The poor mathematics achievement of South African learners is a great shock and reason for concern in our country. The question is asked why the learners achieve so poorly and whether something can be done to improve learners’ mathematics achievement. Research has shown that the field of study orientation is a primary factor for learners’ mathematics achievement. A positive study orientation towards Mathematics has a great influence on the positive achievement of learners in Mathematics. The use of metacognition has also been found to improve learners’ mathematics achievement and their ability to solve problems. It has been decided to find the relationship between learners’ study orientation and metacognition and to determine what the influence of the relationship is on learner's mathematics achievement. Learners’ study orientation is identified as six fields that have an influence on learner's mathematics achievement. The fields are learners’ study attitude in Mathematics, Mathematics anxiety, study habits in Mathematics, problem solving behaviour in Mathematics, study milieu (social, physical well-being and classroom atmosphere) in Mathematics and information processing in Mathematics. Metacognition is described as the learners’ thoughts concerning their own thinking and is divided in two separate components: • Metacognitive knowledge: it addresses the questions of what you know, how you think, when and where to use certain strategies. Metacognitive knowledge consists of strategic knowledge, knowledge of cognitive tasks and self-knowledge. • Self-management: self-management is 'metacognition in action' and learners use it to effectively apply the metacognitive knowledge. Self-management consists of prediction, planning, monitoring and evaluation. The study population comprise of Grade 7-learners in the Potchefstroom district. The schools that participated in the study serve learners from different socioeconomic backgrounds (ex-Model C, multicultural, township, farm and learners living in the township but their school is in an affluent environment. The sample was chosen from an expedient sample. The study consists of a quantitative research as well as a qualitative research. The quantitative research was conducted by making use of the study orientation questionnaire in Mathematics, a metacognitive questionnaire and a mathematics achievement questionnaire for Grade 7. The average of the high achievement learners as well the low achievement learners were determine, intercorrelations between the variables and a regression analysis has been done to find out which fields is a good predictor for mathematics achievement. The qualitative research was conducted, using interviews. The Mathematics teachers (involved in the learner's teaching and learning), high achievement learners and low achievement learners where interviewed. The interviews were interpreted and combined with the qualitative research findings. The study found that both a positive study orientation and use of metacognition in Mathematics can enhance learners’ mathematics achievement. High achieving learners are better orientated towards Mathematics and make use of metacognition in a greater extent than learners that achieve poorly in mathematics. In general learners have a positive attitude towards Mathematics and their study milieu is positive. It has been found that learner's orientation toward study habits is weak and their problem solving behaviour is weak also, especially with solving non routine problems. Out of the correlations it was found that learners which experience a high level of mathematics anxiety and a negative study milieu make less use of metacognition than learners that experience less mathematics anxiety and have a positive study milieu. There is a relationship between metacognition and study-orientation and this relationship has an influence on learners’ mathematics achievement. Recommendations were made concerning metacognition and study orientation. In order to enhance learners’ mathematics achievement, it is necessary to improve their use of metacognition and study orientation towards mathematics / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006

