The use of investigative methods in teaching and learning primary mathematics in Lebowa schools : a case study
- Authors: Sebela, Mokgoko Petrus
- Date: 1999
- Subjects: Mathematics -- Study and teaching (Primary) -- South Africa -- Northern Province -- Case studies Mathematics -- Study and teaching (Primary) -- South Africa -- Northern Province
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1814 , http://hdl.handle.net/10962/d1003700
- Description: This is a report on research conducted in Lebowa (Northern Province) Primary Mathematics Project schools. In view of the high failure rate of matric students, the researcher believes that it is necessary that ways should be devised to improve mathematics understanding from the first level of schooling. A research study was made of constructivist and investigative teaching and learning methods as employed by teachers in a number of primary schools in the area. The researcher believes that investigative and constructivist teaching approaches produce better results than the traditional approach. He further believes that children learn better in a co-operative non-threatening classroom environment. A pilot study was made with two experimental schools and two control schools. The schools were selected from both urban and rural areas. The experimental schools are operating under the PMP and the control schools are not. The experimental schools are also supported by expert teachers called key teachers. Many of these key teachers have attended courses at Leeds University, while others have been trained locally in the theory and practice of constructivist and investigative teaching and learning. Chapter 3 illustrates clearly what is done in the Project schools. The methodology employed in the research included qUestionnaire responses from 174 teachers. Written tests by four schools (350 pupils), and interviews with 55 people, including directors of education, inspectors, principals, teachers and parents. Observations in classes were also done. Another questionnaire was given to 484 pupils. The tests were mitten on two occasions: an initial test was written during November 1993, the second year of the PMP project, while a second test was written the following year. Data collected was analysed and positive results obtained. The results from the tests indicated that pupils in experimental schools where constructivist and investigative approaches are used, perform better than those from schools where the traditional approach is still used. They indicated that children in PMP schools develop a better understanding of mathematics. This would seem to indicate that the constructivist and investigative approach to teaching produces better results than the traditional approaches. The reader will find graphs indicating the results and their analysis in Chapters 4 and 5. It is recommended by the researcher that: - Constructivist and investigative teaching and learning methods be introduced to all schools. - The services of key teachers be supported by the Department - The Department should equip all schools with the necessary materials for proper teaching and learning, or provide materials for schools to make their own teaching aids. - Teachers be involved with materials production where they are given guidance on how teaching aids can be made. - The curriculum for primary school mathematics be revised and changed, especially in view of the fact that at present it does not cater for local needs. It was planned by whites and it caters mainly for those with an European cultural background.
- Full Text:
- Date Issued: 1999
- Authors: Sebela, Mokgoko Petrus
- Date: 1999
- Subjects: Mathematics -- Study and teaching (Primary) -- South Africa -- Northern Province -- Case studies Mathematics -- Study and teaching (Primary) -- South Africa -- Northern Province
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1814 , http://hdl.handle.net/10962/d1003700
- Description: This is a report on research conducted in Lebowa (Northern Province) Primary Mathematics Project schools. In view of the high failure rate of matric students, the researcher believes that it is necessary that ways should be devised to improve mathematics understanding from the first level of schooling. A research study was made of constructivist and investigative teaching and learning methods as employed by teachers in a number of primary schools in the area. The researcher believes that investigative and constructivist teaching approaches produce better results than the traditional approach. He further believes that children learn better in a co-operative non-threatening classroom environment. A pilot study was made with two experimental schools and two control schools. The schools were selected from both urban and rural areas. The experimental schools are operating under the PMP and the control schools are not. The experimental schools are also supported by expert teachers called key teachers. Many of these key teachers have attended courses at Leeds University, while others have been trained locally in the theory and practice of constructivist and investigative teaching and learning. Chapter 3 illustrates clearly what is done in the Project schools. The methodology employed in the research included qUestionnaire responses from 174 teachers. Written tests by four schools (350 pupils), and interviews with 55 people, including directors of education, inspectors, principals, teachers and parents. Observations in classes were also done. Another questionnaire was given to 484 pupils. The tests were mitten on two occasions: an initial test was written during November 1993, the second year of the PMP project, while a second test was written the following year. Data collected was analysed and positive results obtained. The results from the tests indicated that pupils in experimental schools where constructivist and investigative approaches are used, perform better than those from schools where the traditional approach is still used. They indicated that children in PMP schools develop a better understanding of mathematics. This would seem to indicate that the constructivist and investigative approach to teaching produces better results than the traditional approaches. The reader will find graphs indicating the results and their analysis in Chapters 4 and 5. It is recommended by the researcher that: - Constructivist and investigative teaching and learning methods be introduced to all schools. - The services of key teachers be supported by the Department - The Department should equip all schools with the necessary materials for proper teaching and learning, or provide materials for schools to make their own teaching aids. - Teachers be involved with materials production where they are given guidance on how teaching aids can be made. - The curriculum for primary school mathematics be revised and changed, especially in view of the fact that at present it does not cater for local needs. It was planned by whites and it caters mainly for those with an European cultural background.
