School of Science & Mathematics Education

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An investigation into the nature of verbal interactions during the practical training of medical technology students
(University of the Western Cape, 1999) Paulsen, Moira Catherina; Julie, Cyril
various ideas have been propagated regarding the way people come to know in apprenticeship situations. The particular set of social practice theory that informs this study is that related to old-timers and newcomers. The newcomer comes to know by constant engagement in the activities of the community of experts. This study shows that being around the old-timer does not necessarily gibe rise to learning if the contact between these two agents does not occur as a shared practice. This shared practice will facilitate the curriculum that must exist between them. This curriculum be it a learning curriculum and/or a teaching curriculum can only be successful if the shared practice is transparent to the newcomer, and the newcomer is accepted as a legitimate peripheral participant. The participation of the newcomer in the activities of the old-timer ensures learning to occur. As long as the old-timer prevents the newcomer from engaging in the authentic tasks of medical technology, the newcomer will fail to develop a sense of the 'whole' of the trade and learning will be impaired. The old- timer provides a bridge between the development of knowledgeable skill and identity, and the production and reproduction of a community of experts. The author's own experience in Medical Technology training and the increasing challengers to empower learners generated questions around the training of medical technology students. It is argued that learners make sense of theoretical ideas by 'doing' that what is learned in the theory. This necessitates the use of the tools of the trade. During this engagement with the tools various phases can be operated in. These phases include the 'way-in' phase and the 'practice phase'. Medical technology practice i.e. the way medical technologist engages in the trade allows for the development of a community of experts. This however also requires the development of certain skills. These skills can be cognitive- and/or practical skills. This study put emphasis on the nature of verbal interactions during the practical training of medical technology students. The study further provides evidence that apprenticeship training of medical technology students takes the form of imitation, i.e. it is unsystematic and unsupported. The emphasis of the training is on service delivery rather than on teaching. There is visible between learning in the formal academic setting (Site A) and learning in the apprenticeship learning situation (Site B).
The effect of graphic calculators on the mathematical achievement in quadratic functions of urban Eritrean grade 10 students
(University of the Western Cape, 2003) Mebrahtu, Amare Teclemicael; Julie, Cyril
The purpose of this study was to investigate the effect of graphic calculators on the mathematical achievement of Eritrean grade 10 students related to the concepts of quadratic function. The study adopted a quasi-experimental design that involved two groups of students: the graphic calculator group and paper and pencil group. A total of 41 students from two secondary schools were involved in this study. 20 students were in the graphic calculator group and 21 in the paper and pencil group. A quadratic functions test was used to determine whether there is a significant difference in the mean achievement score between the two groups at the pre-test and post-test stages. The groups were compared by using the student's t test for independent samples.
Eritrean grade eight student understanding of algebraic variables
(University of the Western Cape, 2003) Yosief, Tekie Sium; Julie, Cyril
This study investigated Eritrean grade eight students' understanding of algebraic variables. A complete count survey of all secondary schools of one province was done and the one that took part in the study was Gash-Barka province. The study adopted the test and framework developed by Kuchemann (1980). Children's responses and the items themselves were classified into "levels of understanding". Items of the test were classified into four levels based on the name that can be given to letters in solving a problem and the structural complexity of the item. These items were used to classify the Eritean grade eight students' performances into five "levels of understanding".The present study produced results that showed that 72.6 % of the students dealt with letters in algebraic expressions and equations as objects. Whilst 3.7 % of the students were able to regard letters as specific unknowns, only 0.2 Yo of the students were able to consider letters as generalized numbers or variables. That is, almost all (95.9 %) of the tested Eritrean grade eight students were unable to cope consistently with items that can properly be called algebra, that is, items where the use of letters as unknown numbers cannot be avoided. Comparisons by school and gender were done to see if there were relationships among the levels of understanding and the two variables. The findings showed that there was no significant relationship among the levels of understanding and gender of the students. However, the comparison by school showed that there was significant relationship between schools and levels of understanding. The Pearson chi-square test showed that the relationship between the level of understanding and gender was not significant, whereas the relationship between levels of understanding and school was statistically significant at 0.05 level of significance.
Worldview presuppositions and conceptions of force held by junior secondary school science students.
(University of the Western Cape, 2003) Adams, Saleh; Ogunniyi, Meshach B.
