<p>Syftet med avhandlingen är att beskriva och analysera argument för matematik i grundskolan och att förstå varför och hur de officiella argumenten förändras, från de argument som återfinns i styrdokument till de argument som förs fram av undervisande matematiklärare. En utgångspunkt är att skolmatematikens villkor och verklighet kan beskrivas genom analys av officiella argument och av lärarstudenters och lärares personliga argument för matematik i grundskolan. Specifika forskningsfrågor i anslutning till syftet är:</p><p>- Vilka argument för lärarstudenten fram inför yrkesdebuten?</p><p>- Vilka argument för läraren fram under sina första år i yrket?</p><p>- Vilka beskrivningar av skolmatematikens villkor ger lärarna?</p><p>En longitudinell studie har genomförts där en grupp lärarstudenter följts genom utbildningen och under de första åren i yrket. Resultatet visar att lärarstudenter under utbildningen utvecklar en syn på matematik och matematikundervisning som stämmer väl med läroplanen och kursplanen i matematik enligt Lpo 94. De nyblivna lärarna med undervisning i matematik och NO-ämnen upplever i början av yrkeskarriären skilda villkor på olika skolor. Gemensamt för de lärare som undervisar i senare delen av grundskolan är upplevelser av krav på att ”hinna med kursen” inför det nationella provet i årskurs 9. Lärarnas mål med matematikundervisningen i grundskolan blir därför att förbereda eleverna för det nationella provet. En faktor som påverkar är kravet på att elever skall ha betyget godkänd för att vara behöriga till gymnasieskolans nationella program. De nyblivna lärarna upplever en konflikt mellan olika officiella argument för matematik i grundskolan. Faktorer som påverkar lärarnas och matematikämnets villkor och verklighet i grundskolan är bl.a. skolornas organisation i arbetslag och lärarnas kombination av undervisningsämnen.</p> / <p>The aim of this thesis is to describe and analyse arguments for mathematics in compulsory school and to understand why and how the official arguments change, from the arguments written in the national curriculum and course syllabus for mathematics to the arguments presented by mathematics teachers. The point of departure is that the conditions and the reality for school mathematics can be understood through an analysis of official arguments and of personal arguments given by teacher students and teachers. A longitudinal investigation has been carried out; a group of teacher students has been followed during their teacher education and the first three years after their professional debut. The result shows that during their education the teacher students develop a view on mathematics and mathematics education harmonizing with the goals of mathematics in the national syllabus. The novice teachers have mathematics and sciences as their teaching subjects and they experience quite different conditions when they start to work as teachers. Common for those teaching in school years 7–9 is the experience of pressure to “cover the course” before the pupils shall take the national test in school year 9. Preparing the pupils for the national test becomes the most important goal for the novice teachers. A factor influencing the mathematics teacher is the qualification requirement in mathematics from compulsory school to go into the national programs in the upper secondary school. The novice teachers experience a conflict between different goals in the national curriculum and course syllabus for mathematics. Factors that have an influence on mathematics as a school subject are the organization of teachers at the local schools and the teachers’ combination of teaching subjects.</p>

