bluuebunny/crossref_metadata_2025_split huggingface dataset:
Maths concepts in teaching: Procedural and conceptual knowledge
Authors: Long Caroline 
Published: August 2012

In teaching a general course on mathematics for prospective teachers, I have found the theoretical distinction between conceptual knowledge and procedural knowledge (Hiebert & Lefevre, 1986) a useful focus for teaching practice. The constructs provide a scaffold for the learning of mathematics by the students and for thinking about the teaching of mathematics in the school environment. These theoretical insights uncover in part the processes for acquiring knowledge and provide a tool for addressing problematic areas of learning.
Making mathematical meaning: From preconcepts to pseudoconcepts to concepts
Authors: Berger Margot 
Published: August 2012

I argue that Vygotsky’s theory of concept formation (1934/1986) is a powerful framework within which to explore how an individual at university level constructs a new mathematical concept. In particular I argue that this theory can be used to explain how idiosyncratic usages of mathematical signs by students (particularly when just introduced to a new mathematical object) get transformed into mathematically acceptable and personally meaningful usages. Related to this, I argue that this theory is able to bridge the divide between an individual’s mathematical knowledge and the body of socially sanctioned mathematical knowledge. I also demonstrate an application of the theory to an analysis of a student’s activities with a ‘new’ mathematical object.
Teachers’ views on mathematical literacy and on their experiences as students of the course
Authors: Mbekwa Monde 
Published: August 2012

This paper reports on a study undertaken at the University of the Western Cape with a class of 32 in-service teachers who had completed six months of an Advanced Certificate in Education (ACE) course in mathematical literacy in 2004. The teachers completed an evaluation questionnaire, which asked them about their common sense conception of mathematical literacy and their reflections on their student experiences in the first six months of the course at UWC. The study has found that some of these students’ understanding of mathematical literacy corresponds to contradictory conceptions of mathematical literacy, which appear in the literature. Some expected that the course would be a watered-down version or easy mathematics whilst some viewed it as mathematics with applications in everyday life. Whilst some of the teachers perceived the course content to be “difficult”, it is important to note that almost all the teachers, except those who dropped out, have completed and passed the course, which indicates that it was a worthwhile endeavour.
Mathematical knowledge for teaching: Adding to the description through a study of probability in practice
Authors: Kazima Mercy , Adler Jill 
Published: August 2012

In their description of the mathematical work of teaching, Ball, Bass & Hill (2004) describe the mathematical problem solving that teachers do as they go about their work. In this paper we add to this description through our study of teaching of probability in a grade 8 multilingual classroom in South Africa. We use instances of teaching to highlight the mathematical problem solving that teachers might face as they work with learners’ ideas, both expected and unexpected. We discuss the restructuring of tasks as an inevitable feature of teachers’ work, and argue that in addition to scaling up or scaling down of the task as Ball et al. (2004) describe, restructuring can also entail shifting the mathematical outcomes from those intended. We also point out how well known issues in mathematics education, for example working with learners’ everyday knowledge, and the languages they bring to class, are highlighted by the context of probability, enabling additional insights into the mathematical work of teaching.
Concerns about the South African Mathematical Literacy curriculum arising from experience of materials development
Authors: Bowie Lynn , Frith Vera 
Published: August 2012

In this paper we reflect on our experience of developing mathematical literacy material for the Further Education and Training (FET) band in South African schools, adult learners, university students and for participants in a youth development project. We use this experience to highlight some problems and concerns about the South African Mathematical Literacy curriculum for learners in the FET band and offer some cautions and suggestions. In particular we highlight the importance of the educational community in South Africa developing a shared understanding of what Mathematical Literacy is. We discuss the importance of distinguishing between Mathematics and Mathematical Literacy and of clarifying the role of Technology in Mathematical Literacy. We explore the difficulties and importance of a proper understanding of the contexts used to teach Mathematical Literacy and argue that more attention needs to be paid to the integration of Mathematical Literacy with other school subjects. Finally we raise some of the issues that a common final assessment task might have on the learning and teaching of Mathematical Literacy.
Reflections on the role of a research task for teacher education in data handling in a Mathematical Literacy education course
Authors: Frith Vera , Prince Robert 
Published: August 2012

