The failure rate in mathematics at school is high, not only in South Africa, but also internationally. Furthermore, learners with an apparently high general ability or aptitude for mathematics sometimes underachieve in the subject, while some learners with an apparently low general intellectual ability or aptitude for mathematics sometimes achieve well in the subject. Little attention is nonetheless given to learners' study orientation in mathematics, in spite of the fact that research has indicated that school mathematics is one of the best predictors of success in tertiary studies. An investigation into some epistemological approaches to the learning process in mathematics confirms that learners' achievement in mathematics is significantly affected by their study orientation in mathematics. The primary aim of this thesis was the development and evaluation of a study orientation questionnaire (SOM) in mathematics. Data processing procedures especially referred to the following two primary aims with the study: (a) Standardisation of the questionnaire. Steps carried out to evaluate the questionnaire psychometrically, include factor and item analysis. In the case of Grade 8 and 9, three fields (Study habits in mathematics, Mathematics anxiety and Study attitudes in mathematics) were identified. A fourth field, Locus of control regarding mathematics, was identified only in the case of learners in Grade 1 0 and ll. It was established that the SOM apparently has criterion related validity, as well as content and construct validity for the three language groups as a whole. Reliability coefficients for the SOM can in most cases be regarded as satisfactory. (b) Comparative studies to determine the applicability of the SOM. Analysis of variance techniques were used to determine where significant differences between groups (including grade-, mother tongue and sex groups) lay. Where MANOV AS showed significant differences, further investigation was carried out to determine in respect of which individual fields (single variables) groups differed significantly. By means of LSM it was determined which groups differed significantly in regard of the separate fields. Some of the findings include: * It seems that African language speakers in both grade groups are really trying to achieve in mathematics, but that their best efforts are not successful. * It would appear that girfs' level of Mathematics anxiety drops in Grade l 0 and ll. * Learners in Grade l 0 and ll show lower levels of Mathematics anxiety and more sufficient Study habits in mathematics than their counterparts in Grade 8 and9. * Perhaps the most significant finding is the phenomenon that African language learners in Grade l 0 and l l achieved much worse in regard of Locus of control than Afrikaans and English-speaking learners. A number of factors probably contribute towards this state of affairs, including language problems, teachers who are underqualified, African language learners' less than optimal socioeconomic status (SES) in general, a lack of facilities and text books and disruption which is still being experienced in rnnny traditionally black schools. It is recommended that these matters ·are attended to in an effort to create circumstances for more sufficient achievement in mathematics by learners from all language groups. / Thesis (PhD)--University of Pretoria, 1997. / Human Sciences Research Council (South Africa) / Psychology / PhD / Unrestricted

The focus of this research was to compare students’ and their parents’ mathematical attitudes using the Attitudes Towards Mathematics Instrument (ATMI). The sample consisted of 476 newly-enrolled students and 263 parents attending the New Student Orientation and Leadership program at a private historically black university. The sample was predominantly African American, with 96% of the students and 95% of the parents identifying themselves as African American. The ATMI total score and subscale scores of self-confidence, value, enjoyment, and motivation were explored to determine if there was a relationship between the mathematics attitudes of students enrolled at a private historically black university and their parents’. Analysis was conducted to determine if there was a relationship between the students’ mathematics academic achievement as demonstrated on the ACT/SAT by the mathematics subset score and their mathematics attitude. Additional analysis was conducted to determine if there was a relationship between students’ mathematics academic achievement as demonstrated on the ACT/SAT by the mathematics subset score and their parents’ mathematics attitude. The researcher found a statistically significant relationship between mathematics attitudes of students and their mothers as measured by the ATMI total score and subscales: self-confidence, value, enjoyment, and motivation. The researcher found a statistically significant relationship between mathematics attitudes of students and their fathers as measured by the ATMI motivation subscale. No statistically significant relationship was found between students’ mathematics academic achievement as demonstrated on the ACT/SAT by the mathematics subset score and their parents’ iv mathematics attitude total score or the subscale scores. A statistically significant relationship between students’ academic achievement and their attitudes towards mathematics total score and subscale scores: self-confidence, value, enjoyment, and motivation was found in this research. The findings of this study provide a line of research to further explore mathematics attitudes and its relationship to African American student achievement.

The target school used embedded study skills in Algebra I classes to improve attitudes toward mathematics. The purpose of this sequential, explanatory mixed-methods study was to examine the effect of embedded study-skills instruction on students' attitudes toward mathematics. Metacognitive theory was used for this study's framework. Participants were 28 Grade 9 and 10 students who repeated Algebra I. Quantitative data from the Attitudes Toward Mathematics Inventory assessed students' pre- and post-instruction attitudes toward mathematics in 4 domains. Data were analyzed using 4 independent samples t tests for students who did and did not receive embedded instruction. Qualitative data were collected through a semi structured group interview to explore 6 students' perceptions on how the intervention affected their attitudes toward mathematics. Open and axial coding strategies were used to develop themes. Quantitative results indicated no significant differences in students' attitudes toward mathematics, while qualitative findings supported the use of the intervention to develop students' positive attitudes in mathematics. A recommendation was that educators undergo professional learning opportunities to increase awareness of the impact of embedded study skills on student learning and how to use this instruction in lessons. Positive social change may occur if educators are provided with insight in embedded study skills that could improve students' attitudes toward mathematics, which ultimately may encourage students to study higher level mathematics and to pursue mathematics-based careers.