The central concern of this study was to determine 12-13 year old students' worldview about force and how such worldview presuppositions affect their conceptions of force. The study accepted the constructivists' view, viz. that students bring ideas based on prior experience to the classroom, and these ideas or beliefs affect the ways they respond to and interpret instruction in science. A distinctive methodological feature of this study was the way the quantitative information obtained by structured observation and the class environment questionnaires were combined with qualitative data derived from obtained naturalist/interpretive procedures. The experimental design that was chosen for the pilot and main studies was the quasi-experimental model based on a modified Solomon-3-control group design. A battery of instruments was used to assess the cognitive, affective, psychomotor and observational aspects of the study. The main instrument, the Performance on Force Test (POFT), consisted of questions designed to elicit the students' qualitative understanding of the concept force. The POFT was constructed to capture both conceptual and alternative worldviews of the subjects regarding force. A sample of three comparable schools was used in the study. Two schools constituted the experimental (E) and true control (C1) groups and the third school served as the second control group (C2). The E and C2 groups received the experimental Curriculum on Force (COF) intervention; whereas group C1 received the tradition teaching approach. To minimise the effects of contamination, the treatment groups were chosen from different areas of metropolitan Cape Town. A total of three teachers and 91 students were involved in the study. To ameliorate the students' conceptions of force, the teachers were exposed to an exemplary instructional practice model for three weeks. Similarly, the students were exposed to exemplary instructional materials for six weeks. A pretest, post-test and delayed post-test evaluative instruments on the selected dependent variables were administered to the subjects to obtain the data needed for analysis. The collected data were analysed using descriptive statistics (mean, standard deviation, frequencies and percentages) and inferential statistics (analysis of covariance and t-test). Contrary to expectation, the induction programme that the teacher of group C2 went through with the teaching of the COF did not successfully crystalize in her class, unlike the teacher of the experimental class, E. Perhaps with more time, the teacher of group C2 could have implemented the teaching styles that the teacher of group E used successfully in teaching the COF emphasized during the induction programme. All the hypotheses were tested at the 0.05 level of significance. The major findings include: 1. The students involved in this study had already acquired some ideas about force before encountering the concept in the new science lessons. At the pretest level, the students in the experimental group (n = 30) had .x = 20.32, SD= 5.18 and the control group C1 (n = 26), x = 20.44 and SD = 4.63 with t = 0.37 at p = 0.05. 2. The post-test was administered after the students had been exposed to the exemplary instructional material known as the Curriculum on Force (COF) material. The achievement outcomes of the POFT at post-test level gave x = 26.19 and SD = 5.41 for the experimental group and for the control group C1, x = 24.54, SD = 3.71 and control group C2, .x = 23.42 and SD = 5.03 respectively. These mean scores were relatively close to the grand mean score of 24.72. However the mean of C2, where the students also received the treatment, was somewhat lower than C1, where the students were not exposed to the COF treatment. 3. Pairwise comparisons of the post-test scores of the experimental and control groups showed that the difference between E and C1 was not statistically significant (t = 1.34, at p = 0.18). On the other hand, the post-test scores of E and C2 were statistically different (t = 2.18, at p = 0.03), whereas C1 and C2 were not statistically different (t = 0.89, at p = 0.37). 4. The outcomes of the performance on the POFT at the delayed post-test level gave the combined mean score for the three groups of 24.60 and a SD = 4.54. For the Experimental (E) group the mean score was 26.15 and SD = 3.87, whereas for the control groups C1 and C2, the means were 24.54 and 23.11 and the SD's = 3.72 and 5.14, respectively. Although the mean achievement scores of E and C1 were not statistically different (i.e., t = 1.43, p = 0.16 and t = 1.21, p = 0.23, respectively), those for E and C2 were statistically different (t = 2.31 and p = 0.02). 5. a) As regards gender on the subjects' conceptions about force, the females obtained a slightly higher mean than their male counterparts, although the difference was not statistically significant. 5. b) A one way t-test for comparing performance of 12 and 13 year olds on the POFT showed a significant difference in their performance (t = 3.50 at p < 0.05). 5. c) As regards the effect of language, there appeared to be a significant difference between the English and Xhosa speakers when their pretests and post tests were compared (t = 7.74 and p < 0.05). 5. d) The achievement differences between the two religious groups were not statistically significant in the pretest (t = 0.79 at p = 0.05), nor in the posttest (t = 1.29, p = 0.05). 6. As in many earlier studies, it is worth noting that alternative conceptions held by the students about force persisted despite the spirited effort made in the study to attain conceptual change. No doubt, the instructional exemplary model used by the two teachers in both the experimental and control groups contributed to an overall increase in performance of the students on the POFT. The approach did not prove superior to the traditional approach used by the true control group (C1) teacher. The students in C2 obtained the lowest mean score. However, all three groups maintained their relative positions even at the delayed post-test. This probably indicates the retention of what had been learned by the students. Different instruments were used to study classroom dynamics with the experimental and control groups. This was followed by interviews with teachers and their students about various aspects of force. The aim was to obtain a robust picture of classroom transactions during the study period. An analysis of both the quantitative and qualitative data indicates an increased understanding of force by the subjects. However, it was evident that the instructional model would perhaps need to be refined and implemented over a longer period than has been done in this study before any significant impact is achieved. Whether other outcomes might have occurred, the failure to achieve significant conceptual change has once more demonstrated the complexity of the teaching-learning process. By the same token, it has generated a greater respect on the part of the investigator for the work of science teachers and an appreciation for their onerous tasks. Finally, the implications of the findings for teacher training, curriculum and instructional practice, as well as areas warranting further investigations, were highlighted.
