An investigation into the extent and nature of the understanding first year college of education students have of aspects of arithematic and elementary number theory
- Authors: Oliphant, Vincent George
- Date: 1996
- Subjects: Mathematics teachers -- Training of Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1606 , http://hdl.handle.net/10962/d1003488
- Description: First Year College of Education students who have done and/or passed mathematics at matric level, often lack adequate understanding of basic mathematical concepts and principles. This is due to the fact that formal tests and examinations often fail to assess understanding at anything but a basic level. It is against this background that this study uses alternative and more direct means of assessing the level and nature of the understanding such students have of aspects of basic arithmetic and number theory. More specifically, the goals of the study are: 1. To determine the students' levels of understanding of the following number concepts: Rational numbers; Irrational numbers Real numbers and Imaginary numbers. 2. To determine whether the students understand the rules governing operations with negative numbers and with zero as principles rather than conventions. 3. To determine whether the students understand the rule governing the order of operations as a matter of convention rather than as a matter of principle. A survey of the literature concerning the nature of understanding as well as the nature of assessment is given. The students' understanding in the above areas was assessed by means of a written test followid by interviews. A sample of 50 students participated in the study while a sub-sample of 6 were interviewed. Some of the significant findings of the study were : 1. The students largely failed to draw clear distinctions between Real and Rational numbers as well as between Irrational and Imaginary numbers. 2. Very few of the students could explain the rationale behind the rules governing the. operations with negative numbers and zero. 3. Only half of the students had any knowledge of the rule governing the order of operations. Only one student demonstrated an understanding of the rule as a convention.
- Full Text:
- Date Issued: 1996
- Authors: Oliphant, Vincent George
- Date: 1996
- Subjects: Mathematics teachers -- Training of Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1606 , http://hdl.handle.net/10962/d1003488
- Description: First Year College of Education students who have done and/or passed mathematics at matric level, often lack adequate understanding of basic mathematical concepts and principles. This is due to the fact that formal tests and examinations often fail to assess understanding at anything but a basic level. It is against this background that this study uses alternative and more direct means of assessing the level and nature of the understanding such students have of aspects of basic arithmetic and number theory. More specifically, the goals of the study are: 1. To determine the students' levels of understanding of the following number concepts: Rational numbers; Irrational numbers Real numbers and Imaginary numbers. 2. To determine whether the students understand the rules governing operations with negative numbers and with zero as principles rather than conventions. 3. To determine whether the students understand the rule governing the order of operations as a matter of convention rather than as a matter of principle. A survey of the literature concerning the nature of understanding as well as the nature of assessment is given. The students' understanding in the above areas was assessed by means of a written test followid by interviews. A sample of 50 students participated in the study while a sub-sample of 6 were interviewed. Some of the significant findings of the study were : 1. The students largely failed to draw clear distinctions between Real and Rational numbers as well as between Irrational and Imaginary numbers. 2. Very few of the students could explain the rationale behind the rules governing the. operations with negative numbers and zero. 3. Only half of the students had any knowledge of the rule governing the order of operations. Only one student demonstrated an understanding of the rule as a convention.
