed practice and the effect size of the intervention was determined as an indicator of the effectiveness of the intervention. Different effect sizes are reported and the reasons for their acceptance or non-acceptance are presented. Overall the results indicate that if all the different effect sizes are taken into account, the intervention had a medium to high effect. Given that the intervention was driven by aspects of teaching and was done at school, it is recommended that more attention be accorded to those aspects of teaching that enhance achievement in Mathematics.
It has become a policy imperative that the training of future researchers in Education should sta... more It has become a policy imperative that the training of future researchers in Education should start at the Honours level. This training presents particular challenges as students entering the Bachelor of Education Honours (BEd Hons) programme have diverse professional backgrounds and personal motivations for pursuing the programme. Moreover, the majority of the students have fairly substantial experience in schools, one of the primary empirical sites for educational research. This diverse student profile yields several challenges in relation to the teaching of a Research Methods course. In this article, the authors reflect on their experiences of offering a BEd Hons course to induct students into research against the traditional, literature-renditioned components which comprise the practice of research in the Social Sciences. Working with the notions of critical aspects and encounters, the authors found that students experience a tension between their desire to solve their identifie...
International Journal of Science and Mathematics Education
This paper attempts to engage the field in a discussion about what mathematics is needed for stud... more This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what mathematical proficiency means in today's world and what shifts need to be made in both content and pedagogy to prepare students for 21st Century Skills and mathematical reasoning.
218 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.In this study the effects ... more 218 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.In this study the effects of a computer-integrated learning milieu on the levels of understanding novel mathematical concepts were investigated. Secondary questions investigated were the effects of this learning experience on attitudes toward mathematics and computer use in education. The Solomon-Four Group design was used with two classes of preservice elementary teachers in regularly assigned classes in a college of education in a developing population. The one class studied an instructional unit on transformation geometry in a learning environment consisting of manipulatives and computer software which allows the investigation and exploration of transformation geometry concepts. The other class studied the unit using only traditional geometry tools.Six hypotheses were investigated to discover whether significant group differences were achieved in levels of understanding reflections, rotations, and translations, confidence in learning mathematics, attitude toward success in mathematics, and attitude toward computer use in education as a result of studying transformation geometry concepts in a Logo-enriched environment.Half the participants in each group were randomly selected to receive the pretest. No significant pretest group differences were reported. Posttest scores were analyzed using a 2 by 2 analysis of variance technique in which the pretest was considered as another treatment coordinate. Significant group differences were reported for levels of understanding rotations, levels of understanding translations, and confidence in learning mathematics. These results led to the conclusion that integrating computer software which allows the exploration and investigation of mathematical concepts with manipulatives may be a useful activity to enhance students' comprehension of mathematical concepts.A replication of the study, with a different model of levels of understanding, to further validate the results, is recommended. In addition to this, recommendations include teaching-experiment type research to investigate misconceptions and the processes involved in moving from level to level; and a longitudinal study on the effects of experiences of the nature of the study on the teaching methods prospective teachers eventually employ in their classes.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2020
Mathematical literacy is generally viewed as embedded in mathematical modelling and the applicati... more Mathematical literacy is generally viewed as embedded in mathematical modelling and the applications of mathematics. It is therefore not unreasonable to expect that the development of mathematical modelling competencies should be accorded priority in mathematical literacy. In South Africa, mathematical literacy is examined through a nationally set examination at the end of 12 years of schooling. Schemes of marking of five consecutive examinations for mathematical literacy were analysed to ascertain the prioritisation of mathematical modelling competencies in these examinations. It was found that more than 80% of marks were awarded to mathematical calculations and that the formulation of a problem statement and the validation of a model did not appear in any of the schemes of marking. The implications of these results are discussed.
International Reflections on the Netherlands Didactics of Mathematics, 2019
The project Realistic Mathematics Education in South Africa (REMESA) was introduced in South Afri... more The project Realistic Mathematics Education in South Africa (REMESA) was introduced in South Africa during a period when curriculum changes were introduced to fit the educational ideals of the ‘new’ South Africa. In this project, modules based on Realistic Mathematics Education were developed by a team comprising staff from the Freudenthal Institute and the Mathematics Education sector of the University of the Western Cape. The modules were implemented in classrooms. In our chapter, we reflect upon the appropriation by practicing teachers of two modules. Teachers viewed the module Vision Geometry with scepticism whilst the module Global Graphs was more readily accepted. The appropriation was thus differential. In current school mathematics policy documents and learning materials, the major ideas of the module Vision Geometry are virtually invisible. The ideas from the module Global Graphs are more visible. This can be ascribed to the prominence of graphical representations in South ...
... of “a participating citizen in a developing democracy [who has] a critical stance with regard... more ... of “a participating citizen in a developing democracy [who has] a critical stance with regard to mathematical arguments presented in the media and other ... It does allow for reflection on issues of a political nature but remains at an awareness and conscientization level. ...
South African Journal of Childhood Education, 2016
et al., 2016, 'Searching for research results to inform the design of an initial professional tea... more et al., 2016, 'Searching for research results to inform the design of an initial professional teacher education programme for the foundation phase: A systematic review', South African Journal of Childhood Education 6(1), a285.