The purpose of the present study is to investigate the factors affecting mathematical literacy of 15-year-old students in Programme for International Student Assessment (PISA) across different cultural settings. The present study was conducted across three countries. These countries are Brazil, Japan and Norway. The countries were selected on the basis of their rankings in PISA 2000 study. Japan represented a high performing country with an average score of 557, Norway represented an average performing country with an average score of 499, and Brazil represented a low performing country with an average score of 334. The study explored how mathematical literacy is stimulated by predictors related to the students, the families and the school. A separate factor analysis was carried out for each questionnaire such as student questionnaire and cross curricular competencies questionnaire within the data of each country. Since the results of factor analyses of three countries were parallel, the observed variables representing the latent variables were selected from the student questionnaire and cross curricular competencies questionnaire administered in PISA 2000 in order to be used in the structural equation modeling. The included factors affecting mathematical literacy in PISA 2000 are attitudes towards reading, student-teacher relations, climate, communication with parents, usage of technology and facilities, attitudes towards mathematics and reading literacy. The proposed model was tested using structural equation modeling across three different cultures with different performance levels in PISA 2000. The findings of the study show that the latent independent variable having the strongest effect on mathematical literacy is the usage of technology and facilities in Brazil, communication with parents in Japan and attitudes towards reading in Norway. Moreover, the results were as follows: (1) Reading literacy significantly and positively influences mathematical literacy in all three countries. (2) There is a reciprocal relationship between the attitudes towards mathematics and mathematical literacy. In Brazil, the influence of attitudes towards mathematics on mathematical literacy is higher. However, the influence of mathematical literacy on attitudes towards mathematics is higher in Norway. (3) The attitudes towards reading have a negative direct effect and a positive indirect effect on mathematical literacy. (4) The student-teacher relations have a positive effect on mathematical literacy in Japan and Norway. But, in Brazil, this effect is negative. (5) The student-related factors affecting school climate are significantly and positively related to mathematical literacy in Brazil. On the other hand, the effect of climate on mathematical literacy is negative in Japan and non-significant in Norway. (6) Communication with parents significantly and positively influences the mathematical literacy in all three countries. (7) The usage of technology and facilities significantly and positively affects mathematical literacy in Brazil. However, this effect is negative in Japan and non-significant in Norway.

This research study was motivated by a hypothesis, generated on the basis of formal and informal observations, personal and professional experiences, discussions with prospective teachers and a pilot study conducted by this author; that pre-service teachers have a high level of mathematics anxiety and negative attitudes about mathematics. The primary purpose of this research was to examine the relationship between mathematics anxiety and pre-service teachers. The secondary purposes of this study were to examine the relationship between anxiety and performance and to examine the relationship between math anxiety, test anxiety, and stereotype threat. A quantitative experimental research design was used to investigate the research questions. The population consisted of prospective teachers at colleges and universities in Louisiana. The sets of data are mathematics anxiety of prospective teachers, a test anxiety inventory and a mathematics performance task. A personal data questionnaire was used to gather demographic information and attitudinal information about the participants. The implications of this study for elementary teacher education programs point to increased attention on the mathematics anxiety of pre-service teachers. This process is two-fold. One, it is recommended that pre-service teachers be made aware of their mathematics anxiety level and their attitudes about mathematics and two, it is recommended that teacher education programs acknowledge and address the importance of these affective variables and their role in pedagogy.