The effects of an instructional strategy on grade 11 learners' understanding of genetics
(University of the Western Cape, 2004) Siseho, Simasiku Charles; Ogunniyi, Meshach Bolaji
Research into learning genetics has largely focused on issues such as problem solving and the process of meiosis. The central concept of genetics, however, has received very little attention despite the fact that it is one of the concepts that learners find difficult (Ogunniyi, 1999; Bahar, Johnstone and Hansell, 1999; Collins and Stewart, 1989). In view of this, the specific purpose of this study was to investigate: (l) concepts of genetics that grade I I learners hold before and after a period of instruction in genetics (2) the differences in the understanding of genetics held by learners exposed to an instructional model and those not so exposed; and (3) possible influences of gender, age, and language on grade I I leamers' understanding of genetics. The method adopted for this study was a multidimensional approach in which both qualitative and quantitative approaches were used to complement each other. The role of the researcher in this study was that of the participant-as-observer. An induction workshop was conducted for both the combined instructional teacher (i.e. experimental teacher) and the traditional instructional teacher (i.e. control teacher) to help them explore and reflect on their practice with the view to create in them an appreciation for multiple teaching strategies or traditional teaching strategies to teaching and learning respectively.
The relevance of science education: as seen by pupils in Ghanaian junior secondary schools
(University of the Western Cape, 2006) Anderson, Ishmael Kwesi; Sjøberg, Svein; Mikalsen, Øyvind; Julie, Cyril; School of Science and Mathematics Education; Faculty of Education
This thesis was based on a larger international comparative study called the ROSE (Relevance of Science Education) project. The study investigated the affective factors pupils perceive might be of relevance for the learning of science and technology using the ROSE survey questionnaire, and was aimed at providing data that might form part of an empirical basis for local adaptation of the science curriculum.
Malawian secondary school students' learning of science: historical background, performance and beliefs
(University of the Western Cape, 2006) Dzama, Emmanuel Nafe Novel; Kolstoe, Stein Dankert; Holtman, Lorna; Mikalsen, Oyvind; School of Science and Mathematics Education; Faculty of Education
This study explored the problem of poor performance in science among students who are provided secondary school places on merit in Malawi. Existing studies of the problem are inconsistent suggesting that these studies may have shed light on some parts of a complex problem. Questionnaires, interviews and analysis of documents were used to obtain information concerning students’ conceptions of science, science learning and events that eventuated into the problem in the past. The population for this study was 89 government and governmentassisted secondary schools. From that population eighteen schools were randomly selected from each of the six education divisions in the country. One thousand five hundred secondary class 3 students drawn from randomly selected schools participated. The participating students completed a 31item learning beliefs and practices questionnaire with items drawn from the science education literature and adapted to the local situation and a selfefficacy and attribution of failure questionnaire. Forty students were interviewed about their concepts of science and science learning. Relevant documents found in the Malawi National Archives were analyzed to determine the origin of the problem.
Prospective Zimbabwean "A" level mathematics teacher's knowledge of the concept of a function
(University of the Western Cape, 2006) Nyikahadzoyi, Maroni Runesu; Mtetwa, David K.; Julie, Cyril; Torkildsen, Ole Einar; School of Science and Mathematics Education; Faculty of Education
The purpose of the study was to investigate prospective 'A' level mathematics teachers’ knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers' knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers' subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers' underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept. As part of the study a theoretical framework for understanding prospective teachers' knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teacher’s knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.
