The study presents a pragmatic evaluation of the influence of inductive teaching on grade 11 learners in two high schools in Tshwane West District in the Gauteng province in a form of pseudo experiment complemented with a qualitative investigation. The study focussed on the influence of inductive teaching on the nature of conceptualisation of and the learning achievement with regard to functions in Grade 11. A model adopted by O'Callaghan that identifies and applies the four competencies of modelling a function, interpreting a function, translating and reifying a function proved to be relevant for the investigation and hence was adapted for the study. The methodology used included data collection through pretest-posttest control group experimental design complemented with unstructured interviews. The verification of the reliability of research instruments and data analysis was done with the assistance of the Northwest University (Potchefstroom Campus) Statistical Consultation Services and through identification of common perceptions and experiences of participants. The results of the study did indicate positive influence of inductive teaching on the nature and quality of conceptual learning of the function concept. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2009.

Many authors have expressed concern regarding the extent of underachievement in mathematics. The role of language proficiency as a causal factor in this underachievement has been neglected. Researchers found sufficient evidence to conclude that language proficiency is related to mathematics achievement. In mathematics, symbolic language fills a dual role: It serves as an instrument of communication and as an instrument of thought by making the representation of mathematical concepts, structures and relationships possible (Esty & Teppo, 1996:45). According to Van Hiele (1988:5), language structure is a critical factor in the progression through the Van Hiele levels from the visual, concrete structures to the abstract structures. In this study, the influence of language proficiency on geometric thinking is investigated. 152 grade 8 and 9 learners completed two tests each. One test measured language proficiency in the learners' mother tongue. The second is a geometric test based on a Mayberry-type Van Hiele test for assessing learners' geometric thinking levels. Language proficiency was taken as the independent variable, and geometric thinking as the dependent variable. In the analysis of the results, the top 25 % and bottom 25% performers in the language proficiency test were chosen. Cohen's (1988) d-value was used to determine if there was a practical significant difference in the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels. Results showed a practical significant difference between the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels, but also with respect to the geometry test as a whole. In particular, two aspects of language proficiency, namely reading comprehension and vocabulary, appeared to be very strong predictors for geometric thinking on the first three Van Hiele levels (d ≥ 0,8). Key terms for indexing: geometry, geometry learning, mathematics learning, geometric thinking, language, language proficiency, geometry and language, mathematics and language. / Thesis (M.Sc. (Education)--North-West University, Potchefstroom Campus, 2004.

The study presents a pragmatic evaluation of the influence of inductive teaching on grade 11 learners in two high schools in Tshwane West District in the Gauteng province in a form of pseudo experiment complemented with a qualitative investigation. The study focussed on the influence of inductive teaching on the nature of conceptualisation of and the learning achievement with regard to functions in Grade 11. A model adopted by O'Callaghan that identifies and applies the four competencies of modelling a function, interpreting a function, translating and reifying a function proved to be relevant for the investigation and hence was adapted for the study. The methodology used included data collection through pretest-posttest control group experimental design complemented with unstructured interviews. The verification of the reliability of research instruments and data analysis was done with the assistance of the Northwest University (Potchefstroom Campus) Statistical Consultation Services and through identification of common perceptions and experiences of participants. The results of the study did indicate positive influence of inductive teaching on the nature and quality of conceptual learning of the function concept. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2009.

This study investigates the ways in which parents' and teachers' experiences and representations mediate their child's mathematics learning as they make the transition between home and school to either a multiethnic or mainly white school. In particular, it examines if the forms of mediation they adopt can shed light on the academic success of the child in school mathematics. The focus on mathematics learning has been chosen for the study because of its relative neglect, until recent times, to be seen as a subject influenced by cultural representations. Furthermore, there are significant implications in the relative neglect of understanding the achievement of ethnic minority pupils in mathematics. The research was framed by Vygotskian sociocultural theory and Wenger's (1998) communities of practice to explore the construction of meaning, identity and representations of practice. The amalgam of Wenger's communities of practice with sociocultural theory provided three key theoretical facets: (i) multiple levels of understanding in the form of meaning, practice and identity, (ii) the scope to explore the social and cultural worlds of the learner and (iii) understanding the ways that past experiences impact on current practice. Three different forms of qualitative data collection were used within the context of an ethnographic approach: (i) investigations in the form of classroom observations, (ii) in-depth semi-structured interviews and (iii) a child identity task. Twenty-two parents, eight teachers and fifty-eight children took part in the interviews, which form the main part ofthe data analysis. Out ofthese fifty-eight children, twenty-seven undertook the child identity task. The research took place in three schools with different ethnic make-up: a multicultural school, a mainly white school and a predominantly South Asian school. Two year groups were chosen, year 2 (ages 6/7 years) and year 6 (10/11 years), balancing high and low achievers. This study has provided data, which suggests that the way parents and teachers mediate the child's learning involves more than representations of mathematics. In making meaning of the mathematical, they draw on wider representations of the educational world, which include aspects like child development, notions of achievement, past experiences and the child's projected futures. This complex picture emerged from studying the highly interwoven aspects ofthe construction of meaning, identity and representations of practice. Representations of learning can be borrowed from both communities, providing the ethnic minority pupil with the potential to create hybrid representations of learning as they make the transition between home and school, which may be attributed a cultural status within the home. Each social actor has the potential to borrow from the home or school community to a greater or lesser degree. lfthe gap between the shared representations of the home and school are large, then this increases the likelihood of difficulties for the child in transition. However, the data suggests that even if the cultural representations of the home are very different from the school, the identification of high achievement and the engagement in mathematical activity at home can still provide success in learning. From the school community perspective, classrooms were represented by the teacher informants as 'cultureless' in both the multi ethnic and mainly white school. For example, in the multicultural school the teachers felt that there were so many ethnicities that differences were not visible. In the mainly white school, there were so few ethnic minority children that teachers also struggled to identify issues of culture. In the predominantly South Asian school, issues surrounding culture were brought to the forefront of the teacher discourse. However, in many ethnic minority homes, parents described how culture was influential in mediating representations ofleaming. This has implications in the educational arena with respect to the teachers' understanding of the transitional process that ethnic minority children undergo and the levels of visibility that culture and ethnicity is given in the school community.

