D. Tech. Education / This thesis emerges from an analysis of learners' responses to tasks presented to learners studying Mathematics and Mathematical Literacy in South Africa. Officially, Mathematics and Mathematical Literacy are two separate learning areas. Learners from Grade 10 onwards take either one or the other but not both. This means that there is a potential that by the time learners reach Grade 11, they would have acquired different kinds of knowledge and problem solving skills depending on which of these they take. Hence the study sought to investigate Grade 11 learners' approaches to solving context-based Mathematics and Mathematical Literacy tasks. The study was driven by the following key research questions: How do Mathematics learners interact with Mathematical Literacy tasks? How do Mathematical Literacy learners interact with Mathematics tasks? When given a Mathematics task, what variations, if any, exist in the solution strategies of Mathematical Literacy learners and vice versa? What are teachers and facilitators' views on Mathematics and Mathematical Literacy learners' solution strategies?

Includes bibliographies. / This paper seeks to introduce the taxonomy developed by Bloom and also other taxonomies applied to Mathematics. The behavioural basis is considered before the actual taxonomies are presented giving due cognizance to the influence of behavioural objectives. The paper then demonstrates the way in which a taxonomy can be used in setting examination papers, and also gives a survey of the way Bloom's taxonomy and behavioural objectives have been used in instruction. Philosophical criticisms of objectives and the use of Bloom are considered followed by a survey of empirical findings in connection with both of these. Finally suggestions are firstly made as to how the taxonomy be used to examine mathematics question papers in South Africa in its albeit subjective manner, and secondly for further research.

Thesis (Specialist in School Psychology)--Eastern Illinois University, 2009. / Includes bibliographical references (leaves 42-45).

Thesis (M. Ed.)--Ohio University, August, 2004. / Includes bibliographical references (p. 66-71).

Thesis (M.Ed.)--Ohio University, August, 2004. / Title from PDF t.p. Includes bibliographical references (p. 66-71)

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Thesis (M. Ed.)--University of Hong Kong, 1982.

This study examined the nonsymbolic numerical magnitude processing in Chinese first graders with marked mathematics difficulties (MD) and typically achieving peers. The approximate number system (ANS) view has suggested that children with MD may have deficit in the internal representation of magnitudes. Chinese first-graders with MD were compared with age-matched typically achieving children on approximate numerical comparison, approximate addition and multiplication tasks. Children with MD were found to perform significantly worse than their age-matched controls in all tasks. Students before formal instruction in multiplication yielded an above-chance level of performance in approximate multiplication task, which suggested the existence of approximate multiplicative ability. After formal instruction in multiplication, the MD group performed significantly worse than controls in approximate multiplication task and arithmetic tests. Only normally achieving children showed significant improvement after formal instruction. This study provided further evidence for an intuitive numerical processing in arithmetic operation, and the result had significant implication to the diagnosis of MD and intervention on mathematics difficulties. / published_or_final_version / Educational Psychology / Master / Master of Social Sciences

This study investigated young children's construction of meaning for number and explored ways to more comprehensively assess and portray the development of number sense in young children. Greeno's (1991) conceptualization of number sense as situated knowing in a conceptual domain was used to consider both the mathematical tools available to the child and the extent to which the child makes use of these tools. The data consisted of four videotaped interviews for each of sixteen children between the ages of six and eight. Each of the four interviews involved a different number context: doubling, finding missing parts, sharing, and working with money. Each context involved a task presented in a series of increasingly difficult items, with number size predominantly determining the difficulty level. A dynamic interview format was used to encourage children to work beyond their independent level, or "number comfort zone." Cues and scaffolds were provided to support children's construction of meaning within their "number construction zone" and towards the outer limits of their understanding. Analysis focused on the strategies children used to make sense of each item, and the cognitive, affective and contextual aspects which enhanced or constrained their mathematical activity within the number construction zone. Results were reported two ways. The first, specific task performance across children, provided a means of describing the diversity of developmentally appropriate ways children made sense of the different tasks and provided a frame of reference for considering individual performance. The second approach to reporting results considered individual children's performance across tasks, and provided a means of focusing on characteristics of emerging competence. Results of this study illustrate how the nature and use of children's reasoning strategies can provide an indication of developing competence. Results highlight specific conceptual, procedural, functional, and affective characteristics that most directly affected children's capacity to make sense of number situations. No single characteristic alone accounted for children's success or lack of success, rather the inter-relationships of the different characteristics was apparent, with strengths in one area compensating for weaknesses in another. Though conceptual and procedural abilities appeared to shape to a great extent the nature of the number knowledge available to children, affective considerations and functional competence played a major role in shaping the extent to which children drew on this existing knowledge. Issues of context influenced both aspects of number sense: available knowledge and the nature of its use. Number size, context of the tasks, and presentation of tasks influenced children's mathematical activity in important ways. Children's personal number contexts were considered in terms of how they influenced their approaches to tasks. Overall, dynamic assessment techniques proved to offer a viable alternative for exploring the limits of children's ability to make sense of number situations, and for considering children's construction of meaning for number in developmental terms.

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