- Full Text:
- Date Issued: 1996
The pre-service preparation of secondary school mathematics teachers: a case study of curriculum effectiveness
- Authors: Msomi, Dumile Dennis
- Date: 1995
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Curricula Mathematics teachers -- Training of -- South Africa -- KwaZulu-Natal -- Esikhawini College of Education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1711 , http://hdl.handle.net/10962/d1003594
- Description: The quality of education in most historically black schools is a source of concern for many people. The high failure rate in mathematics in particular, is believed to result in part, from the inadequacy of the teacher preparation programs at many of the colleges of education in the country. Esikhawini College of Education in KwaZulu-Natal is one of the colleges which is involved in the preparation of secondary school mathematics teachers. The appropriateness of the mathematics curriculum of this College was the subject of the study. In particular, the study aimed at the following: (i) To analyse aims and philosophies underlying the prescribed mathematics curriculum of the College. (ii) To establish the teacher educators' and student teachers' perceptions of the appropriateness of the curriculum in general. (iii) To establish the teacher educators' and student teachers' perceptions of the mathematics curriculum content and processes. (iv) To establish the quality of available materials used at the College for realisation of the curriculum goals. (v) To offer proposals and recommendations for the improvement of the education of prospective secondary mathematics teachers. Data about the perceptions of the appropriateness of the mathematics curriculum was gathered through a questionnaire which was administered to one hundred and one student teachers. The issues that arose from the questionnaire study were followed up by an interview study. The interview schedule was administered to a sample of fourteen student teachers and all six mathematics teacher educators in the College. In addition, a survey of mathematics materials available at the College library and in the mathematics department was carried out to collect further data. Some of the significant findings of the, study were : • Limitations in the College mathematics curriculum in as far as the curriculum content and processes were concerned. • Inadequacy of mathematics curriculum materials that were available and used at the College. • Low attainment in mathematics at matriculation level of most of the student teachers. • Widespread dissatisfaction with the curriculum, especially that of Mathematics Didactics. The implications of the findings for the College were considered. Amongst other suggestions is the suggestion that the College introduces a preliminary STD course in which prospective student teachers' mathematics background is enriched to enable them to cope with the demands of the College curriculum.
- Full Text:
- Date Issued: 1995
- Authors: Msomi, Dumile Dennis
- Date: 1995
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Curricula Mathematics teachers -- Training of -- South Africa -- KwaZulu-Natal -- Esikhawini College of Education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1711 , http://hdl.handle.net/10962/d1003594
- Description: The quality of education in most historically black schools is a source of concern for many people. The high failure rate in mathematics in particular, is believed to result in part, from the inadequacy of the teacher preparation programs at many of the colleges of education in the country. Esikhawini College of Education in KwaZulu-Natal is one of the colleges which is involved in the preparation of secondary school mathematics teachers. The appropriateness of the mathematics curriculum of this College was the subject of the study. In particular, the study aimed at the following: (i) To analyse aims and philosophies underlying the prescribed mathematics curriculum of the College. (ii) To establish the teacher educators' and student teachers' perceptions of the appropriateness of the curriculum in general. (iii) To establish the teacher educators' and student teachers' perceptions of the mathematics curriculum content and processes. (iv) To establish the quality of available materials used at the College for realisation of the curriculum goals. (v) To offer proposals and recommendations for the improvement of the education of prospective secondary mathematics teachers. Data about the perceptions of the appropriateness of the mathematics curriculum was gathered through a questionnaire which was administered to one hundred and one student teachers. The issues that arose from the questionnaire study were followed up by an interview study. The interview schedule was administered to a sample of fourteen student teachers and all six mathematics teacher educators in the College. In addition, a survey of mathematics materials available at the College library and in the mathematics department was carried out to collect further data. Some of the significant findings of the, study were : • Limitations in the College mathematics curriculum in as far as the curriculum content and processes were concerned. • Inadequacy of mathematics curriculum materials that were available and used at the College. • Low attainment in mathematics at matriculation level of most of the student teachers. • Widespread dissatisfaction with the curriculum, especially that of Mathematics Didactics. The implications of the findings for the College were considered. Amongst other suggestions is the suggestion that the College introduces a preliminary STD course in which prospective student teachers' mathematics background is enriched to enable them to cope with the demands of the College curriculum.
