bluuebunny/crossref_metadata_2025 huggingface dataset:
Species composition and geographic distribution of ticks infesting cattle, goats and dogs in a temperate and in a subtropical region of south-east Africa
Authors: Horak I.G. , Nyangiwe N. , De Matos C. , Neves L.
Published: August 2012

The species and distribution of ticks infesting cattle, goats and dogs in the eastern region of the Eastern Cape Province, South Africa and Maputo Province, Mozambique were determined from collections made from these animals at 72 localities in the former region and 30 in the latter. Eleven ixodid and one argasid species were recovered in the Eastern Cape Province and 15 ixodid species in Maputo Province. The most common ticks infesting cattle and goats in both provinces were Amblyomma hebraeum, Rhipicephalus (Boophilus) microplus, Rhipicephalus appendiculatus and Rhipicephalus evertsi evertsi. The dominant species on dogs were Haemaphysalis elliptica and Rhipicephalus simus. The geographic distributions of the major species and some of the minor species in both regions were plotted. The partial or complete displacement of the indigenous tick Rhipicephalus (Boophilus) decoloratus by the introduced species R. (B.) microplus was a major feature of both surveys.
Description and comparison of the pupae of a further two Culicoides (Avaritia) species from the dung of large herbivores in South Africa (Diptera: Ceratopogonidae)
Authors: Nevill Hilda , Nevill E.M. , Venter G.J.
Published: August 2012

In 2007 Nevill, Venter, Meiswinkel & Nevill demonstrated that the pupae of five Culicoides species belonging to the Imicola complex of the subgenus Avaritia could readily be differentiated from one another using various morphological characters. Three of the described species, Culicoides bolitinos Meiswinkel 1989; Culicoides loxodontis Meiswinkel 1992 and Culicoides sp. # 107 (= C. kwagga, Meiswinkel, unpublished thesis 1995), were reared from the dung of large herbivores, which included buffaloes, elephants, white and black rhinoceroses and zebras. However, during that study a further two Avaritia species, neither of which belonged to the Imicola complex, were reared from dung and these are the subject of the present study. For the past 20 years the adults of these two new closely related species have been known as Culicoides sp. # 54 pale form (p.f.) Meiswinkel and Culicoides sp. # 54 dark form (d.f.) Meiswinkel. The taxonomic description and formal naming of the adults of these two species has yet to be done. The present description and comparison of their pupae show that they are two clearly distinct species; that there is no group of morphological characters that can be used to differentiate these two species from the previously described five species of the Imicola complex; and finally that there was no difference between the pupae of C. sp. # 54 d.f. nor C. sp. # 54 p.f. reared from the dung of different host animals.
The effects of low levels of dietary trace minerals on the plasma levels, faecal excretion health and performance of pigs in a hot African climate
Authors: Boma M.H. , Bilkei G.
Published: August 2012

The present study was performed in order to evaluate the effects of lower than usual industry levels of dietary trace minerals on plasma levels, faecal excretion, performance, mortality and morbidity in growing-finishing pigs in a hot African climate. Group 1 (n =100 pigs) received a diet with common industry levels of trace minerals. Group 2 (n =100 pigs) received reduced dietary trace mineral levels but were fed the same basic diet as Group 1. Mortality, morbidity, pig performance and carcass measurements were evaluated. Two pigs in Group 1 and three pigs in Group 2 died. Thirteen pigs in Group 1 and 27 pigs in Group 2 were medically treated (P < 0.05). Carcass masses, back fat depth, loin depth, and lean percent were not significantly different between the groups. However, the carcasses when evaluated revealed a non-significant higher back fat thickness, lower loin eye area and percentage of fat free lean in barrows compared to gilts within each group. Despite lower initial masses, pigs fed diets containing industry levels of trace minerals were heavier (P < 0.05) and had a higher (P < 0.05) than average daily gains compared to those that received a diet containing lower levels of trace minerals. Faecal zinc excretion was significantly lower (P < 0.05) in pigs fed with lower dietary zinc levels. Copper, manganese and iron excretion were not affected (P > 0.05) by the dietary levels of these trace minerals. Plasma trace mineral concentrations were not affected by the dietary treatment.
Identification and partial sequencing of a crocodile poxvirus associated with deeply penetrating skin lesions in farmed Nile crocodiles, Crocodylus niloticus
Authors: Huchzermeyer F.W. , Wallace D.B. , Putterill J.F. , Gerdes G.H.
Published: August 2012

