Aneshkumar Maharaj

Exploring support strategies for high school mathematics teachers from underachieving schools

Abstract Algebra, trigonometry and calculus concepts are dealt with in grades 10 to 12 of South African high school topics, as prescribed by the Curriculum and Assessment Policy Statement. This paper reports on a study exploring practicing teachers’ subject matter knowledge of certain topics they were expected to teach. The theoretical perspectives for the design and analysis of this study were based on Shulman’s conceptual framework. This study was a qualitative case study (n = 28). Practising teachers from the Pinetown district in KwaZulu-Natal participated in this mathematics’ teacher intervention. Focused tasks on algebra, trigonometry and calculus were designed and administered to those teachers. The researchers analysed the data from those tests and found that certain areas of their pedagogical content knowledge required attention.

Exploring Pre-service Teachers' Mental Constructions When Solving Problems Involving Infinite Sets

Abstract In this study, the researchers explore the meaning of the, is equal to symbol by exposing pre-service teachers (n = 38) to two tasks. The first task was baseequivalence of two countable infinite sets. The second task focused on the comparison of the two numbers 0,9 and 1.The study was carried out at a South African university, where activity sheets comprising the two tasks were completed by pre-service teachers specializing to become high school mathematics teachers. Their written responses were analyzed against the initial itemized genetic decompositions formulated in accordance with APOS (Action-Process-Object-Schema) Theory. The findings of the exploration led to modified itemized genetic decompositions. These modified genetic decompositions have pedagogical implications. They also contribute to the APOS theory.

Some findings on the design and implementation of mathematics tutorials at a university

This paper reports on the design and effectiveness of four tutorial types in the context of first year mathematics tutorials, at a South African university for the period 2003 to 2011. A model for the design of mathematics tutorials was formulated. This model informed the design, implementation and refining of the mathematics tutorials over the nine year period. It was found that mathematics students get greater benefit from tutorials that are more organized and include a completion of homework unit requirement.

Improving Proficiency in Mathematics through Website-based Tasks: A Case of Basic Algebra

Abstract Understanding how university students make sense of mathematics is always of concern to their lecturers. A group of lecturers at a South African university studied written responses of first year students to explore what mental conflicts arose during their students’ formulations of solutions to assigned tasks. The mental conflicts as illustrated by their responses were categorized. One of the sections considered was basic algebra which is the case discussed in this paper. After detecting the common conflicts, the lecturers designed website-based tasks. The tasks were meant to target mental conflicts with the hope of removing these from students’ cognition. The website-based tasks were designed in accordance with the principle of scaffolding. The researchers analysed the various conflicts within the framework of Kilpatrick’s five strands of mathematical proficiency. In this paper the researchers discuss the design of the activities and interactive collaborations during tutorial sessions with students. We found that the website material seemed to have helped in removing common mathematical conflicts of some of our undergraduate mathematics students. Also it was found that non-mathematical terminology used could contribute to students’ mental conflicts.

An Outline of Possible In-course Diagnostics for Functions

Abstract The present paper focuses on in-course sample diagnostic questions relating to functions for students who choose to take a course on differential calculus, in a South African context. However, the diagnostic questions should be useful at many places worldwide. The researchers formulated learning outcomes and in-course diagnostic questions for the technical knowledge and skills required for the section on functions, in the context of differential calculus. The questions were designed to check the relevant learning outcomes that they detected for the section on functions as informed by the literature review and conceptual framework. The learning outcomes and formulation of diagnostic outcomes, although based on a number of assumptions, should improve the performance of students.

A Framework to Gauge Mathematical Understanding:: A Case Study on Linear Algebra Concepts

Abstract A framework is arrived at to help gauge the level of mathematical understanding that could be suggested by an examination of a student’s written responses to mathematical problems. This framework has been to make conclusions on two students’ level of mathematical understanding and use of mathematical symbolism to communicate their understanding of operations on matrices in an external form to others. It was found that for those two students mathematical symbolism served largely as an instrumental role to keep track of their thinking. At times the incorrect use of a mathematical symbol, for example the equal to sign, led the student to make illogical conclusions. Further it was found that drawing students’ attention to their incorrect use of mathematical symbolism and the lack of explicit communication of their thinking to others could help to clarify and even modify existing schema that they use to find possible solutions to given tasks.

Reflections on Support Structures Available to First Year Mathematics Students at a University

Abstract This paper focuses on the support structures offered to first year mathematics students at the University of KwaZulu-Natal (UKZN). The objective was to determine the effectiveness of support structures at UKZN that are intended to help students attain success in their studies by improving communication to students on the requirements for the modules that they are studying. The literature review focused on support structures offered to students at universities in other countries. Data was obtained from the UKZN module websites and responses from academic staff and students It was found that the support structures offered at this university compared favourably with those offered by universities in other countries. The findings indicate that there is a need and scope to improve on the effectiveness of the student support structures that are provided for first year mathematics. These involve policy, administrative and academic issues.

An Outline of Possible In-course Diagnostics for Elementary Logic, Limits and Continuity of a Function

Abstract This paper focuses on in-course sample diagnostic questions relating to elementary logic, and the two concepts of limits and continuity of a function. These are for students who choose to take a course on differential calculus, in a South African context. However, the diagnostic questions could be useful worldwide. Learning outcomes and in-course diagnostic questions for the technical knowledge and skills required for the indicated sections were formulated. The questions were designed to check for the relevant learning outcomes that the researcher detected for the indicated sections as informed by the literature review and conceptual framework. The learning outcomes and formulation of diagnostic outcomes, although based on a number of assumptions, should improve the performance of students. Investigations into the validity of those assumptions, including their attainment levels and student performance correlations to relevant examination questions will be the focus of another paper.

An Outline of Possible In-course Diagnostics for Derivatives and Integrals of Functions

Abstract The research reported in this paper was conducted in an attempt to provide support to first year mathematics students who took a core calculus module for which the relatively low pass rate was of concern. The objective was to make available suitable diagnostic questions to students so that they could detect their strengths and/or weaknesses in particular sections before they took the formal assessments for those sections. In this paper, the researcher documented his findings on the formulation of expected student learning outcomes for derivatives and integrals, in the context of calculus. Those were arrived at after conducting document analyses of the aim, content and past assessment papers for the module. Then the literature review and the expected student learning outcomes were used to document sample diagnostic questions for the sections on derivatives and integrals that should facilitate student learning of concepts in those sections.