- Full Text:
- Date Issued: 1995
'n Ondersoek na die aanwending van 'n enkele mikrorekenaar in die klaskamer as hulpmiddel vir die onderrig van wiskunde in die sekondere skool
- Authors: Mostert, Marthinus Petrus
- Date: 1992
- Subjects: Education, Secondary -- South Africa -- Computer-assisted instruction Mathematics -- Study and teaching (Secondary) -- Data processing Computer-assisted instruction -- South Africa Educational technology -- South Africa
- Language: Afrikaans
- Type: Thesis , Masters , MEd
- Identifier: vital:1679 , http://hdl.handle.net/10962/d1003562
- Description: Suppes beweer dat "All teachers everywhere recognise the help that books give them in teaching students. The day is coming when computers will receive the same recognition. Teachers look on computers as a new and powerful tool for helping them to teach their students more effectively." In hierdie ondersoek word gepoog om op die voordele van die aanwending van een mikrorekenaar as hulpmiddel vir die onderwyser vir die onderrig van wiskunde, te wys. Die belangrikste oorwegings in die ondersoek was: 1. Efektiwiteit van die metode. 2. Bekostigbaarheid van die metode. Die effektiwiteit van hierdie metode van onderrig word hoofsaaklik bepaal deur die geskiktheid van die programmatuur. Programmeringsvaardighede aan die kant van onderwysopgeleide persone versterk hierdie oorweging. Deurdat slegs een mikrorekenaar gebruik word, word deels aan die tweede oorweging, naamllk bekostigbaarheld, voldoen. Programmeringsvaardighede, soos hierbo genoem, kan ook bydra tot die besparing van koste deurdat bogenoemde programmatuur 'intern' ontwikkel word. Die wens word uitgespreek dat hierdie metode van onderrig tot voordeel van die totale leerlingbevolking van die land aangewend sal kan word.
- Full Text:
- Date Issued: 1992
- Authors: Mostert, Marthinus Petrus
- Date: 1992
- Subjects: Education, Secondary -- South Africa -- Computer-assisted instruction Mathematics -- Study and teaching (Secondary) -- Data processing Computer-assisted instruction -- South Africa Educational technology -- South Africa
- Language: Afrikaans
- Type: Thesis , Masters , MEd
- Identifier: vital:1679 , http://hdl.handle.net/10962/d1003562
- Description: Suppes beweer dat "All teachers everywhere recognise the help that books give them in teaching students. The day is coming when computers will receive the same recognition. Teachers look on computers as a new and powerful tool for helping them to teach their students more effectively." In hierdie ondersoek word gepoog om op die voordele van die aanwending van een mikrorekenaar as hulpmiddel vir die onderwyser vir die onderrig van wiskunde, te wys. Die belangrikste oorwegings in die ondersoek was: 1. Efektiwiteit van die metode. 2. Bekostigbaarheid van die metode. Die effektiwiteit van hierdie metode van onderrig word hoofsaaklik bepaal deur die geskiktheid van die programmatuur. Programmeringsvaardighede aan die kant van onderwysopgeleide persone versterk hierdie oorweging. Deurdat slegs een mikrorekenaar gebruik word, word deels aan die tweede oorweging, naamllk bekostigbaarheld, voldoen. Programmeringsvaardighede, soos hierbo genoem, kan ook bydra tot die besparing van koste deurdat bogenoemde programmatuur 'intern' ontwikkel word. Die wens word uitgespreek dat hierdie metode van onderrig tot voordeel van die totale leerlingbevolking van die land aangewend sal kan word.