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

Syftet med avhandlingen är att beskriva och analysera argument för matematik i grundskolan och att förstå varför och hur de officiella argumenten förändras, från de argument som återfinns i styrdokument till de argument som förs fram av undervisande matematiklärare. En utgångspunkt är att skolmatematikens villkor och verklighet kan beskrivas genom analys av officiella argument och av lärarstudenters och lärares personliga argument för matematik i grundskolan. Specifika forskningsfrågor i anslutning till syftet är: - Vilka argument för lärarstudenten fram inför yrkesdebuten? - Vilka argument för läraren fram under sina första år i yrket? - Vilka beskrivningar av skolmatematikens villkor ger lärarna? En longitudinell studie har genomförts där en grupp lärarstudenter följts genom utbildningen och under de första åren i yrket. Resultatet visar att lärarstudenter under utbildningen utvecklar en syn på matematik och matematikundervisning som stämmer väl med läroplanen och kursplanen i matematik enligt Lpo 94. De nyblivna lärarna med undervisning i matematik och NO-ämnen upplever i början av yrkeskarriären skilda villkor på olika skolor. Gemensamt för de lärare som undervisar i senare delen av grundskolan är upplevelser av krav på att ”hinna med kursen” inför det nationella provet i årskurs 9. Lärarnas mål med matematikundervisningen i grundskolan blir därför att förbereda eleverna för det nationella provet. En faktor som påverkar är kravet på att elever skall ha betyget godkänd för att vara behöriga till gymnasieskolans nationella program. De nyblivna lärarna upplever en konflikt mellan olika officiella argument för matematik i grundskolan. Faktorer som påverkar lärarnas och matematikämnets villkor och verklighet i grundskolan är bl.a. skolornas organisation i arbetslag och lärarnas kombination av undervisningsämnen. / The aim of this thesis is to describe and analyse arguments for mathematics in compulsory school and to understand why and how the official arguments change, from the arguments written in the national curriculum and course syllabus for mathematics to the arguments presented by mathematics teachers. The point of departure is that the conditions and the reality for school mathematics can be understood through an analysis of official arguments and of personal arguments given by teacher students and teachers. A longitudinal investigation has been carried out; a group of teacher students has been followed during their teacher education and the first three years after their professional debut. The result shows that during their education the teacher students develop a view on mathematics and mathematics education harmonizing with the goals of mathematics in the national syllabus. The novice teachers have mathematics and sciences as their teaching subjects and they experience quite different conditions when they start to work as teachers. Common for those teaching in school years 7–9 is the experience of pressure to “cover the course” before the pupils shall take the national test in school year 9. Preparing the pupils for the national test becomes the most important goal for the novice teachers. A factor influencing the mathematics teacher is the qualification requirement in mathematics from compulsory school to go into the national programs in the upper secondary school. The novice teachers experience a conflict between different goals in the national curriculum and course syllabus for mathematics. Factors that have an influence on mathematics as a school subject are the organization of teachers at the local schools and the teachers’ combination of teaching subjects.

The purpose of this study was to investigate the nature of changes in preservice elementary mathematics teachers&rsquo / views and reflections about elementary mathematics classes based on their observations in School Experience I and School Experience II courses. Specifically, this study investigated pre-service elementary mathematics teachers&rsquo / views and reflections about instruction, assessment, and classroom management issues in elementary mathematics classes based on their observations in School Experience I and School Experience II courses. The sample consisted of 19 pre-service elementary mathematics teachers from a teacher education program at Middle East Technical University (METU). Pre-service elementary mathematics teachers involved in this study made their observations in their cooperating schools for 3 months during the spring semester of 2004-2005 academic year and the fall semester of 2007-2008 academic year. The data were collected by means of their School Experience I and School Experience II course reports. The results indicated that although there was commonality in the views and reflections of pre-service elementary mathematics teachers&rsquo / about instruction, assessment, and classroom management issues in elementary mathematics classes, there were differences in their knowledge in the way they perceive instruction, assessment, and classroom management as they progressed through their education. In other words, when School Experience I course reports were compared with School Experience II course reports, pre-service teachers perceived the mathematics instruction as more student-centered and they gave more importance to the alternative assessment strategies in their School Experience II course reports. Furthermore, they defended more positive classroom management methods in their School Experience II course reports.