- Full Text:
- Date Issued: 1999
Domino Servite School: an evaluative case study of a private Christian secondary school in rural Natal
- Authors: Davidson, Michael R
- Date: 1996
- Subjects: Christian education -- South Africa Church schools -- South Africa Education -- South Africa -- Kwazulu Private schools -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1500 , http://hdl.handle.net/10962/d1003382
- Description: Domino Servite School (DSS) is a private school, founded in 1986, and situated on KwaSizabantu (KSB) mission station in the Natal midlands. This research into DSS is a case study which aims to present an illuminative evaluation in the Whole School genre, within that branch of educational research concerned with effective schools. The project aimed to make use of a compatibility paradigm accommodating nomothetic and anthropological data. In attempting triangulation of methodological approaches, it tried to establish the extent to which DSS may be considered an efficient and effective 'New Private' school. It also aimed to understand the school's raison d'ětre. In order to illuminate the relevance and social processes of DSS, evaluation made use of internal and external referents. The internal investigation sought to make judgements in reference to the efficiency of the school as an organisation. On the macro-level, whole school evaluation required extensive curriculum evaluation. On the micro-level, appraisal of teaching and assessment of pupil performance was undertaken. This internal investigation required a critical analysis of the school's formal, informal and hidden curriculum. The external evaluation sought to make judgement in reference to the effectiveness of DSS. On the macro-level, this required evaluation of the findings of the internal investigation in terms of a broader South African context. Implications, for example of the school's 'private' status, and its 'Christian' curriculum in respect of multi-culturalism, education for nationhood , and ethnicity were examined. The analysis of these dimensions paid attention to the school's spatial context in terms of both its 'rural' and missionary setting. Here the focus was on the school's formal curriculum. Analysis of the inter-relational context paid attention to its informal curriculum or the way in which the school deals with the commonality and diversity of its clientele and staff. The inter-relational context of the school examined the hidden curriculum, or the relationship between the school and the broader South African Community. A critical ethnographic account of this institution was therefore possible because of the dual focus on the internal and external evaluation reference points. Internal evaluation made extensive use of direct (non-participant) observation, structured and nonstructured interviews, questionnaires, and documentary analysis. Indirect (participant) observation, in particular Clinical Supervision (CS), was also used. Indirect (non-participant) observation made extensive use of Flanders' Interaction Analysis Categories (FIAC). Teacher self-evaluation was also included, while analysis of pupil performance made use of 'standardised' achievement testing and a tracer study. External evaluation required detailed study of local and international literature on issues relating to private schooling, rural and multi-cultural education, education for nationhood and ethnicity. The research found that much of the school's curriculum path is incongruous with its rural context largely because of its association with the former Department of Education and Training (DET), and because of its missionary heritage. As such the school is presently (1) located within a questionable (formal) curriculum tradition which has little relevance to, nor potential for, the transformational needs of either rural Natal or South Africa in general. However, this does not preclude the possibility of the school making a contribution to education for development in South Africa. (2) The school advocates a mono-cultural Christian value system and modified cultural pluralism which attempts to assimilate pupils from diverse socio-economic and ideologically homogeneous backgrounds. Multi-cultural education, plural values, religious and values democracy are therefore not part of the school's raison d'ětre. (3) The school, through its associated organisation Christians for Truth (CFT), represents a social view espousing either a modified cultural pluralism or multi-nationalism which allows for allegiance to a transcendent value system without compromising group. values and associations. This means that the school aims at assimilating or amalgamating diversity into a mono-cultural unity that transcends group identity. This transcendent culture is defined in Christian terms. The study recommends inter alia, further investigation into the educational implications of_values neutrality and the particularism of secular humanism; a comparative analysis of a random sample of private missionary schools and ordinary state controlled rural schools so that more generalisable results might be obtained; and a more thorough investigation into the parental and pupil contributions to the school, their attitudes and perspectives on missionary education and their feelings about the management styles evident in the organisation.
