The purpose of this two year study was to investigate the implications of a high academic ability learning environment on the achievement scores of third grade gifted students who attended the Florida Brevard County Public School System. Learning environment was defined by the students’ academic ability level, whether high academic ability or heterogeneous academic ability, and for this study was the independent variable. Academic achievement, as measured by the 2011 and the 2012 Florida Comprehensive Assessment Test® 2.0 (FCAT 2.0) Mathematics and Reading Developmental Scale Scores (DSS), was the dependent variable. Other student data such as gender and socioeconomic status were also collected and used along with classroom structure to examine the extent to which third grade gifted students’ reading and mathematics performance could be predicted. Random samples of students were drawn from the third grade gifted student population attending Florida Brevard County Public School System in the 2010-2011 and the 2011-2012 school years. Using an independent samples t-test, analysis of the 2011 FCAT 2.0 Reading and Mathematics found a statistically significant difference in both the students’ FCAT 2.0 Mathematics and the students’ FCAT 2.0 Reading achievement test scores based on the classroom structure. Specifically, there was enough evidence to support the claim that third grade gifted students who learned in a homogeneous high academic ability learning environment scored significantly higher on reading and mathematics standardize tests than did third grade gifted students who learned in a heterogeneous academic ability learning environment. Approximately 14% of the variance in reading and mathematics scores could be accounted for by classroom structure. However, different results were found with the 2012 FCAT 2.0 iii Mathematics and Reading scores. The results from the 2011-2012 school year indicated that there was not a significant difference in mean reading and mathematics scores between third grade gifted students who learn in a homogeneous high academic ability learning environment and third grade gifted students who learn in a heterogeneous academic ability learning environment. The recommendations include that subsequent studies incorporate a wider range of grade levels, perhaps even include methods of instructional delivery, types of gifted services provided, and teachers’ years of experience. In addition, recommendations are that future studies address the academic performance of high academic ability non-gifted students who learn in homogeneous high academic ability classroom environments verses those who learn in heterogeneous academic ability classroom structures

In the last few years educational computer games have gained attention as a tool for facilitating learning in different sectors of society including but not limited to military, health, and education. However, advances in computer game technology continue to outpace research on its effectiveness. Few empirical studies have investigated the effects of educational games in the context of formal K-12 settings. The purpose of this study was to examine the effects of a series of mathematics computer games on mathematics achievement and motivation of high school students. In addition, the role of prior mathematics knowledge, computer skill, and English language skill of the participants on their mathematics achievement and motivation when they played the games were investigated. A total of 193 students and 10 teachers from an urban high school in the southeast of the United States of the America participated in this study. The teachers were randomly assigned to treatment and control groups. Students' mathematics achievement was measured using school district benchmark exams and a game performance test generated by the developers of the mathematics games. A mathematics motivation questionnaire based on Keller's (1987a) ARCS model of motivational design measured students' mathematics motivation. Multivariate Analysis of Co-Variance (MANCOVA) was conducted to analyze the data. In addition, interviews were conducted to cross validate the results of the quantitative data. The MANCOVA results indicated significant improvement of the mathematics achievement of the experimental versus control group. No significant improvement was found in the motivation of the experimental versus control group. However, a significant improvement was found on the motivation scores of the students who played the games in their school lab and classrooms compared to the ones who played the games only in the school labs. In addition, the findings indicated that prior mathematics knowledge, computer skill and English language skill did not play significant roles in achievement and motivation of the experimental group. Teachers' interviews revealed that these individual differences had indeed played significant roles in game-playing at the beginning of using the games, but the impacts gradually diminished as the students gained the required game-playing skills. The overall results indicated that the mathematics games used in this study were effective teaching and learning tools to improve the mathematics skills of the students. Using the games in mathematics education was suggested by the teachers as an appropriate alternative way of teaching, as one of the teachers stated: "This is definitely the way that we have to go to teach mathematics in the future." Mathematics games should be integrated with classroom activities if teachers want to increase mathematics class motivation. Teachers' helps and supports are vital in using the games effectively in a population with different prior mathematics knowledge, computer skills, and English language skills.