- Full Text:
- Date Issued: 1992
An investigation into the role that knowledge of the nature of mathematics and other factors play in determining motivation for further study of mathematics after std 7 in selected provincial secondary schools
- Authors: Arguile, David Ian
- Date: 1988
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1352 , http://hdl.handle.net/10962/d1001418
- Description: This study involves an investigation into reasons why pupils continue with mathematics after Std 7. The sample, consisting of Std 8 and Std 10 mathematics pupils at six academic, English-medium high schools in Port Elizabeth, had to complete a short questionnaire during the third term of 1985. It was found that most pupils continue with mathematics because of requirements for certain post-matric courses, to improve their career options and for other reasons classified in this investigation as "extrinsic", i.e. reasons that are not directly related to the nature of mathematics. An attempt is made to determine the extent of the pupils' knowledge of the nature of mathematics. Questions relating to the nature of mathematics are poorly answered by almost all of the pupils, thereby suggesting that this aspect of mathematics is sadly neglected in mathematics courses. The suggestion is made that this lack of knowledge of the nature of mathematics is linked to pupils' decisions to continue with the subject. The conclusion is drawn that unless more attention is given to conveying to pupils something of the nature of mathematics, there will be an increasing proportion of pupils who choose to continue with mathematics for the "wrong" reasons. This, in turn, has possible negative implications for mathematics education in general. Attention is also paid to differences re the above in respect of groupings based on standard, mathematical grade, sex, mathematical achievement and type of schooling. Although no conclusive findings are made other than with regard to specific questions, enough evidence of differences in certain of the groupings is produced to warrant further investigation
- Full Text:
- Date Issued: 1988
- Authors: Arguile, David Ian
- Date: 1988
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1352 , http://hdl.handle.net/10962/d1001418
- Description: This study involves an investigation into reasons why pupils continue with mathematics after Std 7. The sample, consisting of Std 8 and Std 10 mathematics pupils at six academic, English-medium high schools in Port Elizabeth, had to complete a short questionnaire during the third term of 1985. It was found that most pupils continue with mathematics because of requirements for certain post-matric courses, to improve their career options and for other reasons classified in this investigation as "extrinsic", i.e. reasons that are not directly related to the nature of mathematics. An attempt is made to determine the extent of the pupils' knowledge of the nature of mathematics. Questions relating to the nature of mathematics are poorly answered by almost all of the pupils, thereby suggesting that this aspect of mathematics is sadly neglected in mathematics courses. The suggestion is made that this lack of knowledge of the nature of mathematics is linked to pupils' decisions to continue with the subject. The conclusion is drawn that unless more attention is given to conveying to pupils something of the nature of mathematics, there will be an increasing proportion of pupils who choose to continue with mathematics for the "wrong" reasons. This, in turn, has possible negative implications for mathematics education in general. Attention is also paid to differences re the above in respect of groupings based on standard, mathematical grade, sex, mathematical achievement and type of schooling. Although no conclusive findings are made other than with regard to specific questions, enough evidence of differences in certain of the groupings is produced to warrant further investigation
- Full Text:
- Date Issued: 1988
A preliminary investigation into the use of computers in the teaching of mathematics
- Van Hille, Gilles Ernst Willem
- Authors: Van Hille, Gilles Ernst Willem
- Date: 1986
- Subjects: Mathematics -- Computer-assisted instruction Mathematics -- Study and teaching (Secondary) -- Data processing Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1844 , http://hdl.handle.net/10962/d1004382
- Description: Like many South African high school mathematics teachers I have followed the development of computers with interest and I have tried wherever possible to gain some experience on them. Thus when microcomputers became more readily available the mathematics department at our school, Graeme College in Grahamstown, motivated for the school to acquire this powerful new tool. The eventual outcome was that the Old Boys' Association donated to the school 3 BBC B microcomputers with monitors, a disc drive, a printer and two tape recorders. These have now been in the school for three years. The acquisition prompted this research project which takes the following form:- 1) An investigation into some of the uses of microcomputers in schools and, in particular, in the mathematics classroom. 2) A statement on the present position adopted by the Cape Education Department on the use of computers in schools. 3) A study of what the experience has been in other countries, particularly in Britain and the United States of America. 4) A description of an investigation which was undertaken at our school using the method of Action Research and Triangulation. Its aim was to investigate the feasibility of using a microcomputer to aid in the teaching of mathematics and the reaction of the pupils to this innovation. Three different approaches were implemented. a) The algorithmic approach: In this investigation a class of standard eight pupils were required, with the help of the teacher, to write, enter and test a short computer program which would solve any pair of simultaneous linear equations of the form, ax + by = c. Their reaction to this form of instruction was noted by myself and a non-participant observer. The pupils themselves were also asked to express their reactions, both verbally and by filling in a prepared questionnaire. Examples of worksheets, exam questions and analysed questionnaires are given in the appendix. Short programs which examine various other mathematical concepts are also listed and discussed. b) The audio-visual approach: In this case use was made of a graphs software package in which the computer would draw either a straight line, circle, parabola or hyperbola when the appropriate variables were entered. This package also includes a graph game facility where participants are required to find the equation of the graph which will pass through three given points. Points are awarded if the correct type of graph is chosen and the variables are entered within a certain time interval. The pupils involved in this investigation were standard eight higher grade mathematics pupils and their reaction to this form of instruction was again noted using the methods described in (a) above. c) Computer Aided Instruction: Here I was most fortunate to be able to make use of the Rhodes University PLATO Centre. This allowed me to take a class of eighteen standard eight higher grade mathematics pupils to the Centre. Here during four sessions, each of just over an hour, the pupils interacted with the software on the computer terminal. The software used was a set of five lessons written by Barbara Lederman of the Community College Maths Group, of the University of Illinois in 1976. The lessons give instruction and require the pupils to transform, plot and draw the graphs of linear equations of the form, ax + by + c = 0, x = c and y = b. They are also taught and required to find the equations of given straight lines. Their reactions to this form of instruction are discussed after each session. 5) In conclusion some thoughts are given on how computers can best be utilised in the school situation, with particular reference to the teaching of mathematics.