- Full Text:
- Date Issued: 1996
- Authors: Davidson, Michael R
- Date: 1996
- Subjects: Christian education -- South Africa Church schools -- South Africa Education -- South Africa -- Kwazulu Private schools -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1500 , http://hdl.handle.net/10962/d1003382
- Description: Domino Servite School (DSS) is a private school, founded in 1986, and situated on KwaSizabantu (KSB) mission station in the Natal midlands. This research into DSS is a case study which aims to present an illuminative evaluation in the Whole School genre, within that branch of educational research concerned with effective schools. The project aimed to make use of a compatibility paradigm accommodating nomothetic and anthropological data. In attempting triangulation of methodological approaches, it tried to establish the extent to which DSS may be considered an efficient and effective 'New Private' school. It also aimed to understand the school's raison d'ětre. In order to illuminate the relevance and social processes of DSS, evaluation made use of internal and external referents. The internal investigation sought to make judgements in reference to the efficiency of the school as an organisation. On the macro-level, whole school evaluation required extensive curriculum evaluation. On the micro-level, appraisal of teaching and assessment of pupil performance was undertaken. This internal investigation required a critical analysis of the school's formal, informal and hidden curriculum. The external evaluation sought to make judgement in reference to the effectiveness of DSS. On the macro-level, this required evaluation of the findings of the internal investigation in terms of a broader South African context. Implications, for example of the school's 'private' status, and its 'Christian' curriculum in respect of multi-culturalism, education for nationhood , and ethnicity were examined. The analysis of these dimensions paid attention to the school's spatial context in terms of both its 'rural' and missionary setting. Here the focus was on the school's formal curriculum. Analysis of the inter-relational context paid attention to its informal curriculum or the way in which the school deals with the commonality and diversity of its clientele and staff. The inter-relational context of the school examined the hidden curriculum, or the relationship between the school and the broader South African Community. A critical ethnographic account of this institution was therefore possible because of the dual focus on the internal and external evaluation reference points. Internal evaluation made extensive use of direct (non-participant) observation, structured and nonstructured interviews, questionnaires, and documentary analysis. Indirect (participant) observation, in particular Clinical Supervision (CS), was also used. Indirect (non-participant) observation made extensive use of Flanders' Interaction Analysis Categories (FIAC). Teacher self-evaluation was also included, while analysis of pupil performance made use of 'standardised' achievement testing and a tracer study. External evaluation required detailed study of local and international literature on issues relating to private schooling, rural and multi-cultural education, education for nationhood and ethnicity. The research found that much of the school's curriculum path is incongruous with its rural context largely because of its association with the former Department of Education and Training (DET), and because of its missionary heritage. As such the school is presently (1) located within a questionable (formal) curriculum tradition which has little relevance to, nor potential for, the transformational needs of either rural Natal or South Africa in general. However, this does not preclude the possibility of the school making a contribution to education for development in South Africa. (2) The school advocates a mono-cultural Christian value system and modified cultural pluralism which attempts to assimilate pupils from diverse socio-economic and ideologically homogeneous backgrounds. Multi-cultural education, plural values, religious and values democracy are therefore not part of the school's raison d'ětre. (3) The school, through its associated organisation Christians for Truth (CFT), represents a social view espousing either a modified cultural pluralism or multi-nationalism which allows for allegiance to a transcendent value system without compromising group. values and associations. This means that the school aims at assimilating or amalgamating diversity into a mono-cultural unity that transcends group identity. This transcendent culture is defined in Christian terms. The study recommends inter alia, further investigation into the educational implications of_values neutrality and the particularism of secular humanism; a comparative analysis of a random sample of private missionary schools and ordinary state controlled rural schools so that more generalisable results might be obtained; and a more thorough investigation into the parental and pupil contributions to the school, their attitudes and perspectives on missionary education and their feelings about the management styles evident in the organisation.