When large numbers of crocodile skins were downgraded because of the presence of small pin pricklike holes, collapsed epidermal cysts were found deep in the dermis of juvenile crocodiles while forming cysts were observed in hatchlings. Histopathology of these forming cysts showed the presence of intracytoplasmic inclusions in proliferating and ballooning epidermal cells. Pox virions were seen in electron microscope preparations made from the scabs of such early lesions. The partial sequencing of virus material from scrapings of these lesions and comparison of it with the published sequence of crocodile poxvirus showed the virus associated with the deep lesions to be closely related, but different. To differentiate between the two forms of crocodile pox infection it is suggested that the previously known form should be called ''classical crocodile pox'' and the newly discovered form ''atypical crocodile pox''. The application of strict hygiene measures brought about a decline in the percentage of downgraded skins.
The effect of pyridoxal-5-phosphate on serum alanine aminotransferase activity in dogs suffering from canine babesiosis
Authors: Myburgh E.C. , Goddard A.
Published: August 2012

Accurate measurements of serum aminotransferase (ALT) activity in dogs relies on the endogenous pro-enzyme pyridoxal 5-phosphate (P5P). The purpose of this study was to determine whether the exclusion of P5P from the analytical method causes an underestimation of serum ALT activity in dogs suffering from babesiosis and in those manifesting evidence of hepatocellular damage, and to determine if anorexia causes sufficient P5P depletion to affect in vitro serum ALT activity. One-hundred-and-twenty healthy control dogs and 105 Babesia-infected dogs were included in the study. Two methods for ALT measurement were used: Method 1 included P5P, and Method 2 excluded P5P from the reaction mixture. Higher serum ALT activity was measured with Method 1 in the Babesia-infected dogs (P < 0.001), as well as in 14 dogs with suspected hepatocellular damage (P = 0.03). Duration of anorexia had no effect, irrespective of the method used. Although inclusion of P5P to the reaction mixture consistently resulted in higher measured serum ALT activity, the differences were too small to have led to incorrect diagnoses in the Babesia-infected dogs suspected of liver disease.
A retrospective longitudinal study of animal and human rabies in Botswana 1989-2006
Authors: Moagabo K.T. , Monyame K.B. , Baipoledi E.K. , Letshwenyo M. , Mapitse N. , Hyera J.M.K.
Published: August 2012

A longitudinal study of animal and human rabies covering 18 years from 1989 to 2006 was retrospectively conducted in order to highlight the epidemiological features and trends of the disease in Botswana. Over the 18-year period, a total of 4 306 brain specimens collected from various species of animals including human beings with clinical signs consistent with rabies were submitted to the National Veterinary Laboratory in Gaborone for confirmatory diagnosis. Of the samples submitted, 2 419 cases were found to be positive for lyssavirus antigen; this presents an overall prevalence rate of 56.18 ± 1.48 %. About 85.7 % (2 074/2 419) of the cases were from domestic animals, 14.2 % (343/2 419) cases were from wild animals and two cases (0.1 %) were from human beings. During the first half of the study (1989-1997) the prevalence rate of the disease was estimated at 62.79 ± 1.85 % (1 645/2 620 positive) whereas during the second half (1998-2006) it was estimated at 45.91 ± 2.38 % (774/1 686 positive) and the difference between the two estimates was statistically, highly significant (Δ % = 16.88, SE 95) diff % = 3.015, SD = 5.599; P < 0.001). Ruminant rabies accounted for 79.99 % (50.92 % bovine, 28.40 % caprine and 0.67 % ovine) whereas canine (domestic dog) and feline (domestic cat) accounted for 16.01 and 0.87 %, respectively. Equine rabies accounted for 3.13 % with 1.35 and 1.78 %, respectively, for horses and donkeys. Jackal rabies accounted for more than 60 % of the total cases in wild animals. These findings are discussed in relation to the previous epidemiological situation of the disease (1979-1988), its socio-economic impact, monitoring and control in Botswana.
Responses of serum electrolytes of goats to twelve hours of road transportation during the hot-dry season in Nigeria, and the effect of pretreatment with ascorbic acid
Authors: Ayo J.O. , Minka N.S. , Sackey A.K.B. , Adelaiye A.B.
Published: August 2012