Les performances en mathématiques sont associées à de nombreux enjeux dans notre société, des enjeux de nature individuelle et des enjeux de nature sociétale. Malgré le fait que les élèves québécois réussissent très bien sur la scène internationale en mathématiques, dans le cadre des évaluations à grande échelle en éducation, les analyses selon le genre, elles, font état d’écarts préoccupants. En effet, à plusieurs des cycles de ces grandes enquêtes, les filles ont obtenu des résultats statistiquement inférieurs à ceux des garçons. L’anxiété mathématique, pourrait expliquer, à tout le moins en partie, les écarts de performances observés entre les filles et les garçons (Stoet et al., 2016). En effet, les recherches menées sur le sujet depuis les années 70 révèlent que, de manière générale, chez les adolescents et les adultes, les filles ont tendance à se dire davantage anxieuses à l’égard des mathématiques que les garçons (p.ex. Else-Quest et al., 2010; Hyde et al., 1990; Stoet et al. 2016). Également, dans ces mêmes groupes d’âge, une corrélation linéaire négative est observée entre le niveau d’anxiété mathématique des individus et leurs performances en mathématiques (p.ex. Barroso et al.,2021; Hembree, 1990; Ma, 1999; Zhang et al., 2019). En 2003 et en 2012, le PISA s’est intéressé à l’anxiété mathématique. En effet, comme les mathématiques ont constitué le domaine majeur d’évaluation lors de ces deux enquêtes, l’anxiété mathématique a été documentée, à ces occasions, au même titre que bon nombre d’autres facteurs non-cognitifs liés aux performances dans le domaine. Le portrait canadien, issu du PISA de 2003 et de 2012, supporte et renforce l’idée selon laquelle l’anxiété mathématique pourrait contribuer aux écarts de performance observés entre les garçons et les filles, en mathématiques, au Québec. Devant l’absence de portrait québécois en regard du phénomène, et souhaitant, à terme, fournir des leviers en vue de réduire les écarts de performances observés entre les filles et les garçons québécois, nous énonçons l’objectif général de recherche comme suit : quantifier les écarts d’anxiété mathématique entre les filles et les garçons, étudier le lien anxiété mathématique/performances en mathématiques et ensuite, identifier des facteurs ayant le potentiel de réduire les écarts d’anxiété mathématique observés, chez les élèves québécois francophones de 15 ans, à partir d’une analyse secondaire des données du PISA de 2003 et de 2012. Afin de répondre à cet objectif général de recherche, nous définissons trois objectifs spécifiques de recherche. Chacun d’eux est traité dans un des trois articles de cette thèse par articles. Le premier objectif spécifique de notre recherche vise à identifier les considérations méthodologiques inhérentes aux données issues du PISA et à proposer des techniques d’analyse qui permettent de les traiter, adéquatement. Cet objectif spécifique est traité dans le premier article, un article de nature méthodologique. Les deuxième objectif spécifique de notre recherche vise à quantifier les écarts d’anxiété mathématique entre les garçons et les filles francophones de 15 ans du Québec, à partir d’une analyse secondaire des données du PISA de 2003 et de 2012, et à étudier le lien négatif anxiété mathématique/performances en mathématiques, chez ces mêmes élèves. Cet objectif spécifique est traité dans le second article de la thèse, un article de nature empirique, qui prend appui sur les fondements méthodologiques proposés dans l’article 1. Le troisième objectif spécifique de notre recherche vise à identifier des facteurs qui permettent d’expliquer les écarts d’anxiété mathématique observés entre les garçons et les filles francophones du Québec et qui ont le potentiel de guider, à terme, la mise en œuvre d’interventions visant à réduire les écarts observés. Répondre à cet objectif spécifique fait l’objet du troisième article de la thèse. Cet article prend également appui sur les fondements méthodologiques exposés dans l’article 1. Des résultats issus de l’article 2, il ressort que : 1) en moyenne, les filles francophones de 15 ans du Québec font état d’un niveau d’anxiété mathématique statistiquement plus élevé que les garçons et 2) le lien entre l’anxiété mathématique et les performances en mathématiques est un lien négatif et équivalent entre les garçons et les filles francophones du Québec. Des résultats issus de l’article 3, il ressort que les écarts d’anxiété mathématique observés entre les filles et les garçons québécois francophones ayant participé au PISA de 203 et de 2012 pourraient s’expliquer par : 1) un concept de soi en mathématiques plus faible chez les filles et 2) un lien direct genre/anxiété mathématique. Des implications scientifiques et pratiques de ces résultats