Orientador: Nelson Antonio Pirola / Resumo: Esta pesquisa se desenvolveu na perspectiva da Psicologia da Educação Matemática e buscou investigar o desenvolvimento do pensamento algébrico face às crenças de autoeficácia, as atitudes em relação à Matemática e ao conhecimento matemático especializado para o seu ensino nos anos iniciais do Ensino Fundamental. Buscou, também, analisar possíveis relações e influências de aspectos afetivos na solução de problemas algébricos, com foco na capacidade de generalização, cerne do desenvolvimento do pensamento algébrico. A investigação foi ancorada numa abordagem mista, quanti-qualitativa, fundamentada nos estudos de Creswell e Park (2013). Os participantes da pesquisa foram 128 estudantes do curso de Pedagogia (pre-service) de instituições privadas e 119 professores (in-service) dos anos iniciais, da rede pública de ensino. Para tanto, os instrumentos utilizados para essa investigação contaram em sua primeira etapa com um questionário para caracterização dos participantes, sendo um para os pre-service e outro para os in-service; uma Escala de Atitudes traduzida e validada por Brito (1996); um questionário estruturado em duas subescalas do tipo likert, uma sobre as crenças de autoeficácia dos participantes em relação ao conhecimento especializado para o desenvolvimento do pensamento algébrico e a outra para o ensino desse pensamento matemático nos anos iniciais. Na segunda etapa da pesquisa, foram selecionados três pre-service e três in-service considerando suas pontuações nas escal... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This research developed from the perspective of the Mathematics Education psychology and sought to investigate the algebraic thinking development in relation to the self-efficacy beliefs, attitudes towards Mathematics and specialized mathematical knowledge for its teaching in the early years of Elementary School. It also sought to analyze possible relationships and influences of affective aspects in solving algebraic problems, focusing on the generalization capacity, the core of the algebraic thinking development. The research was anchored in a mixed, quanti-qualitative approach based on the studies of Creswell and Park (2013). The participants of the study were 128 students from the pre-service pedagogy course, from private institutions and 119 teachers (in-service) from the early years of the public school system. To do so, the instruments used for this research had in their first stage a questionnaire to characterize the participants, one for pre-service and the other for in-service; a Scale of Attitudes translated and validated by Brito (1996); a questionnaire structured in two likert type subscales, one on the participants' self-efficacy beliefs regarding the specialized knowledge for the algebraic thought development and the other for the teaching of this mathematical thought in the early years. In the second stage of the research, three pre-service and three in-service were selected considering their scores on the scales (below, median and above the central point) for ... (Complete abstract click electronic access below) / Mestre

Assessment, as an integral part of teaching and learning, gained unprecedented prominence in the curriculum in South Africa post 1994. When the new curriculum was introduced, it was assumed that teachers would effortlessly adapt their teaching and assessment practices, and swiftly implement the curriculum. Fourteen years after the inception of the new curriculum, majority of teachers are still grappling with issues of assessment. Previously, there was an exclusive bias towards summative assessment, which is mainly learning product–orientated and less or no focus on the other assessment typologies such as diagnostic and formative assessment, which are learning process–orientated. Of these typologies, diagnostic assessment is not being used maximally to enhance mathematics learning and inform the nature of the interventions to attend to learners’ needs. The study focused on diagnostic assessment by investigating the impact of a particular model, GIST model, on the learning barriers and learner achievement in mathematics among the grade 9 learners. The investigation of the impact of the GIST model was done through the experimental design in four schools with class sizes of d > 40. Data were collected quantitatively through Study Orientation Questionnaire (SOM) and Mathematics Achievement Test (MAT) as well as qualitatively through interviews, observations and document analysis. The t–test and the analysis of covariance (ANCOVA) revealed that the GIST model improved the learner achievement practically significantly (d = 0.79). However, the GIST model could not mitigate the learning barriers and improve correlations between SOM and MAT. The study, however, does find grounds to conclude that the latter findings can be attributed to teachers’ lacking understanding and implementation of diagnostic assessment, in particular the GIST components. Hence, certain recommendations are posed with regard to the applicable training of teachers in order to empower them to effectively utilize diagnostic assessment and to guide learners in overcoming learning barriers in mathematics. / Thesis (Ph.D. (Mathematics Education))--North-West University, Potchefstroom Campus, 2011.

Assessment, as an integral part of teaching and learning, gained unprecedented prominence in the curriculum in South Africa post 1994. When the new curriculum was introduced, it was assumed that teachers would effortlessly adapt their teaching and assessment practices, and swiftly implement the curriculum. Fourteen years after the inception of the new curriculum, majority of teachers are still grappling with issues of assessment. Previously, there was an exclusive bias towards summative assessment, which is mainly learning product–orientated and less or no focus on the other assessment typologies such as diagnostic and formative assessment, which are learning process–orientated. Of these typologies, diagnostic assessment is not being used maximally to enhance mathematics learning and inform the nature of the interventions to attend to learners’ needs. The study focused on diagnostic assessment by investigating the impact of a particular model, GIST model, on the learning barriers and learner achievement in mathematics among the grade 9 learners. The investigation of the impact of the GIST model was done through the experimental design in four schools with class sizes of d > 40. Data were collected quantitatively through Study Orientation Questionnaire (SOM) and Mathematics Achievement Test (MAT) as well as qualitatively through interviews, observations and document analysis. The t–test and the analysis of covariance (ANCOVA) revealed that the GIST model improved the learner achievement practically significantly (d = 0.79). However, the GIST model could not mitigate the learning barriers and improve correlations between SOM and MAT. The study, however, does find grounds to conclude that the latter findings can be attributed to teachers’ lacking understanding and implementation of diagnostic assessment, in particular the GIST components. Hence, certain recommendations are posed with regard to the applicable training of teachers in order to empower them to effectively utilize diagnostic assessment and to guide learners in overcoming learning barriers in mathematics. / Thesis (Ph.D. (Mathematics Education))--North-West University, Potchefstroom Campus, 2011.