Twenty goats which served as the experimental group were administered ascorbic acid (AA) per os at a dosage rate of 100 mg/kg body mass, while 20 others served as controls and were given 10 mt each of sterile water. Forty minutes after the administration and loading, the goats were transported for 12 h. Handling and loading of the experimental and control groups of goats decreased (P < 0.05) the potassium and sodium serum concentrations. The concentration of serum chloride, sodium and calcium increased significantly (P< 0.05) immediately post-transportation, while potassium and magnesium decreased (P < 0.05) in the control goats. In AA-treated goats sodium and magnesium concentrations decreased abruptly (P< 0.05), while calcium increased significantly (P< 0.05) after transportation. Handling, loading and transportation adversely affected the electrolyte balance of the goats which suggested respiratory alkalosis, dehydration and muscular damage in the transported goats, and the administration of AA alleviated the adverse effects of road transportation stress on serum electrolytes.
The Brody effect induced by premature ventricular complexes in the ovine heart
Authors: Ker J. , Webb E.C. , Van Papendorp D.
Published: August 2012

The QRS response of the electrocardiogram to bleeding has been a source of interest to the physiologist for more than a century. Studies in the dog, cat and chicken have shown a reduction in QRS amplitude in response to bleeding. This effect has been explained by the so-called Brody effect, in which the intraventricular mass of blood acts as a conducting medium, augmenting radial conduction, thus resulting in the subsequent reduction in QRS amplitude in conditions where the intraventricular mass of blood is reduced. The aim of this study was to evaluate whether the Brody effect will be present in the ovine heart and, furthermore, to evaluate if the right and left ventricles will demonstrate the same QRS change if the Brody effect is indeed present. This study clearly demonstrated that the Brody effect is present in the ovine heart. Furthermore, two unique aspects emanating from this study are firstly the fact that this is the first study to show that premature ventricular complexes are able to induce the Brody effect and, secondly that there is a very clear difference in the response of the right and the left ventricles when the Brody effect is induced in the ovine heart.
A site-based model for professional development in mathematics at the elementary school level
Authors: Mewborn Denise S. , Huberty Patricia D.
Published: August 2012

Teaching is a profession in which one must continue to learn because there is no one right way to teach, and one does not “master” teaching. Students change, curricula change, and schools change; thus there is always a need to grow as teachers. Heaton (1994, 2000), an experienced teacher who engaged in a year-long self-study as she tried to change her teaching practice to be consistent with current calls for reform, characterized teaching as “inherently under construction … and continuous invention” (p. 341).
World view theory and the conceptualisation of space in mathematics education
Authors: Schäfer Marc
Published: August 2012

The cornerstone of current education trends that recognise prior knowledge as fundamental to the learning process, is the notion that beliefs and experiences that learners bring to the classroom influence their learning experiences in the classroom (Cobern, Gibson and Underwood, 1999).  World view research in science education has proved an important tool in unravelling learners’ beliefs and perceptions in an attempt to better understand what experiences they bring to a classroom situation. Cobern (1991, 1993, 1994, 1996, 1997) has successfully spearheaded much of the world view research in that field, with particular emphasis on learners’ perceptions and  understanding of nature.
Eastern Cape teachers’ beliefs of the nature of mathematics: Implications for the introduction of in-service mathematical literacy programmes for teachers
Authors: Webb Lyn , Webb Paul
Published: August 2012