découlent des recommandations en vue de réduire les écarts d’anxiété mathématique observés entre les filles et les garçons francophones du Québec, de même que des avenues de recherche à explorer dans le futur. Ces recommandations et avenues de recherches sont présentées au terme de la thèse. / Performance in mathematics is linked to a number of issues in our society, both individual and societal. Even though Quebec students are doing very well internationally in mathematics, in large-scale educational assessments, gender-based analyses reveal disturbing gaps. Over the course of several cycles of these large-scale surveys, girls achieved statistically lower results than boys. Mathematics anxiety could at least partially explain the performance gaps observed between girls and boys (Stoet et al., 2016). Indeed, research conducted since the 1970s has shown that, in general, in adolescents and adults, girls tend to report greater anxiety about mathematics than boys (e.g.Else-Quest et al., 2010; Hyde et al., 1990; Stoet et al. 2016). Furthermore, in these same age groups, there is a negative linear correlation between individuals' level of anxiety in mathematics and their performance in mathematics (e.g.Hembree, 1990; Ma, 1999; Zhang et al., 2019). In 2003 and 2012, PISA turned its attention to mathematics anxiety. Indeed, since mathematics was the main domain of assessment in both surveys, mathematical anxiety was documented on these occasions, along with many other non-cognitive factors related to performance in the domain. The Canadian portrait, from both the 2003 and 2012 PISA surveys, supports and reinforces the idea that mathematics anxiety could explain, at least in part, the observed performance gaps between boys and girls in mathematics in Quebec. Given the absence of a Quebec portrait of the phenomenon, and wishing, in the long run, to provide levers for reducing the observed performance gaps between Quebec girls and boys, we state the general research objectives as follows: 1) quantify the gaps between girls and boys with respect to mathematics anxiety, 2) study the link between mathematics anxiety and mathematical performance, and finally 3) identify factors that may reduce the gaps observed in mathematical anxiety among 15-year-old French-speaking students in Québec, based on a secondary analysis of the 2003 and 2012 PISA data. 7 In order to meet this overall research objective, three specific research objectives are identified. Each of these is discussed in one of the three articles of the present thesis per article. The first specific objective of our research is to identify the methodological considerations inherent to the PISA data and to propose analytical techniques that will allow us to adequately address them. This specific objective is discussed in the first article, a methodology article. The second specific objective of our research is to quantify the differences in mathematical anxiety between 15-year-old French-speaking boys and girls in Quebec, based on a secondary analysis of the 2003 and 2012 PISA data, and to investigate the negative relation between mathematical anxiety and mathematical performance in these same students. This specific objective is discussed in the second article of the thesis, an empirical article, which is based on the methodological bases proposed in Article 1. The third specific objective of our research is to identify factors that contribute to explaining the differences observed in mathematical anxiety between French-speaking boys and girls in Quebec and have the potential to guide, over the long run, the implementation of interventions aimed at reducing the observed gaps. The third paper in the thesis focuses on this specific objective. This article is also based on the methodological bases set out in Article 1. The results of Article 2 show that: 1) on average, French-speaking 15-year-old girls in Quebec report a statistically higher level of mathematical anxiety than boys and 2) the relationship between mathematical anxiety and mathematical performance is negative and equivalent between French-speaking boys and girls in Quebec. From the results of Article 3, it appears that the differences in mathematical anxiety observed between Quebec French-speaking girls and boys who participated in PISA 2003 and 2012 can be explained by: 1) a lower perception of mathematical competence among girls and 2) a direct gender/mathematical anxiety link. The scientific and practical implications of these results lead to recommendations to reduce the differences observed in mathematical anxiety among French-speaking girls and boys in Quebec, as well as lines of future research. These recommendations and lines of research are presented at the end of the thesis.