The introduction of the subject “Mathematical Literacy” in the Further Education and Training band from 2006 has created an urgent need for large numbers of teachers to be educated about the nature of mathematical literacy and to become effective teachers of it. In this paper we report on an attempt to contribute to this goal through a curriculum component in an “Advanced Certificate in Education” course. This curriculum component on data handling was structured around a research task which required the teachers on the course to practise mathematical literacy in a context where there is close linkage with other vital competencies, such as verbal reasoning, writing and computer literacy. This approach articulates well with the kind of teaching envisaged by the curriculum statement for “Mathematical Literacy”. We report on an initial analysis of the teachers’ reflections on their experience of the curriculum-embedded research task on this course, the manner in which this task contributed to their understanding of mathematical literacy as a practice and themselves as practitioners.
Does ‘African mathematics’ facilitate access to mathematics? Towards an ongoing critical analysis of ethnomathematics in a South African context
Authors: Horsthemke Kai , Schäfer Marc 
Published: August 2012

Mosibudi Mangena, the Minister of Science and Technology, said in an address to the Annual Congress of the South African Mathematical Society at the University of the Potchefstroom, November 2, 2004: “There is one thing we need to address before anything else. We need to increase the number of young people, particularly blacks and women, who are able to successfully complete the first course in Mathematics at our universities.” How is this to be achieved? A popular trend involves a call for the introduction and incorporation of so-called ethnomathematics, and more particularly ‘African mathematics’, into secondary and tertiary curricula. Although acknowledging the obvious benefits of so-called ethnomathematics, this paper critically analyses three aspects of ethnomathematics that have been neglected in past critiques. Our focus is not on the relationship as such between ethnomathematics and mathematics education. Our critique involves (1) epistemological and logical misgivings, (2) a new look at practices and skills, (3) concerns about embracing ‘African mathematics’ as valid and valuable – just because it is African. The first concern is about problems relating to the relativism and appeals to cultural specificity that characterise ethnomathematics, regarding mathematical knowledge and truth. The second set of considerations concern the idea that not all mathematical practices and skills are necessarily culturally or socially embedded. With regard to the validity and viability of ‘African mathematics’, our misgivings not only concern the superficial sense of ‘belonging’ embodied in the idea of a uniquely and distinctly African mathematics, and the threat of further or continuing marginalisation and derogation, but the implicitly (self-)demeaning nature of this approach. This paper serves as a reminder that a critical position in the deliberations of ethnomathematics needs to be sustained. It warns against the bandwagon syndrome in a society where political correctness has become a prominent imperative. This paper is framed by many unanswered questions in an attempt to inspire and sustain a critical discourse in the ethnomathematics movement.
Designing mathematical-technological activities for teachers using the Technology Acceptance Model
Authors: Stols Gerrit 
Published: August 2012

The objective of this study was the design and development of mathematical technological activities. The guiding model in developing these activities was the Technology Acceptance Model (TAM). The two main issues to address, according to the model, are the “perceived ease of use” and the “perceived usefulness” of the software. The activities were used, refined and tested in a professional development programme which consisted of five hands-on laboratory sessions, lasting 2 hours each, spaced over a 3-month period. The study found that the approach of letting teachers experience technology while engaged in authentic mathematical tasks promotes the perceived usefulness of Geometer’s Sketchpad (GSP) by the teachers. At the end of the series of workshops, 91% of the teachers indicated in the summative evaluation that these workshops helped them to understand geometry better. This finding was supported by the 21.5% increase in the pre-test and post-test average score.
Teaching geometry in schools: An investigative rather than instructive process
Authors: Sanni Rasheed 
Published: August 2012

Research has documented the prevalence of lessons characterised by homework check, followed by teacher lecture and demonstration, followed in turn, by learner practice sequence of classroom instructional activities in our classrooms. This sequence of classroom activities does not allow for the development of sound mathematics practices and mathematical proficiency. Meanwhile, curriculum reforms in South Africa as well as in other parts of the world recommend classroom activities where teachers create opportunities for, listen to and extend learners. This paper presents a sequence of activities to be used in the teaching of geometry and surface areas of solid shapes in a grade 8 classroom. The sequence portrays the teaching of these concepts as an investigative rather than instructive process.
Using a task analysis approach within a guided problem-solving model to design mathematical learning activities
Authors: Maharaj Aneshkumar 
Published: August 2012

The FET Curriculum Statements for Mathematics advocates that knowledge integrates theory, skills and values. This paper focuses on a guided problem-solving teaching model that provides a framework to do this. A task analysis approach is used within this framework to illustrate how educators could frame mathematical questions based on the relevant mathematical content.
Pythagoras is going places …
Authors: Olivier Alwyn 
Published: August 2012

Council has made the principled decision to go the open access route, where Pythagoras will be freely available to everyone. We are starting a new website where Pythagoras will be freely available. To do this, we will be using an open source journal management program that will streamline the process. Nearly everything should happen “automatically”: authors will submit their papers online, the program will acknowledge receipt, then suggest reviewers, send the paper with a covering letter to reviewers, reviewing will likewise be online, etc.
Mathematics as a social construct: Teaching mathematics in context
Authors: Barnes Hayley , Venter Elsie 
Published: August 2012