- Full Text:
- Date Issued: 1996
A classroom-based investigation into the potential of a computer-mediated criterion-referenced test as an evaluation instrument for the assessment of primary end user spreadsheet skills
- Authors: Benn, Kenneth Robert Andrew
- Date: 1994
- Subjects: Education -- Data processing Electronic spreadsheets Criterion-referenced tests Educational tests and measurements
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1447 , http://hdl.handle.net/10962/d1003328
- Description: The demand for innovative end users of information technology is increasing along with the proliferation of computer equipment within the workplace. This has resulted in increasing demands being made upon educational institutions responsible for the education of computer end users. The demands placed upon the teachers are particularly high. Large class groups and limited physical resources make the task especially difficult. One of the most time consuming, yet important, tasks is that of student evaluation. To effectively assess the practical work of information technology students requires intensive study of the storage media upon which the students'efforts have been saved. The purpose of this study was to assess the suitability of criterion-referenced testing techniques applied to the evaluation of end user computing students. Objective questions were administered to the students using Question Mark, a computer-managed test delivery system which enabled quick and efficient management of scoring and data manipulation for empirical analysis. The study was limited to the classroom situation and the assessment of primary spreadsheet skills. In order to operate within these boundaries, empirical techniques were used which enabled the timeous analysis of the students' test results. The findings of this study proved to be encouraging. Computer-mediated criterion-referenced testing techniques were found to be sufficiently reliable for classroom practice when used to assess primary spreadsheet skills. The validation of the assessment technique proved to be problematic because of the constraints imposed by normal classroom practice as well as the lack of an established methodology for evaluating spreadsheet skills. However, sufficient evidence was obtained to warrant further research aimed at assessing the use of computer-mediated criterion-referenced tests to evaluate information technology end user learning in situations beyond the boundaries of the classroom, such as a national certification examination.
- Full Text:
- Date Issued: 1994
- Authors: Benn, Kenneth Robert Andrew
- Date: 1994
- Subjects: Education -- Data processing Electronic spreadsheets Criterion-referenced tests Educational tests and measurements
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1447 , http://hdl.handle.net/10962/d1003328
- Description: The demand for innovative end users of information technology is increasing along with the proliferation of computer equipment within the workplace. This has resulted in increasing demands being made upon educational institutions responsible for the education of computer end users. The demands placed upon the teachers are particularly high. Large class groups and limited physical resources make the task especially difficult. One of the most time consuming, yet important, tasks is that of student evaluation. To effectively assess the practical work of information technology students requires intensive study of the storage media upon which the students'efforts have been saved. The purpose of this study was to assess the suitability of criterion-referenced testing techniques applied to the evaluation of end user computing students. Objective questions were administered to the students using Question Mark, a computer-managed test delivery system which enabled quick and efficient management of scoring and data manipulation for empirical analysis. The study was limited to the classroom situation and the assessment of primary spreadsheet skills. In order to operate within these boundaries, empirical techniques were used which enabled the timeous analysis of the students' test results. The findings of this study proved to be encouraging. Computer-mediated criterion-referenced testing techniques were found to be sufficiently reliable for classroom practice when used to assess primary spreadsheet skills. The validation of the assessment technique proved to be problematic because of the constraints imposed by normal classroom practice as well as the lack of an established methodology for evaluating spreadsheet skills. However, sufficient evidence was obtained to warrant further research aimed at assessing the use of computer-mediated criterion-referenced tests to evaluate information technology end user learning in situations beyond the boundaries of the classroom, such as a national certification examination.