Various studies have shown that what teachers consider to be optimal ways of teaching mathematics is influenced by their beliefs about the nature of mathematics, and that it is advantageous to determine teachers’ conceptions of the nature of mathematics before developing curriculum interventions. With the imminent introduction of Mathematical Literacy in the FET phase in South Africa this study provides a snapshot of beliefs of teachers in the Eastern Cape, South Africa. Various methods were employed to stimulate teachers to both reflect on their beliefs and to make them explicit. A questionnaire was administered to 339 in-service teachers in urban and rural areas of the Eastern Cape. A sample of ninety-five of these teachers completed a second questionnaire based on videotapes of lessons recorded during the TIMSS (1995) study that they had viewed. These teachers also ranked their own teaching on a continuum ranging from traditional to constructivist approaches and provided explanations for their ranking. A further sub-sample of thirty-six teachers participated in individual interviews, which explored their perceptions of the nature of mathematics and their own teaching practice. In order to investigate whether these beliefs were mirrored in practice, four teachers were observed and videotaped in their classrooms. The data generated by this study suggest that the participating teachers’ espoused beliefs of the nature of mathematics tended to be innovative, and correlated with innovative views of teaching and learning; however these views were often not reflected in their practice. The implications that the apparent inability of teachers to translate their beliefs into practice have for the introduction of a contextual, problem-based Mathematical Literacy curriculum for teachers is explored.
Chanting as mathematical enculturation
Authors: Watson Anne
Published: August 2012

Unison response is a major teaching strategy in mathematics throughout the world. The spoken word is the dominant source of mathematical stimulus, the dominant shaper of the mathematical environment in which school learners construct mathematical meaning. The teachers’ utterances are intended to be expert, and the creation of learner responses is intended to involve learning of some kind.
Modelling of real-world problems is often the starting point for proof
Authors: Mudaly Vimolan
Published: August 2012

In this paper I claim that modelling should be seen as the first stage of the proving process. I discuss an experiment conducted with grade 10 (15 year old) learners in a small suburb in South Africa. There is little emphasis placed on modelling in our schools and it is just beginning to make an appearance in our new Outcomes Based Curriculum. The research shows that as a result of the modelling process learners felt the need to know why the result was true. There is ample evidence that a lot of work on a similar topic has been done elsewhere in the world, but not much has been done in South Africa. The research was conducted using Sketchpad as a mediating tool. This in itself was a difficult task because our learners have not really been exposed to dynamic geometry environments.
Mathematics teacher retention and the role of Identity: Sam’s story
Authors: Graven Mellony
Published: August 2012

This paper provides a vignette of one teacher’s identity transformation from a temporary teacher of mathematics to a professional mathematics teacher (with a long-term trajectory within the profession) during the course of his participation in an In-Service Education and Training (INSET) program. Thus the paper elaborates, from Wenger’s (1998) social practice perspective, the role of identity (one of Wenger’s four learning components) in teacher learning and teacher retention within the profession.The vignette provides textured insight into the way in which Sam’s identity transformation was pivotal in his learning through participation within INSET and other overlapping mathematics education communities. Furthermore, I argue that identity (learning as becoming) was a key component of learning that kept Sam in the profession of mathematics teaching. From Sam’s vignette I argue that positive identity transformation should be one of the most important intended learning outcomes of INSET and as such needs deliberate and focused attention in the design and implementation of teacher education programs. I therefore conclude the paper with some implications of Sam’s vignette for the design of mathematics INSET programs.
Limits of functions – how do students handle them?
Authors: Juter Kristina
Published: August 2012

This paper aims at formulating and analysing the development of 15 students in their creations of mental representations of limits of functions during a basic mathematics course at a Swedish university. Their concept images are sought via questionnaires and interviews. How do students respond to limits of functions? The data indicate that some students have incoherent representations, but they do not recognise it themselves.
Dynamic geometry: An agent for the reunification of algebra and geometry
Authors: Hockman Meira
Published: August 2012

This paper investigates the degree of separation or unity between the algebraic and geometric modes of thought of students in tertiary education. Case studies indicate that as a student is inducted into the use of algebra the insightful and visual components of geometrical and graphical modes of thought are sidelined. Based on Vygotsky’s taxonomy of the psychogenesis of cultural forms of behaviour, I suggest that this separation occurs because the algebraic methods remain fixed at a naïve or algorithmic stage. The algebraic concepts may fail to be internalised because the stage of instrumental functioning of algebra as a ‘tool’ or ‘method’ of geometry is not successfully transitioned.  I suggest that this stage of instrumental functioning may be stimulated by using dynamic geometry programs to promote the formation of images in conjunction with algebraic representations in problem solving. In this way the modes of thought in algebra and geometry in mathematics may be reunified.
Mathematics for teaching: What is it and why is it important that we talk about it?
Authors: Adler Jill
Published: August 2012

