This thesis examines number sense in primary mathematics. I begin by presenting literature to demonstrate how a cognitive definition of number sense, dominates understandings of mathematical development. I argue that this has influenced fixed-ability practices in mathematics (e.g. Boaler, 1997; Marks, 2014) presenting number-sense as a natural ability. I outline the political landscape and explore data which demonstrates that mathematics education systematically disadvantages some people (Zevenbergen, 2001). After reviewing mathematics learning from a range of theoretical perspectives, I demonstrate a gap in the literature: a sociological exploration of number sense in primary school and illustrate the need to examine school structures and their implications for equitable outcomes for all children. To address this gap I have employed Bourdieusian tools of habitus, field and capital, to explore number sense development. Through ethnographic methods in Year 4 classrooms, I examine how number sense positions children in the field of primary mathematics. This research was undertaken during the first year of statutory implementation of the National Curriculum (DfE, 2013) allowing insight into the lived experiences of children at this time. My findings show that facts, fluency and flexibility are key ways children demonstrate their number sense. Through rapid recall of facts children are seen by their teachers, peers and themselves as ‘able’ at mathematics, leading to explicit reproduction of social class, as these facts are usually learned at home. Similarly, a demand for fluency has led to a focus on procedural accuracy with calculation. Based on this, children are sorted into ability groups magnifying infinitesimally small differences between them (Bourdieu, 1986). Finally, children demonstrate flexibility through different calculation strategies; however, lessons usually rehearse single methods, hiding this key mathematical practice. Each aspect of number sense differentiates children, advantaging those with middle-class habitus and therefore reproducing educational inequalities.

Exploring the relationship between early oral reading fluency ability and reading comprehension achievement among an ethnically and racially diverse sample of young learners from low-income families, attending elementary school within a large public school district in southeast Florida is the purpose of this longitudinal study. Although many studies have been conducted to address the relationship between oral reading fluency ability and reading comprehension achievement, most of the existing research failed either to disaggregate the data by demographic subgroups or secure a large enough sample of students to adequately represent the diverse subgroups. The research questions that guided this study were: (a) To what extent does early oral reading fluency ability measured in first, second, or third grade correlate with reading comprehension achievement in third grade? (b) To what extent does the relationship of early oral reading fluency ability and reading comprehension achievement vary by demographic subgroup membership (i.e., gender, race/ethnicity, socioeconomic status) among a diverse sample of students? A predictive research design using archived secondary data was employed in this nonexperimental quantitative methods study of 1,663 third grade students who attended a cohort of 25 Reading First funded schools. The data analyzed derived from the Dynamic Indicators of Basic Early Literacy Skills Oral Reading Fluency (DIBELS ORF) measure administered in first, second, and third grades and the Florida Comprehensive Assessment Test of the Sunshine State Standards (FCAT-SSS) Reading administered in third grade. Linear regression analyses between each of the oral reading fluency and reading comprehension measures produced significant positive correlations. Hierarchical regression analyses supported the predictive potential of all three oral reading fluency ability measures toward reading comprehension achievement, with the first grade oral reading fluency ability measure explaining the most significant variance in third grade reading comprehension achievement. Male students produced significant overall differences in variance when compared to female students as did the Other student subgroup (i.e., Asian, Multiracial, and Native American) when compared to Black, White, and Hispanic students. No significant differences in variance were produced between students from low and moderate socioeconomic families. These findings are vital toward adding to the literature of diverse young learners.

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This experiment investigated lateralized hemispheric regulation of the autonomic nervous system (ANS) among high anxious and nonanxious university undergraduate men using a novel laboratory paradigm. Specifically, this three phase paradigm entailed the administration of a verbal fluency (left frontal) and nonverbal fluency (right frontal) task with or without the threat of a painful stimulus (cold pressor) to high anxious and nonanxious participants. Thus, the cerebrums are hypothesized to be engaged in a dual-task experience requiring the regulation of the ANS and concurrent performance on the verbal or the nonverbal fluency measure. Given the literature which supports relative right hemisphere activation among anxious individuals, it was hypothesized that high anxious men would (1) demonstrate greater physiological arousal to the cold pressor, (2) perform relatively worse on nonverbal fluency measures and demonstrate greater difficulty regulating cardiovascular functioning, and (3) demonstrate relatively lower nonverbal fluency scores and increased physiological arousal when presented with the nonverbal fluency task and cold pressor stimulus simultaneously. The results are evaluated using three perspectives: Heller's (1993) hypothesis, Kinsbourne's Functional Cerebral Distance principle, and lateralized regulation of the sympathetic and parasympathetic nervous system. The results only partially supported the right hemisphere activation hypothesis for anxious individuals, as many of the significant results were counter to hypotheses. Specifically, high anxious men demonstrated lower verbal fluency scores and greater heart rate during the combined stimulus of the cold pressor and verbal fluency task. The data are supportive of relative anterior deactivation among high anxious men. The discussion extends the findings to present questions regarding cerebral regulation of the ANS. Future experiments which may add to the current understanding of lateralized regulation of the sympathetic nervous system (SNS) and parasympathetic nervous system (PNS) are suggested. / Ph. D.

Low levels of learner performance in Mathematics in the Senior Phase (Grades 7-9) in South Africa is often attributed to insufficient mathematics content knowledge among teachers. Although this view might be justifiable, it is often incorrect to assume that content knowledge alone will solve the problem of low performance in mathematics. This study, therefore, argues that understanding learner misconceptions and/or errors and their underlying intricacies could provide the basis for instructional decision making, subsequently improved performance in mathematics. The purpose of the study was to explore the implications of teachers’ understanding of learner errors for mathematics learning. The study was guided by qualitative methods using a case study design which involved data collection from two schools, followed by in-depth data analysis. Two theoretical lenses, namely, Cognitively Guided Instruction (CGI) and Constructivist theory were used to explore the main research question: What are the implications of the teachers’ understanding of learner errors on the learning of school mathematics in the Senior Phase (specifically Grade 9)? Data was collected through lesson observations, analysis of learners’ test responses and interviews. The findings revealed that teachers’ understanding of learner errors from written responses differed notably from intricacies of same errors emanating from interviewing the learners as well as the same errors analysed by the researcher. The implications of these findings suggest the likelihood of a mismatch between teachers’ instructional decision making and learner misconception/errors and this may hamper effective learning of mathematics. / Dissertation (MEd)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / MEd / Unrestricted

Philosophiae Doctor - PhD / Internationalisation is an important worldwide phenomenon, and amongst others, presents as a major trend in higher education and continues to be on the agenda of higher education providers worldwide. It is significant for the sustainability of higher education at a national level, and subsequently, the contribution that higher education makes to the development of a nation, its people and its ability to compete in the global market. Internationalisation within universities continues to develop apace as institutions move from equating international strategies with international student recruitment to developing mature internationalisation agendas that incorporate recruitment, research collaborations and capacity-building.