- Full Text:
- Date Issued: 1994
Social constructivist mathematics education in a Ciskeian secondary school classroom
- Authors: Raghavan, Prasannakumary
- Date: 1994
- Subjects: Mathematics -- Curricula -- South Africa -- Ciskei -- Case studies Mathematics -- Study and teaching (Secondary) -- South Africa -- Ciskei
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1767 , http://hdl.handle.net/10962/d1003652
- Description: The researcher's experience as a high school mathematics teacher in several African countries convinced her that a good number of mathematics learners exhibit serious difficulties in conceptualising mathematics properly. Her experience in teaching the subject in the Ciskei since 1990 reinforced this conviction. The researcher's natural curiosity to probe into the causes of the poor state of mathematics education in the region served as the springboard into her investigation. Her thoughts developed in line with the emerging educational theories of social constructivism. This provided a conceptual framework for the solution of the problem, the feasibility of which was put to test practically in a Ciskeian classroom. She explicates that the difficulties experienced by the pupils in conceptualising mathematics are philosophically deep rooted and latent in the present system of mathematics education itself, which, in Ciskei, impedes the learners' conceptualisation owing to numerous problems related to their linguistic and cultural situatedness. In the analysis of the present system of mathematics education in the Ciskei she reviews a few recently published mathematics text books in the context of the topics chosen for her research study. The results of her classroom investigation establish that a possible solution to the problem lies in the social constructivist teaching approaches.
- Full Text:
- Date Issued: 1994
- Authors: Raghavan, Prasannakumary
- Date: 1994
- Subjects: Mathematics -- Curricula -- South Africa -- Ciskei -- Case studies Mathematics -- Study and teaching (Secondary) -- South Africa -- Ciskei
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1767 , http://hdl.handle.net/10962/d1003652
- Description: The researcher's experience as a high school mathematics teacher in several African countries convinced her that a good number of mathematics learners exhibit serious difficulties in conceptualising mathematics properly. Her experience in teaching the subject in the Ciskei since 1990 reinforced this conviction. The researcher's natural curiosity to probe into the causes of the poor state of mathematics education in the region served as the springboard into her investigation. Her thoughts developed in line with the emerging educational theories of social constructivism. This provided a conceptual framework for the solution of the problem, the feasibility of which was put to test practically in a Ciskeian classroom. She explicates that the difficulties experienced by the pupils in conceptualising mathematics are philosophically deep rooted and latent in the present system of mathematics education itself, which, in Ciskei, impedes the learners' conceptualisation owing to numerous problems related to their linguistic and cultural situatedness. In the analysis of the present system of mathematics education in the Ciskei she reviews a few recently published mathematics text books in the context of the topics chosen for her research study. The results of her classroom investigation establish that a possible solution to the problem lies in the social constructivist teaching approaches.
- Full Text:
- Date Issued: 1994
A classroom-based investigation into the potential of the computer spreadsheet as a learning tool within the secondary school mathematics curriculum
- Authors: Funnell, Lynette
- Date: 1992
- Subjects: Mathematics -- Computer-assisted instruction Mathematics -- Study and teaching (Secondary) Electronic spreadsheets
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1448 , http://hdl.handle.net/10962/d1003329
- Description: The influence of modern technology on education is becoming more noticeable and has implications for the curriculum and the teaching methods of mathematics. The microcomputer can be used effectively as a powerful teaching and learning aid within the mathematics classroom. This study considers the role of the computer as an aid to teachers and pupils in the teaching and learning of mathematics and shows it as having great potential. At present relatively few schools in South Africa are using the computer as a teaching aid in the mathematics classroom. The researcher proposes that some reasons are a shortage of suitable programs, the fact that few teachers have adequate skills in educative uses of the computer and most teachers are not skilled in programming techniques. Based on this assessment of the problem, spreadsheet programs related to some mathematics lessons, together with teaching notes and pupils' material have been developed. Besides describing the potential of the computer in mathematics, this study outlines the development of three spreadsheet packages and suitable teaching methodologies used for each package, and assesses an action research investigation undertaken by the researcher, teachers and pupils when using these spreadsheet packages in six classes. The findings of the investigation are most encouraging. The overall conclusion is that computer spreadsheet packages can assist the teacher in making the learning of mathematics more effective, more interesting and more enjoyable.