I begin this paper with a brief discussion of what can be considered systemic ‘problems’ in mathematics education before moving on to the research problem I am currently investigating. This broad introduction will help locate the QUANTUM research project – a study of the mathematical work of teaching – that forms the substantive part of this paper. I will describe the research we are doing, its questions and objects.
Developing teachers, developing as a teacher: A story about a story
Authors: Bennie Kate
Published: August 2012

In this paper I reflect on my changing roles as a mathematics educator, that is, as a teacher educator and as a classroom teacher in a secondary school. This is a personal account of the challenge of translating my beliefs about mathematics teaching and learning into everyday classroom practice. The presentation I use is based on the work of Rowland − the account is presented in the form of personal reflections on a story written about playing the two different roles of teacher educator and classroom teacher. I use the process of writing to try to make sense of my experiences and to explore the use of story as a research methodology. Although the story is intensely personal, there are identifiable themes that run through the narrative, which I suggest may resonate with the experience of other mathematics educators.
Assessment standards, Van Hiele levels, and grade seven learners’ understandings of geometry
Authors: Feza Nosisi , Webb Paul
Published: August 2012

A number of researchers in mathematical education assert that the instruction in geometry offered in South African schools is inadequate and that traditional teaching strategies do little to promote teachers understandings of their learners’ levels of mathematical thought. Van Hiele specifically states that the inability of many teachers to match instruction with their learners’ levels of geometrical understanding is a contributing factor to their failure to promote meaningful understandings in this topic.  This study investigated whether a sample of grade seven learners in previously disadvantaged primary schools met both the assessment criteria for geometry as stated by the South African Revised National Curriculum Statement and the implied Van Hiele thinking levels.  The data generated suggest that none of the 30 learners who participated in this study had attained these requirements and that language competency in general is a barrier to the attainment of higher levels of understanding amongst this group of second-language learners. It is suggested that not only Van Hiele Levels and Assessment Standards, but also learners’ cultural background and their specific use of words in the vernacular context, need to be taken into consideration by teachers when developing learning programmes. Possible strategies to meet these requirements are suggested.
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.
Contextual factors of the mathematics learning environment of grade 6 learners in South Africa
Authors: Kotze G. S. , Strauss J. P.
Published: August 2012

The aim of this article is to provide insight into the personal characteristics and family backgrounds that South African grade 6 learners bring to the learning process as well as how they interact with the resources and practices that characterise the schools they attend. The research method is historiographic, offering insights into current conditions. An analysis of content is done through examining evidence gathered from an international project. Gender, socio-economic groupings and other major aspects associated with differences in mathematics achievement among learners and schools are addressed. An overall picture of contextual factors that may impact on mathematics achievement is presented. Although the essential conclusions of the investigation are largely straightforward, valuable contextual information emerged that may have implications for mathematics education within the context of South Africa as a developing country.
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.
Erratum
Authors: Office Editorial
Published: August 2012

I will use the above theory to explain how a first-year mathematics major student at a South African university moves from an idiosyncratic usage of signs (using, I claim, preconceptual thinking) to a conceptual (or perhaps pseudoconceptual) usage of signs. The activity took place during an interview which I conducted, video-taped and later transcribed and analysed in 2002 (Berger, 2002). John had been given the following definition which he has not seen before, although he is familiar with the definite integral and the notion of a limit.
Mathematical Literacy as a school subject: Failing the progressive vision?
Authors: Christiansen Iben Maj
Published: August 2012

The National Curriculum Statement (NCS) for Mathematical Literacy (ML) is part of a progressive agenda for increased democracy and social justice. It claims that the new school subject Mathematical Literacy will provide learners with awareness and understanding of the role that mathematics plays in the modern world. However, the analysis developed in this paper indicates that the superficial engagement with complex applications of mathematics implied by the ML NCS is not likely to live up to its claim. In addition, we do not understand enough about the connections between mathematical, technological and reflective knowledge/knowing/competencies to know how to facilitate the awareness and understanding that is part of the vision of the ML NCS.
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.
From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics
Authors: Gierdien M. Faaiz
Published: August 2012