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This study explored the link between teachers’ inputs and process and students’ academic achievement in Junior Secondary Certificate (JSC) Mathematics for the period 2006 to 2010.The outcome (teacher effectiveness) was obtained by means of value added measures (students’ aggregate JSC Mathematics scores for 2006 to 2010 by school). One hundred and fifty JSC schools out of a total of 573 constituted the units of analysis for the study. The data regarding teachers were obtained by means of self-administered questionnaires, and JSC Mathematics results from 2006 to 2010 were obtained from the Directorate of National Examinations and Assessment (DNEA). Multi-correlation and regression techniques at alpha =0.001; 0.05 and 0.10 were used to analyse the link between teachers’ inputs and processes, and students’ academic achievement in JSC Mathematics. The null hypotheses formulated for the study were tested at the 0.05 (5%) level of significance. In summary, it appears that the various aspects of teachers’ inputs (teachers’ educational qualifications, teaching experience, subject specialisation etc.), processes (standards-based professional development, standards-based classroom activities, and classroom management beliefs) are related to students’ academic achievement in JSC Mathematics. In particular, a linear combination of the following variables had a significant and positive association with students’ academic achievement in JSC Mathematics: teachers’ major in Mathematics (teachers’ inputs); teachers’ usage of whole class discussion (standards-based classroom activities); perceived knowledge of algebra; teachers’ professional development in interdisciplinary instruction; teachers’ review of students’ homework/assignments; and students talking to other students about how to solve mathematics problems. Teachers’ pedagogical content knowledge (PCK) in general, and some classroom practices were not significantly related to students’ academic achievements. This study, therefore, recommends that teachers’ professional development should focus on the subject matter that the teachers will be teaching, as well as alignment of teachers’ learning opportunities with real work experience using actual curriculum materials and assessment. / Educational Studies / D. Ed. (Didactics)

This study investigated the relationships between diverse variables and secondary school pupils' Mathematics achievement. It also dealt with the relative contribution of each variable to Mathematics achievement and the significance of differences in Mathematics achievements when pupils' gender and home background as well as teachers' experience, gender, education, in-service education, homework assignment and testing frequency are taken into account. A questionnaire was administered on 163 standard 8 pupils. I The most important findings of this study were: {1) There was a significant relationship between pupil variables and Mathematics achievement. (2) Pupil variables, particularly self-concept, contributed significantly towards the variance in Mathematics achievement. (3) Pupils who wrote tests often (more than once per term) achieved significantly less than students who wrote tests less often / Psychology of Education / M. Ed. (Psychology of Education)

Wiskunde as taal van die wetenskap en tegnologie is een van die weinige vakke wat spesifiek as voorvereiste vir die bestudering van sekere studierigtings gestel word. Leerlinge met Wiskunde-angs word verhoed om hul ware potensiaal in Wiskunde te verwesenlik en word sodoende gediskwalifiseer om hul regmatige plek in die beroepswereld in te neem. Die doel van hierdie studie was om te bepaal of hipnoterapie aangewend kan word om Wiskunde-angs tot werkbare vlakke te beperk sodat leerlinge optimaal in Wiskunde kan presteer. Die aard, oorsake, aanvang, herkenning, verklaring, gevolge, voorkoms en meting van Wiskunde-angs, die verband daarvan met Wiskundeprestasie en die hulp wat onderwysers en hulpprogramme kan lewer, is nagegaan. Daarna is hipnose en hipnoterapie beskou om te bepaal of dit as terapeutiese hulpmiddel pedagogies verantwoordbaar is. 'n Hipnoterapieprogram is in werking gestel en daar is bevind dat die proefpersone almal tot 'n mindere of meerdere mate daarby gebaat het. / Mathematics as the language of science and technology is one of few subjects used as entrance requirement to certain fields of study. Mathematics anxiety prohibits certain pupils to reach their full potential in Mathematics and thus to obtain their rightful place in the world of work. The aim of this study was to determine whether hypnotherapy can be used to lower Mathematics anxiety levels to such an extend that pupils can optimally achieve in Mathematics. The nature, causes, extent, recognition, explanation, consequences, incidence and measurement of Mathematics anxiety, its relationship to achievement in Mathematics, as well as the help that can be rendered by teachers and treatment programmes were studied. Hypnotherapy was then examined to determine whether its use was pedagogically justifiable. A hypnotherapy treatment programme was introduced which was found to be to some extent beneficial to all the subjects used. / Psychology of Education / M. Ed. (Voorligting)