- Full Text:
- Date Issued: 1992
- Authors: Funnell, Lynette
- Date: 1992
- Subjects: Mathematics -- Computer-assisted instruction Mathematics -- Study and teaching (Secondary) Electronic spreadsheets
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1448 , http://hdl.handle.net/10962/d1003329
- Description: The influence of modern technology on education is becoming more noticeable and has implications for the curriculum and the teaching methods of mathematics. The microcomputer can be used effectively as a powerful teaching and learning aid within the mathematics classroom. This study considers the role of the computer as an aid to teachers and pupils in the teaching and learning of mathematics and shows it as having great potential. At present relatively few schools in South Africa are using the computer as a teaching aid in the mathematics classroom. The researcher proposes that some reasons are a shortage of suitable programs, the fact that few teachers have adequate skills in educative uses of the computer and most teachers are not skilled in programming techniques. Based on this assessment of the problem, spreadsheet programs related to some mathematics lessons, together with teaching notes and pupils' material have been developed. Besides describing the potential of the computer in mathematics, this study outlines the development of three spreadsheet packages and suitable teaching methodologies used for each package, and assesses an action research investigation undertaken by the researcher, teachers and pupils when using these spreadsheet packages in six classes. The findings of the investigation are most encouraging. The overall conclusion is that computer spreadsheet packages can assist the teacher in making the learning of mathematics more effective, more interesting and more enjoyable.
- Full Text:
- Date Issued: 1992
Making pupils think: the development of a microcomputer-inspired adaptation of the Standard 7 mathematics curriculum
- Authors: Norman, Maxie
- Date: 1992
- Subjects: Mathematics -- Study and teaching (Secondary) -- Data processing Computer-assisted instruction
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1667 , http://hdl.handle.net/10962/d1003550
- Description: This half-thesis gives an overview of the influence of the microcomputer on the way in which mathematics is done, taught and learnt. The nature of mathematics and the nature of the tutor, tool and tutee modes of microcomputer usage are discussed as background. A case is made for the use of action research methods and a classroom-based curriculum development model to facilitate innovation and the integration of the microcomputer into the mathematics classroom. A curriculum development cycle of situation analysis. planning, trial and evaluation is advocated. This approach is used to develop a microcomputer-based course aimed at enhancing the reasoning skills of standard 7 pupils. Pupils, working in groups of three, interact with the PROLOG system to build up databases of facts and rules. The microcomputer is used in tutee mode. In "teaching" this tutee, pupils discover the need for formal language and logical reasoning. Active learning is promoted by pupils' interaction with the PROLOG system and by discussions within groups. In this environment the teacher becomes a consultant and constructive critic rather than a lecturer. Findings suggest that the microcomputer plays an important role in terms of pupil motivation and that the microcomputer-based course enables pupils to experience formal language usage and logical reasoning·as relevant activities. Pupil databases provide evidence of the pupils' ability to make appropriate use of rules and to distinguish between and-conditions and or-conditions. The objective of making pupils think was largely achieved. It is recommended that the course be incorporated in the standard 1 or standard 8 curriculum to complement or replace parts of the Euclidean geometry sections as a vehicle for developing logical reasoning skills. Suggestions for the further use of the microcomputer as an investigative tool in mathematics classes and for further microcomputer-inspired courses are also made. The provision of appropriate training to enable teachers to make effective and innovative use of the microcomputer in mathematics lessons is advocated.