本研究運用PISA 2003資料庫為例，說明數學焦慮之認知與情意，如何影響學生數學內在動機、自我概念與成就的機制。本研究的研究對象，為香港十五歲學生，並採取整列剔除法（listwise deletion）刪除作答不全的缺失值與極端值，共計取得有效樣本為4,397人，其中男生2,168位，女生2,229位。研究結果顯示：第一、數學焦慮之認知與情意模式獲得驗證；第二、數學焦慮之認知與情意除了直接影響數學成就之外，還能經由數學內在動機與自我概念，對數學成就產生間接影響。 / The purpose of the present study was to assess the influence of mathematics anxiety (including the cognitive and affective dimensions), mathematics intrinsic motivation, and mathematics self-concept on mathematics achievement. Participants were 4,397 9th-grade students from Hong Kong who attended PISA 2003 study. The results of confirmatory factor analyses supported the theoretical distinction between cognitive and affective dimensions of mathematics anxiety. The analysis of structural equation modeling confirmed that the cognitive and affective dimensions of mathematics anxiety can predict mathematics achievement through the mediating effect of mathematics intrinsic motivation and mathematics self-concept.

為瞭解國民中小學學生學習電腦相關行為及現況,本研究以台北市國民中學三年級學生1251人及國小六年級學生1201人為研究對象,經運用電腦經驗調查表.認知需求量表.數學焦慮量表.電腦態度量表及電腦素養測驗卷等研究工具,獲得所需的資料,再以chi-square考驗.皮爾遜積差相關. t-test.典型相關.多元(逐步)迴歸及因徑分析等方法進行統計分析,結果 有以下幾點發現: 一. 國民中小學學生電腦經驗.電腦資源.電腦態度與電腦素養現況方面 1. 國中與國小學生之電腦經驗有顯著的差異存在. 2. 國中與國小學生之電腦資源部份有顯著的差異. 3. 國中與國小男女學生之電腦經驗部份有顯著的差異存在. 4. 國中與國小男女學生之電腦資源部份有顯著的差異存在. 5. 國中學生與國小學生在電腦焦慮與電腦有用性兩電腦態度上有顯著差異. 6. 國民中小學男學生之電腦態度(焦慮與自信)顯著較女生好. 7. 國中學生之電腦素養(軟硬體.應用與影響.操作.倫理)顯著較國中學生佳. 8. 國民中小學男學生之電腦素養(軟硬體.應用與影響.操作)顯著較女生佳. 二. 影響國中小學生電腦態度方面 1. 電腦經驗與國中小學生之電腦態度有顯著之正相關. 2. 電腦資源與國中小學生之電腦態度有顯著之正相關. 3.認知需求與國中小學生之電腦態度有顯著之正相關. 4. 數學焦慮與國中小學生之電腦態度有顯著之相關. 5. 數學成就與國中小學生之電腦態度有顯著之正相關. 6. 認知需求.每星期使用電腦的時間.每星期閱讀電腦書籍及雜誌的.家中電腦週邊設備的情形.自己或與他人共同使用電腦以及是否有電腦學前經驗等六個變項對國中小學生之電腦態度有顯著的預測效果,預測解釋力為32%. 三. 影響國中小學生電腦素養方面 1. 電腦經驗與國中小學生之電腦素養有顯著之正相關. 2. 電腦資源與國中小學生之電腦素養有顯著之正相關. 3. 認知需求與國中小學生之電腦素養有顯著之正相關. 4. 數學焦慮與國中小學生之電腦素養有顯著之相關. 5. 數學成就與國中小學生之電腦素養有顯著之正相關. 6. 每星期閱讀電腦書籍及雜誌的時間.家中電腦週邊設備的情形.自己或與他人共同使用電腦.電腦焦慮.電腦自信以及電腦喜歡等六個變項對國中小學生之電腦素養有顯著的預測效果,預測解釋力約為52%.四.整合模式分析方面1. 國中學生之電腦經驗與電腦資源對其電腦素養之影響,主要是來自直接效果的影響(經驗:57.32%;資源:73.31%), 而認知需求對電腦素養之影響主要是透過電腦態度間接效果的影響(89.06%).2. 電腦經驗與電腦資源對國小學生電腦素養之影響, 來自間接效果的影響約佔(經驗: 67.55%;資源:52.32%),認知需求對國小電腦素養的影響主要是透過電腦態度的間接效果,佔61.29%. With the expansion of computer technology, it is important to prepare individuals for success in our increasingly computerized society. Therefore,factors that impact decisions regarding attitude and literacy of computer should be expored. Several factors should be considered: (1) individual characteristics, (2) computer experience, (3) computer resource, (4) cognitiveneed, (5) mathematics anxiety, and (6) mathematics achievement. The purposes of this study were : (1) To find out the situation of information education in junior secondaryand primary school at present; (2) To find out the situation of the computer attitude and literacy in junior secondary and primary school students at present; (3) To examine the relationship and effects toward computer attitudes and literacy of many factors. 1251 junior secondary and 1201 primary school students were measured by (1)individual characteristics and computer experience questionnare, (2) Cognitive Need Scale , (3) Mathematics Anxiety Scale , (4) Computer Attitude Scale, and(5) Computer Literacy Test. The mainly statistical methods are chi-square, pearson product moment correlation, t-test, canonical correlation analysis, multiple(stepwise) regression analysis and path analysis. The results of the analysis of data indicated the following : (1) There were significant sex and school level differences of attitude and literacy toward computer. Boys were better than girls. Primary school students were better than junior secondary school; (2) There were significant correlations between computer experience, computer resource, cognitive need, mathematics anxiety, mathematics achievement, and computer attitude; (3) There were significant correlations between computer experience, computer resource, cognitive need, mathematics anxiety, mathematics achievement, and computer literacy; (4) Computer experience, computer resourse, cognitive need and computer attitude were significant predictors for computer literacy. Computer attitude was the best significant predictor. Recommendations were made for information education , school , family,educational organization and future additional research , to improve the attitude and literacy toward computer of junior secondary and primary school students.