- Full Text:
- Date Issued: 1986
- Authors: Van Hille, Gilles Ernst Willem
- Date: 1986
- Subjects: Mathematics -- Computer-assisted instruction Mathematics -- Study and teaching (Secondary) -- Data processing Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1844 , http://hdl.handle.net/10962/d1004382
- Description: Like many South African high school mathematics teachers I have followed the development of computers with interest and I have tried wherever possible to gain some experience on them. Thus when microcomputers became more readily available the mathematics department at our school, Graeme College in Grahamstown, motivated for the school to acquire this powerful new tool. The eventual outcome was that the Old Boys' Association donated to the school 3 BBC B microcomputers with monitors, a disc drive, a printer and two tape recorders. These have now been in the school for three years. The acquisition prompted this research project which takes the following form:- 1) An investigation into some of the uses of microcomputers in schools and, in particular, in the mathematics classroom. 2) A statement on the present position adopted by the Cape Education Department on the use of computers in schools. 3) A study of what the experience has been in other countries, particularly in Britain and the United States of America. 4) A description of an investigation which was undertaken at our school using the method of Action Research and Triangulation. Its aim was to investigate the feasibility of using a microcomputer to aid in the teaching of mathematics and the reaction of the pupils to this innovation. Three different approaches were implemented. a) The algorithmic approach: In this investigation a class of standard eight pupils were required, with the help of the teacher, to write, enter and test a short computer program which would solve any pair of simultaneous linear equations of the form, ax + by = c. Their reaction to this form of instruction was noted by myself and a non-participant observer. The pupils themselves were also asked to express their reactions, both verbally and by filling in a prepared questionnaire. Examples of worksheets, exam questions and analysed questionnaires are given in the appendix. Short programs which examine various other mathematical concepts are also listed and discussed. b) The audio-visual approach: In this case use was made of a graphs software package in which the computer would draw either a straight line, circle, parabola or hyperbola when the appropriate variables were entered. This package also includes a graph game facility where participants are required to find the equation of the graph which will pass through three given points. Points are awarded if the correct type of graph is chosen and the variables are entered within a certain time interval. The pupils involved in this investigation were standard eight higher grade mathematics pupils and their reaction to this form of instruction was again noted using the methods described in (a) above. c) Computer Aided Instruction: Here I was most fortunate to be able to make use of the Rhodes University PLATO Centre. This allowed me to take a class of eighteen standard eight higher grade mathematics pupils to the Centre. Here during four sessions, each of just over an hour, the pupils interacted with the software on the computer terminal. The software used was a set of five lessons written by Barbara Lederman of the Community College Maths Group, of the University of Illinois in 1976. The lessons give instruction and require the pupils to transform, plot and draw the graphs of linear equations of the form, ax + by + c = 0, x = c and y = b. They are also taught and required to find the equations of given straight lines. Their reactions to this form of instruction are discussed after each session. 5) In conclusion some thoughts are given on how computers can best be utilised in the school situation, with particular reference to the teaching of mathematics.
- Full Text:
- Date Issued: 1986
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