- Full Text:
- Date Issued: 1992
- Authors: Norman, Maxie
- Date: 1992
- Subjects: Mathematics -- Study and teaching (Secondary) -- Data processing Computer-assisted instruction
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1667 , http://hdl.handle.net/10962/d1003550
- Description: This half-thesis gives an overview of the influence of the microcomputer on the way in which mathematics is done, taught and learnt. The nature of mathematics and the nature of the tutor, tool and tutee modes of microcomputer usage are discussed as background. A case is made for the use of action research methods and a classroom-based curriculum development model to facilitate innovation and the integration of the microcomputer into the mathematics classroom. A curriculum development cycle of situation analysis. planning, trial and evaluation is advocated. This approach is used to develop a microcomputer-based course aimed at enhancing the reasoning skills of standard 7 pupils. Pupils, working in groups of three, interact with the PROLOG system to build up databases of facts and rules. The microcomputer is used in tutee mode. In "teaching" this tutee, pupils discover the need for formal language and logical reasoning. Active learning is promoted by pupils' interaction with the PROLOG system and by discussions within groups. In this environment the teacher becomes a consultant and constructive critic rather than a lecturer. Findings suggest that the microcomputer plays an important role in terms of pupil motivation and that the microcomputer-based course enables pupils to experience formal language usage and logical reasoning·as relevant activities. Pupil databases provide evidence of the pupils' ability to make appropriate use of rules and to distinguish between and-conditions and or-conditions. The objective of making pupils think was largely achieved. It is recommended that the course be incorporated in the standard 1 or standard 8 curriculum to complement or replace parts of the Euclidean geometry sections as a vehicle for developing logical reasoning skills. Suggestions for the further use of the microcomputer as an investigative tool in mathematics classes and for further microcomputer-inspired courses are also made. The provision of appropriate training to enable teachers to make effective and innovative use of the microcomputer in mathematics lessons is advocated.
- Full Text:
- Date Issued: 1992
The spiral curriculum, integrated teaching and structured learning of mathematics at the secondary level
- Authors: Alummoottil, Joseph Michael
- Date: 1990
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa Learning -- Mathematical models -- Research
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1769 , http://hdl.handle.net/10962/d1003654
- Description: The investigator's experience of teaching mathematics at a college of education since 1983 has reinforced his conviction that trainee students come to college with significant gaps, weaknesses and faults in their (mathematical) conceptual structures, probably as a result of shortcomings in the mathematics teaching to which they have been exposed. The theme of this investigation is thus a natural choice that appeared to be of immediate relevance to secondary school mathematics teaching. The analysis of the issue leads to a unified perspective: the problem is placed in a theoretical framework where Bruner [spiral curriculum], Ausubel [structured learning] and Skemp [relational understanding] are brought together. How the curriculum, textbooks and examination influence school mathematics teaching is examined in some depth and the consequences investigated. Two specific topics, viz. the generalised Pythagorean relation and absolute value are investigated in relation to published work, curriculum and textbooks, and each (topic) is presented as a unifying theme in secondary mathematics to standard 9 pupils. The classroom exercise is assessed to test the hypothesis that structured, integrated presentation around a spiral curriculum promotes "relational understanding". Analysis of results supports the hypothesis.
- Full Text:
- Date Issued: 1990
- Authors: Alummoottil, Joseph Michael
- Date: 1990
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa Learning -- Mathematical models -- Research
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1769 , http://hdl.handle.net/10962/d1003654
- Description: The investigator's experience of teaching mathematics at a college of education since 1983 has reinforced his conviction that trainee students come to college with significant gaps, weaknesses and faults in their (mathematical) conceptual structures, probably as a result of shortcomings in the mathematics teaching to which they have been exposed. The theme of this investigation is thus a natural choice that appeared to be of immediate relevance to secondary school mathematics teaching. The analysis of the issue leads to a unified perspective: the problem is placed in a theoretical framework where Bruner [spiral curriculum], Ausubel [structured learning] and Skemp [relational understanding] are brought together. How the curriculum, textbooks and examination influence school mathematics teaching is examined in some depth and the consequences investigated. Two specific topics, viz. the generalised Pythagorean relation and absolute value are investigated in relation to published work, curriculum and textbooks, and each (topic) is presented as a unifying theme in secondary mathematics to standard 9 pupils. The classroom exercise is assessed to test the hypothesis that structured, integrated presentation around a spiral curriculum promotes "relational understanding". Analysis of results supports the hypothesis.