To follow
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.
An analysis of the influence of question design on learners’ approaches to number pattern generalisation tasks
Authors: Samson Duncan , Schäfer Marc
Published: August 2012

This paper reports on a study of the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil-and-paper exercises based on linear generalisation tasks set in both numeric and two-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. The method or strategy adopted was analysed and classified into one of seven categories. In addition, a meta-analysis focused on the formula derived for the nth term in conjunction with its justification. The results of this study strongly support the notion that question design can play a critical role in influencing learners’ choice of strategy and level of attainment when solving pattern generalisation tasks. An understanding of the importance of appropriate question design has direct pedagogical application within the context of the mathematics classroom.
Developing inquiry-based teaching and learning in Family Maths programme facilitators
Authors: Austin Pam , Webb Paul
Published: August 2012

The inquiry-based Family Maths professional development programme, offered by the Nelson Mandela Metropolitan University, attempts not only to support the transformative education practices targeted by the South African National Department of Education, but also to extend them beyond the school walls to the community at large. This study investigates the extent to which this programme develops facilitators’ ability to implement inquiry-based learning. The research undertaken uses both qualitative and quantitative methods in an empirical study of 39 facilitators. The facilitators’ inquiry beliefs and ability to implement inquiry learning was measured by means of questionnaires, observation schedules and interviews. Data generated by the study reveal that both the facilitators’ understanding and practice of inquiry improved as they progressed through the novice, intermediate and veteran categories of the Family Maths professional development programme.
Proof and proving in secondary school
Authors: Mudaly Vimolan
Published: August 2012

This paper argues that mathematics should be a human activity in which the process of guided invention takes the learner through the various stages and steps of the discovery of mathematical ideas and concepts. The central premise is that proof functions as an explanation, where experimental mathematics is used to empirically convince the learner that the conjecture holds true. Inductive reasoning used while working with the computer software Sketchpad assists learners in arriving at and testing their conjectures.
Mathematical Literacy – mathematics and/or literacy: What is being sought?
Authors: Venkat Hamsa
Published: August 2012

Mathematical Literacy was introduced as an alternative option to Mathematics in the Further Education and Training (FET) phase (Grades 10-12, learners generally aged 15-18) in South Africa in January 2006. As a new subject in the FET phase, and with aims that differ somewhat from the notion of mathematical literacy that figured within the Mathematical Literacy / Mathematics / Mathematical Sciences (MLMMS) learning area in the General Education and Training (GET) phase, teachers are faced with implementing a subject which does not have established aims, understandings and practices associated with it.
Introducing discussion into multilingual mathematics classrooms: An issue of code switching?
Authors: Webb Lyn , Webb Paul
Published: August 2012

The Department of Education in South Africa advocates collaborative and constructivist learning; however, observations indicate that little discussion occurs in most multilingual mathematics classes. In this paper we draw on a pilot study set in the Eastern Cape where teachers were introduced to the theory and practice of exploratory talk, and then tasked to perform an action research project on introducing discussion in their own multilingual mathematics classrooms. The results of the study suggest some successes in terms of teachers initiating exploratory talk and highlight the fact that these successes were only achieved where code switching between English and isiXhosa formed an integral part of the process.
Mother tongue policies and mathematical terminology in the teaching of mathematics
Authors: Kazima Mercy
Published: August 2012

The Department of Education in South Africa advocates collaborative and constructivist learning; however, observations indicate that little discussion occurs in most multilingual mathematics classes. In this paper we draw on a pilot study set in the Eastern Cape where teachers were introduced to the theory and practice of exploratory talk, and then tasked to perform an action research project on introducing discussion in their own multilingual mathematics classrooms. The results of the study suggest some successes in terms of teachers initiating exploratory talk and highlight the fact that these successes were only achieved where code switching between English and isiXhosa formed an integral part of the process.
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.
Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining
Authors: De Villiers Michael
Published: August 2012

This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.
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.