Views of teaching: implications for the didactic training of mathematics teachers. School mathematics teaching is an essential learning area in South African schools. Owing to persistent traditional positivist-based views and approaches, it still suffers from a variety of teaching-learning problems. Various national attempts have already been made to develop an effective teaching-learning program for school mathematics. Prominent researchers reveal that the failure of teaching-learning programmes often have to be attributed to the lack of an underlying grounded didactic theory. Therefore this study focused on the development of a grounded teaching-theoretical framework for school mathematics teaching. A further problem regarding school mathematics is that its teaching and learning traditionally are viewed from a narrow school subject disciplinary perspective. Therefore this study departed from a general didactic-theoretical perspective, creating the opportunity to approach and solve problems from a wider angle. A constructivist-based post-positivist view of effective teaching was developed, before entering the field of school mathematics. In this way an integrated ontologicalcontextual view of teaching was developed in terms of six identified ontological essential features, and their contextual coherence, namely: intention, teacher, leamer, interaction, content and context. Contrary to traditional positivist views, no causal relationship between teaching and learning was imposed, and teaching was not qualified in terms of learning products. Instead, teaching was characterised and qualified on ontological grounds, departing from the phenomenon itself. In this way the limitations of positivist process-product views of teaching could be identified, explained and overcome. Alternatively, a dynamic integrated view of teaching as a human act, directed at the facilitation of relevant and meaningful learning, was grounded and developed. Based on this general ontological-contextually based view, a specific ontologicalcontextual view of effective school mathematics teaching was grounded and developed. To this end a variety of prominent contemporary views of and approaches to school mathematics, and its teaching and learning, needed to be analysed in a critical way. According to this analysis school mathematics, and its teaching and learning should be viewed and approached from a constructivist-based dynamic change-and-grow perspective as human acts. In addition, it could have been proved that the perspective concerned can facilitate the treatment and solving of the currently experienced teaching-learning problems. This requires the reconsideration, from a similar perspective, of the current school mathematics curriculum, as well as the preservice didactic training of mathematics teachers. Specific implications of the developed ontological-contextual view of effective school mathematics teaching were identified, and practically tested in the corresponding preservice didactic training situation in the North West Province. Based on this an integrated model for the training concerned was formulated. It was found that the current training largely contributed to the continuation of traditional views of and approaches to school mathematics teaching, and its essential features. From the developed integrated ontological-contextual perspective definitive proposals regarding the transformation of school mathematics teaching and the corresponding didactic training were made and motivated. Further areas for investigation and development, resulting from this study, were identified, as well. This study aimed at investigating, and revealing for further exploration, the specific and broadening interaction between the general teaching and subject didactical fields and research, particularly in the two contexts of effective school mathematics teaching and the corresponding preservice didactical training. A particular attempt was made to accomplish this in a grounded and integrated way, to the benefit of both fields. / Thesis (PhD)--PU for CHE, 1998.

Views of teaching: implications for the didactic training of mathematics teachers. School mathematics teaching is an essential learning area in South African schools. Owing to persistent traditional positivist-based views and approaches, it still suffers from a variety of teaching-learning problems. Various national attempts have already been made to develop an effective teaching-learning program for school mathematics. Prominent researchers reveal that the failure of teaching-learning programmes often have to be attributed to the lack of an underlying grounded didactic theory. Therefore this study focused on the development of a grounded teaching-theoretical framework for school mathematics teaching. A further problem regarding school mathematics is that its teaching and learning traditionally are viewed from a narrow school subject disciplinary perspective. Therefore this study departed from a general didactic-theoretical perspective, creating the opportunity to approach and solve problems from a wider angle. A constructivist-based post-positivist view of effective teaching was developed, before entering the field of school mathematics. In this way an integrated ontologicalcontextual view of teaching was developed in terms of six identified ontological essential features, and their contextual coherence, namely: intention, teacher, leamer, interaction, content and context. Contrary to traditional positivist views, no causal relationship between teaching and learning was imposed, and teaching was not qualified in terms of learning products. Instead, teaching was characterised and qualified on ontological grounds, departing from the phenomenon itself. In this way the limitations of positivist process-product views of teaching could be identified, explained and overcome. Alternatively, a dynamic integrated view of teaching as a human act, directed at the facilitation of relevant and meaningful learning, was grounded and developed. Based on this general ontological-contextually based view, a specific ontologicalcontextual view of effective school mathematics teaching was grounded and developed. To this end a variety of prominent contemporary views of and approaches to school mathematics, and its teaching and learning, needed to be analysed in a critical way. According to this analysis school mathematics, and its teaching and learning should be viewed and approached from a constructivist-based dynamic change-and-grow perspective as human acts. In addition, it could have been proved that the perspective concerned can facilitate the treatment and solving of the currently experienced teaching-learning problems. This requires the reconsideration, from a similar perspective, of the current school mathematics curriculum, as well as the preservice didactic training of mathematics teachers. Specific implications of the developed ontological-contextual view of effective school mathematics teaching were identified, and practically tested in the corresponding preservice didactic training situation in the North West Province. Based on this an integrated model for the training concerned was formulated. It was found that the current training largely contributed to the continuation of traditional views of and approaches to school mathematics teaching, and its essential features. From the developed integrated ontological-contextual perspective definitive proposals regarding the transformation of school mathematics teaching and the corresponding didactic training were made and motivated. Further areas for investigation and development, resulting from this study, were identified, as well. This study aimed at investigating, and revealing for further exploration, the specific and broadening interaction between the general teaching and subject didactical fields and research, particularly in the two contexts of effective school mathematics teaching and the corresponding preservice didactical training. A particular attempt was made to accomplish this in a grounded and integrated way, to the benefit of both fields. / Thesis (PhD)--PU for CHE, 1998.