- Full Text:
- Date Issued: 1990
Sequence in the mathematics syllabus : an investigation of the Senior Secondary Mathematics Syllabus (July 1984) of the Cape Education Department attempting to reconcile the demands of the strictly mathematical order and the developmental needs of pupils, modified by the mathematical potential of the electronic calculator : some teaching strategies resulting from new influences in the syllabus
- Authors: Breetzke, Peter Roland
- Date: 1988
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Calculators , Mathematics -- South Africa -- Outlines, syllabi, etc.
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1364 , http://hdl.handle.net/10962/d1001430
- Description: This study was motivated by the latest revision of the mathematics syllabuses of the Cape Education Department. The most important changes to content in the Senior Secondary Mathematics Syllabus (July 1984) are the introduction of calculus and linear programming, the substitution of a section on analytical geometry for vector algebra and the recall of the remainder and factor theorems. The way in which these changes were introduced left the task of integrating them into the teaching process in the hands of individual teachers. This is a task of extreme importance. If one's classroom practice is to simply plough one's way through the syllabus, one loses many opportunities to make the study of mathematics meaningful and worthwhile. Accepting the view of the spiral nature of the curriculum where one returns to concepts and procedures at increasing levels of sophistication, one needs to identify the position of topics in this spiral and to trace their conceptual foundations. Analytical geometry is in particular need of this treatment. Similarly there are many opportunities for preparing for the introduction of calculus. If the teaching of calculus is left until the last moments of the Standard 10 year without proper groundwork, the pupil will be left with little time to develop an understanding of the concepts involved. It is the advent of calculators which presents the greatest challenge to mathematics education. We ignore this challenge to the detriment of our teaching. Taken seriously calculators have the potential to exert a radical influence on the content of curricula and examinations. They bring into question the time we spend on teaching arithmetic algorithms and the priority given to algebraic manipulation. Numercial methods gain new prominence. Calculators can even breathe new life into the existing curriculum. Their computing power can be harnessed not only to carry out specific calculations but also to introduce new topics and for concept reinforcement. The purpose of this study has been to bring about a proper integration of the new sections into the existing syllabus and to give some instances of how the calculator can become an integral part of the teaching/learning process
- Full Text:
- Date Issued: 1988
- Authors: Breetzke, Peter Roland
- Date: 1988
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Calculators , Mathematics -- South Africa -- Outlines, syllabi, etc.
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1364 , http://hdl.handle.net/10962/d1001430
- Description: This study was motivated by the latest revision of the mathematics syllabuses of the Cape Education Department. The most important changes to content in the Senior Secondary Mathematics Syllabus (July 1984) are the introduction of calculus and linear programming, the substitution of a section on analytical geometry for vector algebra and the recall of the remainder and factor theorems. The way in which these changes were introduced left the task of integrating them into the teaching process in the hands of individual teachers. This is a task of extreme importance. If one's classroom practice is to simply plough one's way through the syllabus, one loses many opportunities to make the study of mathematics meaningful and worthwhile. Accepting the view of the spiral nature of the curriculum where one returns to concepts and procedures at increasing levels of sophistication, one needs to identify the position of topics in this spiral and to trace their conceptual foundations. Analytical geometry is in particular need of this treatment. Similarly there are many opportunities for preparing for the introduction of calculus. If the teaching of calculus is left until the last moments of the Standard 10 year without proper groundwork, the pupil will be left with little time to develop an understanding of the concepts involved. It is the advent of calculators which presents the greatest challenge to mathematics education. We ignore this challenge to the detriment of our teaching. Taken seriously calculators have the potential to exert a radical influence on the content of curricula and examinations. They bring into question the time we spend on teaching arithmetic algorithms and the priority given to algebraic manipulation. Numercial methods gain new prominence. Calculators can even breathe new life into the existing curriculum. Their computing power can be harnessed not only to carry out specific calculations but also to introduce new topics and for concept reinforcement. The purpose of this study has been to bring about a proper integration of the new sections into the existing syllabus and to give some instances of how the calculator can become an integral part of the teaching/learning process
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- Date Issued: 1988
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