published_or_final_version / Education / Master / Master of Education

M.Ed. (Psychology of Education) / Please refer to full text to view abstract

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Signed on 10 September 2016 in Austin, Texas, USA. / This dissertation investigated the possible connection between the two constructs of metacognition and the strands of mathematical proficiency. Using a small convenience sample of Grade 12 learners at a public all-girls high school in Johannesburg, South Africa, the teacher/researcher examined if training in metacognitive knowledge influenced the learners’ conceptual understanding, procedural fluency, strategic competence and heuristic strategy use. Two instruments (pre-test and post-test) developed by the researcher and completed by the students were on-line assessments of metacognition utilising written self-reports of strategy use that occurred simultaneously with mathematical problem solving. Qualitative analyses were applied to the data and learners demonstrated declarative, procedural and conditional metacognitive knowledge in their explicit heuristic and content-specific strategies. The learners also demonstrated strategies which could be inferred from their working. The study showed evidence of mixed transferability of metacognitive training to mathematical proficiency. Questions for further research are provided. / LG2017

This research report confirms the value of the Framework of Growth Points in a learner’s mathematical development in the area of functions in equation form. The study also shows that learners advance through the various growth points in a progressive, sequential fashion, which mirrors the results of Ronda’s study, on which a part of this study was based. The study was carried out in a high school in Johannesburg. Learners in Grades 9, 10 and 11 were required to do an assessment which tested for their achievement in different growth points. This study also explores the discourse of learners while they talked about the tasks in the assessment. A smaller sample of learners was interviewed so that the researcher could explore the nature of their discourse. This research report shows that there are patterns in the discourse of learners which can be related to the growth points that they achieve.

A research report submitted to the school of Education, Faculty of Science, University of the Witwatersrand in partial fulfilment for the degree of Master of Science Johannesburg 2017 / South African learners perform poorly in national and international mathematics assessments (Howie, 2004). A contributing factor to this poor performance is low mathematics knowledge of mathematics teachers in South Africa (Howie, 2003). One means of addressing this is professional development programs. The Wits Maths Connect Secondary Project runs such a program. A test is required by the project in order to assess whether learners are making learning gains after being taught by teachers who participated in this program. The focus of this study is the design of a test used to assess learners’ algebraic attainment. The aim is to design an informative and fair test using Rasch analysis. A sample of 235 learners’ responses to 47 questions was analysed using the Rasch model. In this study, the mean person measure was 2,87 (SD=1,38) logits, while the mean item measure was 0,41 (SD=2,25) logits, suggesting that overall, the test was too difficult. For the learners who wrote this test the person separation index is 1,78 and the person reliability 0,76. This implies that the test may not be not sensitive enough to distinguish between learners of high attainment from learners with low attainment. Various ways of improving the test are discussed. / MT 2018

Thesis (M.A.)--Chinese University of Hong Kong. / Bibliography: leaves 56-59.

Typescript (photocopy). / Digitized by Kansas Correctional Industries / Department: Mathematics.

This dissertation is devoted to the history of the Albanian system of education in general, its mathematics education program in particular, and, specifically, the Albanian high school mathematics assessment. Historical in terms of its research methodology, and mathematical-pedagogical in terms of the objects of the study, this research explores and compares the Albanian high school mathematics graduate examinations during 1970s and 2006 – 2015: two decades during two different historical periods. It analyzes the general structure of the examinations, their mathematical task design, and the history of their changes under the influence of political and social processes. The units of analysis here are the questions of each examination, which are examined both individually and in context as part of the examination, investigating the examinations’ topic coverage and comparing the latter to the intended national curriculum. This study was based on multiple primary sources, including documents from the Albanian Ministry of Education, the Central State Archive of the Republic of Albania, the Internet archive (http://www.arsimi.gov.al), memoirs of former teachers, high school textbooks during the respective years, and other sources. The analysis showed that Albanian mathematics education was not immune to political and social change: both its curriculum and assessment were affected. Examination administration, format, topic coverage, and item characteristics, even the pure mathematical problems, represented in some ways the Albanian social, economic, and political views of the time.

The purpose of this study was to develop a valid and reliable, instrument for determining the mathematics subject matter knowledge of Thai preservice elementary teachers at eight (8) teachers' colleges in eight (8) provinces in northern Thailand. The focus of the content of interest was the operation of division of rational numbers in the context of an appropriate taxonomy of the cognitive domain categories suggested by Wilson (1971). The Delphi technique, item analysis, and "known group" techniques were utilized in the instrument development phases of the study. Hypotheses were tested to determine whether significant differences existed between colleges and between teachers with different backgrounds. The dependent variable was the mean test score for preservice teachers at eight Thai teachers' colleges. The study included the testing of significance for colleges, background, and whether there was significant interaction between colleges and teachers' backgrounds (liberal arts and science). The pilot instrument consisted of 52 items representing four cognitive levels (computation, comprehension, application, and analysis). Based on an analysis of pilot test data, 10 items were eliminated. The final draft instrument consisted of 42 items and was administered to 272 preservice elementary teachers. When field test data were analyzed and compared to "known group" data, 10 items were found to be outside of the acceptability range for difficulty. Item difficulty was used for selecting items for inclusion in the final instrument to measure the operation of division of rational numbers with Thai college preservice elementary teachers. This step in the research served to reduce the number of test items to 32, which constituted the content for the final instrument. The internal consistency reliability was .81 for the 42-item instrument. Content and construct validity were verified by various procedures. / Graduation date: 1994

This was a qualitative study carried out with learners from a grade twelve Standard Grade mathematics class from a South Durban school in the province of KwaZulu-Natal, South Africa. The main purpose of this study was to explore learners‟ understanding of the concept of the derivative. The participants comprised one class of twenty seven learners who were enrolled for Standard Grade mathematics at grade twelve level. Learners‟ responses to May and August examinations were examined. The examination questions that were highlighted were those based on the concept of the derivative. Additionally semi-structured interviews were carried out with a smaller sample of four of the twenty seven learners to gauge their perceptions of the derivative. The learners‟ responses to the examination questions and semi-structured interviews were exhaustively analysed. Themes that ran across the data were identified and further categorised in a bid to provide answers to the main research question. It was found that most learners‟ difficulties with the test items were grounded in their difficulties with algebraic manipulation skills. A further finding was that learners overwhelmingly preferred working out items that involved applying the rules. Although the Higher and Standard grade system of assessing learners‟ mathematical abilities has been phased out, with the advent of the new curriculum, the findings of this study is still important for learners, teachers, curriculum developers and mathematics educators because calculus forms a large component of the new mathematics curriculum. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2008.