The importance of learning mathematics and using it in daily life is obvious. On the other hand, the results from many national and international assessment studies show that the achievement of Turkish students are very far away from the bare minimum performance. However, in the measurement and evaluation procedures of both primary and secondary educational system, there is a lack of identification of this &ldquo / bare minimum&rdquo / or qualitative and clear descriptors for performance levels. A great importance is dedicated to the national exam results expressed in percentage terms of the correct responses, or in total score points in weighted scale scores, but there is still no system of presenting to students their scores with descriptions of these scores in terms of levels of skills that they did or did not reach. Therefore, this study has aimed to identify the knowledge and skills required for different performance levels defined by setting cut points for the results of a 4th grade mathematics achievement test. The test was conducted in 2007-2008 academic year with 269 fourth grade students in eight different private primary schools in Istanbul. Then, in 2008-2009 academic year, a group of ten teachers of mathematics and assessment experts took part in the study for identifying the performance level descriptors for 4th grade mathematics performance. Two different methods of standard setting were used. One of the methods was based on the oneparameter model of Item Response Theory (IRT) and mostly named as Bookmark Method. The method depended on the statistical identification of the cut points on the scale for performance levels such as Below Basic, Basic, Proficient, and Advanced. The other method was a judgmental method which required the participant teachers to classify the item as carrying the characteristics of performance levels, again, as Below Basic, Basic, Proficient, and Advanced. The study revealed that the item mappings from two methods were congruent to each other. There was a hierarchical ordering in terms of skills among the performance levels. Also, the results demonstrated that understanding and computation skills were heavily characteristics of Below Basic and Basic levels, whereas, problem solving skill was reached by the students of Proficient and Advanced levels.

Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2008

Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2008

The aim of the study was to investigate what influence the use of computers using MS Excel and RJS Graph software has on grade 11 Eritrean students' understanding of functions in the learning of mathematics. An empirical investigation using quantitative and qualitative research methods was carried out. A pre-test (task 1) and a post-test (task 2), a questionnaire and an interview schedule were used to collect data. Two randomly selected sample groups (i.e. experimental and control groups) of students were involved in the study. The experimental group learned the concepts of functions, particularly quadratic functions using computers. The control group learned the same concepts through the traditional paper-pencil method. The results indicated that the use of computers has a positive impact on students' understanding of functions as reflected in their achievement, problem-solving skills, motivation, attitude and the classroom environment. / Educational Studies / M. Ed. (Math Education)

No description available.

This study aimed to examine the effectiveness of video self-modelling (VSM) and the iPad application (Fast Fact Math, FFM) interventions on a group of Year 5 students to increase their knowledge of basic number facts. This study also aimed to measure the intervention group’s self-efficacy levels (Patterns of Adaptive Learning Scales, PALS) before and following the interventions. Participants were drawn from a decile 9 primary school in a suburban area (teaches Year 1 to Year 6). The Test (pre-, mid-, and post-test phases) were administered by a class teacher to all Year 5 students. Following consultation with the teacher, eight students whose scores fell below the 25th percentile were invited to participate in the study. The intervention group took a specific level test to ascertain their basic number facts performance on all four operations (addition, subtraction, multiplication, and division). The videos and the FFM app were personalised to each intervention group’s members in an effort to elicit from the errors that they made on specific level test. At the completion of each intervention sessions, session probes were conducted. Meanwhile, the researcher gave a self-efficacy test (PALS) to the participants before and following intervention phases. Results showed that, although more than half of the intervention group increased their basic number fact performance level following the interventions, their overall self-efficacy rating on PALS did not change. Results also showed that VSM is a time-efficient and rapid learning method to use with the intervention group as opposed to the iPad app, which took two times longer to complete a session. Further areas of study are suggested.

Magister Philosophiae - MPhil / The South African schools act, (number 5, 1996), asserts that all learners have a right to access both basic and quality education without discrimination of any sort. Since the implementation of the Millennium Development Goals there has been a drive by the Department of Education to ensure that all learners have access to basic education by 2015. However what remains a challenge after almost 20 years of democracy is the poor quality of education and this is clear from the results of international assessment studies. Results from studies like the Trends in International Mathematics and Science Study and Southern and East Africa Consortium for Monitoring Educational Quality, show that South African children perform well below international averages. In this study learner Mathematics achievement scores taken from the Trends in International Mathematics and Science Study 2011 cycle will serve as a proxy for educational quality. Using multilevel analysis the current study aims to use a 2-level Hierarchical Linear Model to firstly; determine the learner and family background factors associated with education quality. Secondly; factors at the school level will be identified and proven to be associated with education quality. Variables selected for the study was based on Creamer’s theory of school effectiveness which looked at school, classroom level inputs as well as learner background variables to explain student level achievement. The results show that at the learner’s level the most significant factors were the age of the leaner, in the sense that grade age appropriate learners obtained higher scores than overage learners. Learner’s perception of mathematics is extremely important and has a positive effect on mathematics performance. In the current study mathematics perception refers to learners valuing and liking mathematics as well learner confidence in learning mathematics. Learners who said they were bullied as school generally scored lower than learners who were not bullied. At the school level the most significant factors were teacher working conditions, teachers’ specialisation in mathematics, school socio-economic status, and general infrastructure. Interesting to note at the school level is when socioeconomic status was included in the model as a single variable the score difference between low socio-economic status and high socio-economic status schools was almost 46 points. However when the factors mentioned above were added to the model the difference in scores dropped by almost half.

學習表現為教育社會學中的重要議題，其中城鄉間的學習表現差距受到重視。過去研究認為家庭背景與地區的教育資源是影響學生學習表現的主要因素，然而這些研究缺乏班級因素與同儕效果的分析。因此本研究使用台灣教育長期追蹤資料庫（Taiwan Education Panel Survey, TEPS）在2001年與2003年的國中生樣本，以階層線性模型（Hierarchical Linear Modeling, HLM）分析國一班級同儕學習投入對國三數學表現的影響，學習投入以學生為課業所付出的時間為指標。分析結果發現：(1)學生數學表現的總變異中有24%來自班級因素的影響，76%為學生因素。(2)國三數學表現、個人學習投入與班級同儕學習投入有城鄉差距。(3)在控制其他變項下，個人學習投入、班級同儕學習投入對數學表現有正向效果。(4)班級所在地區的都市化程度透過班級同儕學習投入間接影響國三數學表現。 / Academic performance has been an important topic of research on educational sociology for a long time, while urban-rural differences have been already well documented in literatures. In the past, the literature indicated that the key factors to affecting academic performance are family background and the educational resources. But these researches have ignored the factors of class level and peer effects. In this study, the data are from Taiwan Education Panel Survey (TEPS) in 2001 and 2003, use Hierarchical Linear Modeling (HLM) to assess how peer engagement affects junior high students’ mathematics performance. The time students spend in studying is an index of engagement. The main finding are: (1) This research model accounts for 76% of the variation in student level and for 24% of the class variation in class level with regard to mathematical performance. (2) Students in the urban and rural city show a differences in their mathematics performance, student’s own engagement and peer engagement. (3) When controlling variables, student’s own engagement and peer engagement have positive effect on mathematics performance. (4) Urbanization levels indirectly affect mathematics performance through peer engagement.

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.