Thesis (M.S.)--Kutztown University, 1988. / Source: Masters Abstracts International, Volume: 45-06, page: 2811. Abstract precedes title page. Includes bibliographical references (leaves 71-78).

Thesis (Ph.D.)--Tufts University, 1988. / Submitted to the Dept. of Child Study. Includes bibliographical references. Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Master's thesis - - State University of New York College at Cortland, 2007 - - Department of Mathematics. / Includes bibliographical references (p.40).

Thesis (Ph.D.)--University of Central Florida, 2008. / Adviser: Rebecca A. Hines. Includes bibliographical references (p. 94-109).

O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa, dos 74 alunos 19 foram selecionados para participar da intervenção pedagógica, sendo que 12 deles apresentaram graves dificuldades e 7 moderadas dificuldades em matemática. Durante o desenvolvimento da intervenção, foi utilizada uma combinação de ensino direto e ensino de estratégia de Swanson e Sachse-Lee (2000). As intervenções foram realizadas em grupos de 4 e 5 alunos, perfazendo um total de 12 encontros. Na terceira etapa, foi realizada avaliação utilizando os mesmos instrumentos da primeira etapa. Após a quantificação dos dados, os resultados revelaram que a diferença de pontuação entre o pré-teste e pós-teste foi estatisticamente significativa nos dois grupos de alunos. Os resultados indicaram que os alunos com graves e moderadas dificuldades na aprendizagem da matemática se beneficiaram com a prática pedagógica, pois, na resolução de fatos aditivos básicos, houve progressos do uso de estratégias e procedimentos de contagem para processos apoiados na memória. A combinação de abordagens de ensino direto e ensino de estratégias mostrou que é possível estimular a aprendizagem dos alunos indicando progressos no mesmo período escolar. / The use of immature counting procedures and the slow retrieval of basic addition facts of long-term memory has been suggested by research as being deficit developed abilities in children with difficulties in mathematics. Therefore, in this study a pedagogical practice was developed with 4th grade elementary school students who presented difficulties in mathematics learning aiming at enhancing the use of retrieval of basic addition facts. The study was divided into three phases. In the first phase, an evaluation was performed with 74 students aging from 9-11 years-old from three public schools in Porto Alegre. In order to evaluate their arithmetic performance, the Arithmetic Test by Capovilla, Montiel, & Capovilla (2007) was applied. To evaluate procedures and strategies counting and retrieval of addition facts from memory, two adapted tasks from Siegler & Shrager (1984) and Geary, Hamson & Hoard (2000) were used. After the evaluation, the results were statistically analyzed, and the total scores of the Arithmetic Test, besides being used to evaluate the arithmetic performance, were used as a base to divide the group into a severe anda moderate difficulties. In the second phase, 19 of the 74 students were selected to participate of the pedagogical intervention, with 12 presenting with severe difficulties and 7 with moderate difficulties in mathematics. During the intervention development process, a combination of direct teaching and strategy teaching by Swanson and SachseLee (2000) was used. Interventions were performed in groups of 4 and 5 students, with a total of 12 meetings. In the third phase, an evaluation was performed with the same tools used in the first phase. After data quantification, results revealed that the difference between the pre-test and post-test scores was statistically significative in the two groups of students. Results indicated that students with severe and moderate difficulties in mathematics learning would benefit from the pedagogical practice, because, while solving the basic addition facts, there was progress in using counting strategies and procedures to memory-based processes. A combination of direct teaching and strategy teaching approaches showed to be possible to stimulate learning while indicating progress during the same school term.

This thesis reports the findings of my study of students with visual-spatial deficits in my specialist school in the city of New York. It is comprised of a pilot study, mathematical interviews, and interventions with students and teachers. This study is qualitative and primarily uses case studies to explain the interventions with both the students and the teachers. The study is made up of interventions with two students, and interventions with several teachers who work in my specialist K-12 school which includes both primary and secondary school teachers. Since very little research has been conducted in this field to this point, the findings presented in this thesis aim to give teachers, especially secondary school mathematics teachers, an understanding of the challenges that secondary school students with visual-spatial deficits face when they are learning mathematics. In addition, this research also discusses intervention sessions that I conducted with teachers that gives some insights into educating secondary school mathematics teachers about mathematics learning disabilities and their impact on the students that they teach. The main findings of this research are that there are effective interventions for both students and teachers that help students with visual-spatial deficits learn mathematics. A successful theme that has emerged is centring which helps students to start questions that they find challenging, and also focus their attention on obtaining a solution. It can sometimes lead to a greater understanding of mathematics as well.