Traditionally, geometry at school starts on a formal level, largely ignoring prerequisite skills needed for formal spatial reasoning. Ignoring that geometry conceptualisation has a sequential and hierarchical nature, causes ineffective teaching and learning with a long lasting inhibiting influence on spatial development and learning. One of the current reform movements in mathematics education is the appropriate use of dynamic computer technology in the teaching and learning of mathematics. Concerning mathematics education, the lecturers may involve the introduction of both dynamic computer technology and mathematics in meaningful contexts that will enable interplay between the two. Pre-service mathematics teachers (PMTs) can be encouraged to become actively involved in their learning and, therefore, less frustrated in their study orientation in mathematics. Therefore, such learning environments may be essential to enhance the conceptual understanding of PMTs. To be able to reach their eventual learners, PMTs' own conceptual understanding of geometry should be well developed. When PMTs have conceptual understanding of a mathematical procedure, they will perceive this procedure as a mathematical model of a problem situation, rather than just an algorithm. This study aimed at investigating the effect of a technologically enhanced learning environment on PMTs' understanding of geometry concepts and their study orientation in mathematics, as prerequisite for deep conceptualisation. A combined quantitative and qualitative research approach was used. The quantitative investigation employed a pre-experimental one-group pre-test post-test design. A Mayberry-type test was used to collect data with regard to PMTs' conceptualisation of geometry concepts, while the Study Orientation in Mathematics (SOM) questionnaire was used to collect data with regard their study orientation in mathematics. The qualitative investigation employed phenomenological interviews to collect supplementary information about the participating PMTs' experiences and assessment of the influence of the use of the dynamic software Geometer's Sketchpad (GSP) on their learning and conceptualisation of geometry concepts. During post-testing the participating group of PMTs achieved practically significantly higher scores in the Mayberry-type test, as well as in all fields of the SOM questionnaire. Results seem to indicate that PMTs gained significantly in the expected high levels of conceptualisation, as well as high degrees of acquisition of those levels during the intervention programme. The main conclusion of the study is that a technologically enhanced learning environment (such as GSP) can be successfully utilised to significantly enhance PMTs' conceptualisation and study orientation, as prerequisite for deep conceptualisation, in geometry. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2010.

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2010.

The study was undertaken to identify the factors that influence standard seven pupils when they choose whether to continue with mathematics at senior secondary level or not. The relative importance of the factors was also determined. The literature study identified the following factors: attitude towards mathematics, utility of mathematics, family members' influence, mathematics teacher's influence, peer group influence, achievement and gender. The empirical study dealt with the following: * A 77 item questionnaire was completed by 201 standard seven pupils. * The statistical analysis revealed significant differences between pupils who chose mathematics and those who did not, with regard to all variables except gender. * A regression analysis identified the most influential factors as achievement, family members' influence, attitude and the mathematics teacher. * The overall implications were: - Pupils be made to experience success so that their attitudes may change. - Parents must be involved in their children's education. / Psychology of Education / M. Ed. (Psychology of Education)