This study explored the influence of irrational beliefs on adolescent secondary school learners’ Mathematics achievement in Zimbabwe. Learner, home and school factors which influence secondary school learners’ Mathematics achievement were discussed and relevant studies were scrutinised. The theoretical views of Albert Ellis regarding the characteristics, effects, acquisition and maintenance of irrational beliefs were discussed together with the major irrational beliefs and their possible relationship with learners’ Mathematics achievement. A sample of 306 randomly selected adolescent Mathematics learners comprising 182 girls and 124 boys in the 14 to 18 year age range participated in the study. A composite questionnaire with subscales on learners’ irrational beliefs, socio-affective variables and perceptions was used during the empirical investigation. Six major hypotheses were tested. The study established that learners’ irrational thoughts about Mathematics correlate negatively with their Mathematics achievement. Learners’ irrational thoughts about Mathematics correlated negatively with motivation, self-concept, parental involvement, and teacher-learner relationships and positively with stress, anxiety and faulty perceptions. Regression analysis proved that learners’ irrational beliefs, socio-affective variables and perceptions jointly explain a greater proportion of the variance in Mathematics achievement than any one of these factors on its own. Therefore, learners’ Mathematics achievement is affected by irrational beliefs together with their socio-affective variables and perceptions. Practical recommendations were given to Mathematics education stakeholders such as teachers, school counsellors, parents and learners to minimise poor Mathematics achievement attributable to irrational beliefs and the allied variables explored in this study. / Psychology of Education / D. Ed. (Psychology of Education)

The purpose of this study was to explore solution strategies that can enhance the achievement of low-performing Grade 12 learners in the following mathematical aspects: finding the general term of a quadratic sequence, factorising third degree polynomials, determining the centre and radius of a circle, and calculating the angle between two lines. A convenience sample of twenty-five low-performing Grade 12 learners from a secondary school in Capricorn District of Limpopo Province participated in the study which adopted a repeated-measures research design. Learners were exposed to multiple solution strategies and data were collected using achievement tests. Findings indicated significant differences in learners‟ average scores due to the solution strategies used. In determining the general term of a quadratic sequence, learners‟ scores were significantly higher when they used formula and the table method than with the method of residues and solving simultaneous equations. Synthetic division made learners to achieve better scores than long division and equating coefficients in factorising third degree polynomials. The use of formulae to find the centre and radius of a circle made learners to have better achievement scores than completing the square. In calculating the angle between two lines learners‟ scores were better using formula and the cosine rule than using theorems. It was concluded that exposing low-performing Grade 12 learners to multiple solution strategies would enhance their achievement in the mathematical aspects explored in the study. Some of the solution strategies that made learners to achieve better results were not in the prescribed mathematics textbooks. The study therefore recommends that mathematics teaching should not be textbook-driven and that low-performing Grade 12 learners should not be regarded as beyond redemption. / Mathematics Education / M.Sc. (Mathematics, Science and Technology Education)

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.

本研究目的，在利用PISA 2003資料庫為例，分辨數學自我概念、自我效能與數學成就關係之模式的建構。本研究選香港為研究對象，以參加PISA 2003的4402名香港的15歲學生為樣本來進行本研究。本研究運用探索性因素分析(EFA)檢視自我概念與自我效能之測量指標的信效度。分析結果顯示，「自我概念」與「自我效能」的測量模式的建構達良好的信效度。另一研究結果顯示，學生數學自我概念對數學成就之間沒有直接的影響效果，但會透過數學自我效能此中介變項，而產生對數學成就的間接影響效果。此外，在雙交叉驗證方面，顯示研究二組樣本具有交叉效度，研究模式之接受性均相當高。 / The purpose of this study was to examine the relationship among self-concept, self-efficacy, and performance in mathematics. The PISA 2003 Hong Kong data was used as an example. There were 4402 15-year-old participants in this survey. Explore factor analysis was used to identify the good measurement models of self-concept and self-efficacy in PISA 2003. The results showed that the measurement models had high reliability and validity. The other result showed self concept had no direct effects on the mathematics achievement. But under the mediation of the mediator, such as self-efficacy, there was indirect effect on the mathematics achievement. Analysis also showed that the two sets of samples have presented cross validity, the research model is highly acceptable.