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2009.

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.

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2009.

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.

The pass rate in mathematics is unsatisfactory both in South Africa and internationally. Historically disadvantaged students tend to underachieve even more due to a variety of hampering factors. An investigation into the reasons for underachievement in mathematics prompted the researcher to launch a study through which she wanted to remediate some of these identified problems. The research project took place at Technikon Northern Gauteng (TNG), and comprised of the implementation of tutorial sessions. The study was conducted by means of a quasi-experimental design using action research. The primary goal of this dissertation is to report on the process, outcomes and recommendations in order to facilitate improvement in practice. The researcher's overarching hypothesis was that tutorials in mathematics would have a positive effect on the achievement of first year mathematics students at TNG. The following questions were focussed on during the course of the study: ¨ What is the impact of mathematics tutorials on problem-solving abilities and critical thinking? ¨ What is the impact of tutorials on the self-image of the students, with reference to mathematics and mathematics achievement? ¨ What is the impact of tutorials on mathematics achievement? ¨ Which role could tutors play in the creation of role models? ¨ Do students have the need to communicate mathematically in their mother tongue? ¨ How successfully could portfolio assessment be implemented? Quantitative and qualitative data were gathered through a standardised questionnaire, the SOM, a specifically designed, structured questionnaire, observations, focus group interviews, reflective diaries and student records. Some of the findings include: ¨ Historically disadvantaged students § often possess a unsatisfactory study orientation; § apply inefficient time management; § suffer from mathematics anxiety; § do not show a correlation in terms of grade 12 symbols and success at tertiary level § often experience milieu deficit; § do not achieve according to their expectations; and § do not have a learning culture (COLT) at their disposal. ¨ Students generally perceived the tutorials as positive and contributing towards success. The students § did not often speak in their mother tongues; § appreciated the relaxed work tempo; and § utilise the support system of the smaller group. ¨ During the focus group interviews students recognised the following success factors: § regular class attendance; § completion of homework § planning and revision according to a study timetable. ¨ Students shared some personal experiences with the researcher, namely that § the tutorials boosted their self-image and make them willing to ask questions during lectures; § some tutors acted as positive role models; and § the consistent involvement of the lecturer motivated students. The statistical procedures revealed that the students in the experimental group did not perform significantly better than those in the control group, yet that does not diminish the value of the study in any way. The researcher recommends further research in the tertiary mathematics environment in order to empower students. / Dissertation (MEd (Curriculum Studies))--University of Pretoria, 2005. / Curriculum Studies / unrestricted

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