A comparison between the contexts grade 8 to 10 urban and peri-urban learner's context preference... more A comparison between the contexts grade 8 to 10 urban and peri-urban learner's context preferences for Mathematical Literacy. The study explored the comparison of grade 8 to 10 urban and peri-urban learners' contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas; least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners. iv DECLARATION I declare that A comparison of grade8 to 10 urban and peri-urban learners' context preferences for mathematical literacy is my work, that it has not been submitted before for any degree or examination in any other university, and that all the sources I have used or quoted have been indicated and acknowledge as complete references.
When one studies the above table one would be able to reflect on how to teach mathematics better ... more When one studies the above table one would be able to reflect on how to teach mathematics better to grade 7 learners so that they enhance their mathematics performance. The decline in grade 9 mathematics performances might emanate from the teaching strategies applied in the phase and lower grades. Another rationale for this study is to provide a turn-around strategy in teaching mathematics so that learners understand and master the subject. One assumes that it is every teacher's wish to improve learners' performance in his or her subject by the end of the year. In this research project learners were encouraged to understand integers. Learners were also provided with an improved introduction of integers through using temperature model as a basic means of understanding integers. Another indirectly motivating factor of this study comes from South African learners' poor performance in large scale national and international studies such as TIMSS and the Southern and Eastern Africa Consortium for Monitoring Educational Quality (SACMEQ), (Department of Education (DoE), 2005; Mothibeli, 2005). The aim of this study was to investigate how grade 7 learners deal with the introductory constructs of integers when they are introduced through a temperature model. How do grade 7 learners deal with the introductory constructs of integers when they are introduced to it through a temperature model? Key terms of this study and their definitions The grade 7 curriculum and assessment policy statement (CAPS) document (Department of Basic Education, 2011, p.16) requires learners to be able to compare, order and recognise integers as skills that should be attained before adding and subtracting integers. Recognising and using commutative and associative properties of addition and multiplication for integers is regarded as a primary skill.
International Perspectives on the Teaching and Learning of Mathematical Modelling
The chapter concerns prescriptive mathematical modelling and the development of critical competen... more The chapter concerns prescriptive mathematical modelling and the development of critical competence. The potential of such modelling examples to promote critical discussions about the role of mathematical models in society is argued. A study is presented in which Norwegian and South African prospective teachers critically discuss a task dealing with a mathematical model, the Body Mass Index. The question posed in this chapter focuses on critical issues that come to the fore during the discussions. Four themes were identified, connected to several limitations of the model and to possible alternative models. The themes are discussed in relation to prior research on critical discussions of mathematical models in society and teacher education.
International Perspectives on the Teaching and Learning of Mathematical Modelling
The extra-mathematical domains that feature prominently for mathematical modelling and the applic... more The extra-mathematical domains that feature prominently for mathematical modelling and the applications of mathematics in ICTMA deliberations are the physical, biological, economic, environmental, social and engineering sciences. This chapter focuses on the deployment of mathematics in domains other than these dominant ones. Sources such as novels, stories, monographs, journalistic-like commentaries on mathematics, anecdotal accounts on mathematics by ordinary people and so forth were mined to ascertain the uses mathematics is put to in such sources. The uses are classified as backgrounding storylines through encryption and decryption; depictions of cleverness, dissent/avoidance and madness; rendering political commentary; and entertainment through humour. It is suggested that students should be afforded opportunities to put mathematics to use in a similar manner.
This study reports on an intervention that emanated from a concern a mathematics teacher had abou... more This study reports on an intervention that emanated from a concern a mathematics teacher had about the unsatisfactory performance of grade 12 learners in the school-based mid-year examination. The intervention was based on distributed practice and the effect size of the intervention was determined as an indicator of the effectiveness of the intervention. Different effect sizes are reported and the reasons for their acceptance or non-acceptance are presented. Overall the results indicate that if all the different effect sizes are taken into account, the intervention had a medium to high effect. Given that the intervention was driven by aspects of teaching and was done at school, it is recommended that more attention be accorded to those aspects of teaching that enhance achievement in Mathematics.
It has become a policy imperative that the training of future researchers in Education should sta... more It has become a policy imperative that the training of future researchers in Education should start at the Honours level. This training presents particular challenges as students entering the Bachelor of Education Honours (BEd Hons) programme have diverse professional backgrounds and personal motivations for pursuing the programme. Moreover, the majority of the students have fairly substantial experience in schools, one of the primary empirical sites for educational research. This diverse student profile yields several challenges in relation to the teaching of a Research Methods course. In this article, the authors reflect on their experiences of offering a BEd Hons course to induct students into research against the traditional, literature-renditioned components which comprise the practice of research in the Social Sciences. Working with the notions of critical aspects and encounters, the authors found that students experience a tension between their desire to solve their identifie...
International Journal of Science and Mathematics Education
This paper attempts to engage the field in a discussion about what mathematics is needed for stud... more This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what mathematical proficiency means in today's world and what shifts need to be made in both content and pedagogy to prepare students for 21st Century Skills and mathematical reasoning.
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