Why is teaching in context an important option to consider in the teaching of mathematics? What does it mean to teach mathematics from and in contexts? And what are the possible challenges associated with this practice? The aim of this paper is not to provide a comprehensive answer or solution to these questions. We attempt rather to address these questions specifically with regard to South Africa and the theory of Realistic Mathematics Education. In this article we consider a vignette of a more formal and traditional mathematics lesson and then suggest possible reasons why we need to be teaching more in context. Furthermore we discuss the application of the theory of Realistic Mathematics Education as a potential approach to facilitate teaching in context. Finally we present some challenges associated with this practice.
A case study of the development of in-service teachers’ concept images of the derivative
Authors: Likwambe Botshiwe , Christiansen Iben M. 
Published: August 2012

This research focuses on the development of the concept images of the derivative concept of five students enrolled in the in-service programme Advanced Certificate in Education (ACE) at the University of KwaZulu-Natal, Pietermaritzburg campus. For comparison, the concept images of two qualified teachers not enrolled in the programme were included. The findings show that of the five ACE students who were interviewed, only one had a profound concept image in all the three layers of the derivative, with multiple representations as well as connections among representations within the layers. This one student also passed the calculus module with a distinction. The other four students had the ratio layer and graphical representation in their concept images, while the other layers and representations were pseudo-structural with very few connections. Two of these students passed the calculus module, while the other two failed. All the students showed progression in their concept images, which can probably be credited to the ACE calculus module. However, it is clear that even upon completion of this module, many practicing teachers have concept images of the derivative which are not encompassing all the layers and more than one or two representations. The research suggested that historically disadvantaged students experience continued inequalities in learning. The research also showed the need to expand the framework of Zandieh (2000), developed to describe concept images of derivative.
A snapshot in time: Beliefs and practices of a pre-service mathematics teacher through the lens of changing contexts and situations
Authors: Webb Lyn , Webb Paul 
Published: August 2012

For the last decade research on teachers’ beliefs has made a distinction between mathematics teachers’ professed and attributed beliefs (practice) and studies have either found some or no correlation between the two. In this paper we investigate the beliefs and practices of a novice teacher and conclude that inconsistency between beliefs and practices may be an observer’s perspective that is not necessarily shared by the teacher, and that the view that there is a possible disjuncture does not do justice to the complexity of the practitioner’s tasks nor to the rapidly changing contexts and situations that may occur within a single lesson.
Collaborative learning in a multilingual class
Authors: Brijlall Deonarain 
Published: August 2012

The solving of word problems dealing with fractions was investigated. Two sets of learners worked in solving the same tasks on fractions. One set of learners worked collaboratively and the other group consisted of learners working independently. The selected participants consisted of two Grade 8 classes at a high school in Pietermaritzburg, South Africa. The study was a qualitative one involving lesson observations, analysis of learner worksheets, questionnaires and interviews. The two tasks were presented in the form of word problems and the classroom comprised of multilingual learners. Data yielded by these research instruments confirmed assumptions and literature claims. Although it was a small scale qualitative research, interesting observations were made that could have pedagogical implications.
Can multiple choice questions be successfully used as an assessment format in undergraduate mathematics?
Authors: Huntley Belinda , Engelbrecht Johann , Harding Ansie 
Published: August 2012

In this study we propose a taxonomy for assessment in mathematics, which we call the assessment component taxonomy, to identify those components of mathematics that can be successfully assessed using alternative assessment formats. Based on the literature on	assessment models and taxonomies in mathematics, this taxonomy consists of seven mathematics assessment components, hierarchically ordered by cognitive level, as well as the nature of the mathematical tasks associated with each component. Using a model that we developed earlier for measuring the quality of mathematics test items, we investigate which of the assessment components can be successfully assessed in the provided response question (PRQ) format, in particular multiple choice questions (MCQs), and which can be better assessed in the constructed response question (CRQ) format. The results of this study show that MCQs can be constructed to evaluate higher order levels of thinking and learning. The conclusion is that MCQs can be successfully used as an assessment format in undergraduate mathematics, more so in some assessment components than in others. The inclusion of the PRQ assessment format in all seven assessment components can reduce the large marking loads, associated with continuous assessment practices in undergraduate mathematics, without compromising the validity of the assessment.
The relationship between Leadership, Job satisfaction and Organisational Commitment
Authors: Stander Marius , Rothmann Sebastiaan 
Published: August 2012

