Department of Mathematics Education
http://hdl.handle.net/10500/6424
2016-12-05T08:30:14ZReflective Abstraction and Mathematics Education: The Genetic Decomposition of the Chain Rule-Work in Progress
http://hdl.handle.net/10500/21217
Reflective Abstraction and Mathematics Education: The Genetic Decomposition of the Chain Rule-Work in Progress
Jojo, Zingiswa; MAHARAJ, ANESHKUMAR; Brijlall, Deonarain
Students have experienced difficulty in understanding and using the chain rule. This study aims at assisting the students to understand and apply the chain rule and thus inform the author’s teaching for future learning of students. A questionnaire will be designed to explore the conceptual understanding of the concept of the chain rule by first year university of technology students using APOS (action-processes-objects-schema) which proposes in the form of the genetic decomposition a set of mental constructions that the students might make in order to learn the concept of the chain rule in calculus and accessing it when needed. This instrument will be used to collect data on how students learn derivatives of trigonometric functions in calculus, using the chain rule. This will be with a view to clarify their understanding of the composition of functions, derivative and the chain rule. The study consists of two phases, both using a qualitative approach. A structured way to describe an individual student’s understanding of the chain rule is developed and applied to analyzing the evolution of the understanding for each of 30 first year students. Other ways to collect data include tests, written exercises and classroom observations. The purpose of the questionnaire will be to establish the correlation between the students’ ability to deal with composition of functions and using the chain rule successfully. Students (n = 10) will then be interviewed based on their written responses to elicit their thinking involved when answering. The analysis of written responses and interviews should establish whether the instrument provided substantial information for identification of certain mental constructions that the researches proposed to consider.
2012-01-01T00:00:00ZThe Use of Indigenous Materials in the Teaching and Learning of Geometry
http://hdl.handle.net/10500/21216
The Use of Indigenous Materials in the Teaching and Learning of Geometry
Jojo, Zingiswa
This paper reports on an exploration of grade nine learners’ experiences in the design and construction of double-storey artefacts project at a secondary school in KwaZulu Natal, South Africa. The project engaged a process of drawing and construction of those artefacts in a technology education classroom to enhance and inform the teaching of geometry and to allow learners to both reflect and use the Geometry they know as a springboard for further study of Euclidean Geometry. This was qualitative study in which data was collected through observations of artefacts and semi-structured interviews with a purposefully selected sample of five learners. The analysis of data revealed that Geometry taught in a free environment allows learners to reflect and share their experiences for better understanding mathematics concepts.
2015-01-01T00:00:00ZFrom Human Activity to Conceptual Understanding of the Chain
http://hdl.handle.net/10500/21215
From Human Activity to Conceptual Understanding of the Chain
Jojo, Zingiswa; MAHARAJ, ANESHKUMAR; Brijlall, Deonarain
This article reports on a study which investigated first year university
engineering students’ construction of the definition of the concept of the chain
rule in differential calculus at a University of Technology in South Africa. An
APOS (Action-Process-Objects-Schema) approach was used to explore
conceptual understanding displayed by students in learning the chain rule in
calculus. Structured worksheets based on instruction designed to induce
construction of conceptual understanding of the chain rule were used. A number
of students used the straight form technique in differentiating complicated tasks
while very few used either the link and Leibniz form techniques. In this manner
differentiation of each function within the composite function was
accomplished. Students either operated in the Inter- or Trans stages of the
Triad. It was found that even students who had inadequate understanding of
composition of functions, performed well in the application of the chain rule.
2013-01-01T00:00:00ZComparative study on structural organisation of Mathematics Continuous Professional Development (MCPD) in selected Sub-Saharan countries
http://hdl.handle.net/10500/21207
Comparative study on structural organisation of Mathematics Continuous Professional Development (MCPD) in selected Sub-Saharan countries
Jojo, Zingiswa
This paper reports on a comparative study on mathematics continuous professional development (MCPD) programs piloted in selected developed and developing Sub-Saharan countries. The study sought to examine the status of existing professional development practice and the challenges practitioners experience in the implementation of such programs in the different countries. The study was piloted in eleven countries namely, South Africa, Botswana, Namibia, Singapore, Zimbabwe, Swaziland, Poland, South Korea, Ireland, Morocco, and Tanzania. The participants in each country were teachers, principals, subject advisors, district officials, provincial officials, service providers and facilitators. Data were collected by means of questionnaires for the teachers, interviews for other participants and observations for the facilitators. Data was then analyzed and compared using both qualitative and quantitative methods. The findings of the study indicated that teachers were exposed to different professional development programs ranging from lesson reflections in South Korea and Singapore to at least cluster workshops in underdeveloped countries.
2015-01-01T00:00:00Z