Shift-share analysis of employment as a measuring instrument for human resource management is proposed by this study. The results obtained through this technique can assist human resource
management on the macro-level in making informed and strategic decisions regarding future employment practices and trends. This technique is often applied to studies of economic geography,
and is illustrated in this article through its application to the estimation of future employment potential of manufacturing industries of South Africa’s Southern District Municipality. The economy in this region is mainly dependent on gold mining, which is declining as gold reserves are becoming depleted. As a result, a large section of the area’s population will be unemployed in future, causing adversity and other development needs. Shift-share analysis provides insight into the shifts of employment in the various sectors over time, as well as insight into the national share effect on employment in the region, including the regional-industrial mix and the competitive share effects. It was found that the
sectors with the highest employment creation potential are: transport equipment, wood and paper products, metal products, and furniture. Some suggestions are also made regarding the ways that this information can be utilised in human resource management.
'N Pragmatiese benadering tot die Ontwikkeling van Geweegde Aansoekvorm
Authors: Fick L. J. 
Published: August 2012

Simplified procedures for the development of a weighted application blank to combat labour turnover of co loured employees in the clothing industry are outlined and discussed. Opsomming Vereenvoudigde prosedures vir die ontwikkeling van ‘n geweegde aansoekvorm ter bekamping van arbeidsomset onder gekleurde werknemers in die klerasiebedryf, word sistematies bespreek.
Necessity for a comprehensive psychometric policy within an organization
Authors: Veldsman T. H. 
Published: August 2012

Psychometric testing is an important, valuable, widespread and legally protected activity in South Africa. Within the ambit of the organizational context a psychometric policy is required to guide and direct this activity. The purpose of this article is to show how the need for such a policy within an organization can be fulfilled. The article proceeds as follows: firstly, the positioning of a psychometric policy within the overall human resource management of an organization is discussed; secondly, a definition of the term 'psychometric policy' and the aims thereof are given; thirdly, a suggested content for such a policy is outlined; fourthly a method of generating this policy is proposed; and lastly, the role of the psychologist in this regard is indicated. Opsomming Psigometriese toetsing is 'n belangrike, waardevolle, algemene en wetlik beskermde aktiwiteit in Suid-Afrika. Binne organisatoriese verband word 'n psigometriese beleid benodig om hierdie aktiwiteit te lei en rig. Die doel van hierdie artikel is om aan te toon hoe die behoefte aan sodanige beleid in 'n organisasie vervul kan word. Die artikel verloop soos volg: eerstens, word die plasing van 'n psigometriese beleid binne die algemene menslike hulpbronbestuur van die organisasie bespreek; tweedens, word 'n definisie van die begrip "psigometriese beleid" en die doelwitte daarvan gegee; derdens, word 'n voorgestelde inhoud vir sodanige beleid aan die orde gestel; uierdens, word 'n metode aangedui waarvolgens hierdie beleid daargestel kan word; en laastens, word die rol van die sielkundige in hierdie area aangedui.
The mature female clothing shopper: Profiles and shopping behaviour
Authors: Visser E. M. , Du Preez R. , Du Toit J. B. 
Published: August 2012

This study was designed to profile the mature female clothing shopper. More specifically certain variables that could be attributed to differences in consumer behaviour were investigated. Mature female clothing shoppers were segmented as clothing moderates, clothing enthusiasts and the clothing unconcerned. These three cluster groups significantly differed regarding clothing involvement, clothing orientation, activities, interests, opinions, family orientation, needs and media usage. No significant differences were found among the three groups regarding evaluative criteria for clothing and clothing store attributes. Profiles of the clusters were developed, along with applicable marketing implications. Recommendations for further research are made. Opsomming Hierdie studie is onderneem ten einde die vroulike kledingverbruikers van 55 en ouer te tipeer. Die veranderlikes wat 'n bydrae kon lewer ten opsigte van die verskille in verbruikersgedrag is ondersoek. Die verbruikers is gesegmenteer as die kledinggematigdes, kleding- entoesiaste en die kleding-onbetrokkenes. Die drie groeperings verskil beduidend van mekaar ten opsigte van die volgende veranderlikes naamlik: kleding-betrokkenheid, kleding-oriëntasie, aktiwiteite belangstellings, opinies, familie oriëntasie, behoeftes en media gebruik. Geen beduidende verskille kon gevind word tussen die drie groeperings ten opsigte van die veranderlikes evalueringskriteria van klere en winkeleienskappe nie. Profiele van die verskillende trosse is ontwikkel en die bemarkingsimplikasies is uitgewys. Aanbevelings vir verdere navorsing word gedoen.