Recent transformations in West-Coast Renosterveld: patterns, processes and ecological significance
(University of the Western Cape, 2008) Newton, Ian Paul; Faculty of Science
The incorporation of the geometry involved in the traditional house building in mathematics education in Mozambique: the cases of zambezia and sofala provinces
(2009) Soares, Daniel Bernardo; Persens, Jan
The incorporation of the geometry involved in the traditional house building in Mathematics Education in Mozambique The cases of Zambézia and Sofala Provinces D. B. Soares PhD thesis, Department of Didactics, University of the Western Cape Moved for (i) curiosity and interest for architecture, (ii) necessity of cultural preservation of traditional house building techniques and (iii) will for identifying the mathematics, especially the geometry, involved in the traditional house building, in order to suggest it’s incorporation in Mathematics Education, I decided to do this research as theme of Ethnomathematics, then Ethnomathematics can be seen as the study of the relationship between Culture,Mathematics and Mathematics Education.I made my research guided through two main questions:(1) What mathematics is involved in the traditional house building?(2) How can this knowledge be incorporated in Mathematics Education?In this study I consider traditional house in Mozambique a house with (i) walls made with reed, sticks, wood or bamboo strips, covered with mud, with grass or straw, and (ii) roofs thatched with grass, reeds or straw.For the data collection I (1) made interviews and observations in southern Zambézia (by Echuwabu speaking house builders) and in central and northern Sofala (by the Cisena speaking house builders), (2) studied some works on African house building, (3) read some inquiries from the years 1980s about house types, kindly lended by Sofala’s Cultural Heritage Archive, and read some works that relate socio-cultural activities and mathematics education.Among others I came across eight methods for the rectangle construction,two methods for placing posts vertically, two methods for placing beams horizontally and the translation of 27 (from 28) basic terms for Elementary Geometry into Echuwabu and into Cisena. All these methods are geometrically analyzed and some tasks for the school mathematics suggested.Some of the conclusions of the study were that traditional house building is only learnt by observation and active participation, that the mathematics involved in it can be incorporated in the category of folk mathematics, given that it develops in a working activity, and that the incorporation of the mathematics related to traditional house building in mathematics education has the advantage that house building in rural Zambézia and Sofala is gender free (both male and female people participate in traditional house building), and that teachers and future teachers recognize that the origin of the geometry is the practice -- and that can facilitate the incorporation of mathematics related to traditional house building in Mathematics (and teacher) Education in Mozambique.One of the suggestions of the thesis is that more cultural aspects and production techniques related not only to mathematics, but also to other sciences(and technology?) must be investigated and then used, so that, at least in the first school grades, the pupils can work with concrete examples of their daily lives and culture, and not only with examples from the “standard” text books.The pages in the thesis are indicated through numbers “1, 2, 3 …” and with de indication of the chapter, in the footer. Before chapter 1, Introduction, the vii pages will be indicated with “i, ii, iii, … ”. In the Appendix the pages are indicated with “A.1, A.2, A.3, …”.All page numerations lie below, at the right-hand side of the page. October 2009
Fitted numerical methods for delay differential equations arising in biology
(2009) Bashier, Eihab Bashier Mohammed; Patidar, Kailash C.
Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.
A comparison of grade 8 to10 urban and peri-urban learners context preferences for mathematical literacy
(University of the Western Cape, 2009) Blaauw, Christopher; Julie, Cyril; Mbekwa, Monde; NULL; Faculty of Education
The study explored the comparison of grade 8 to 10 urban and peri-urban learners' contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas; least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners.
Effects of a Dialogical Argumentation Instructional Model on Grade 10 Learners' Conception of Fermentation
(University of the Western Cape, 2010) Diwu, Christopher; Ogunniyi, Meshach B.; Langenhoven, Keith R.; Faculty of Education
The study catered for empirical and metaphysical dimensions of science and IKS. The study employed a quasi-experimental design as well as a qualitative research design. Two cohorts of students from a fictitiously named Culture Secondary School have been used in this study. The list of instruments for data collection were as follows: Conceptions of Fermentation (COF) questionnaire which was used to elicit learnerss pre- and post-test conceptions of fermentation with special reference to traditional beer or Umqombothi an Attitudes to Science (ATS) questionnaire which was used to find out the learners' worldviews, a Science Achievement Test (SAT) which was used to assess the learners' generalised knowledge of fermentation, a classroom observation schedule as well as a focus group interview schedule to gather additional qualitative data. All the instruments were in English with all technical and difficult terms in both English and isiXhosa (the learners’ home language). Both groups were exposed to Science/IKS-based lessons. The only difference between the two groups was that, the experimental group (E group) was exposed to a Dialogical Argumentation Teaching Model (DAIM) and the comparison group (C group) to a traditional teaching approach. The data gathered were both analyzed in terms of qualitative and quantitative descriptions.
Relevance of science education in Zimbabwe from the perspective of secondary school children - the voice of the learner about science and technology in a developing country
(2011) Mavhunga, Francis Zvidzai; Sjøberg, Svein; Mikalsen, Øyvind; Julie, Cyril
In all countries, regardless of culture and level of development, science and technology(S&T) are seen as key areas for further material development and welfare. A certain proportion of the population needs to develop S&T-related skills and competences at a high level. But also for the majority, who will not enter such careers, S&T are key subjects to master the challenges in everyday life and for full participation in democracy. In our efforts to make S&T attractive as careers and as a key subject for mastering challenges in everyday life, we need to know more about the interests, concerns and values of the learners.The study of Zimbabwean learners sought to find what students like to learn in science, their interest in science lessons, use of science principles in everyday life and what attitudes they have about the environment. Learners’ attitudes to S&T were also measured by an open ended question that sought their ideas on what they would like to research on if they were scientists.The empirical basis for this thesis is data collected with the ROSE instrument, developed by a team of international scholars in S&T education. Data used in this thesis is from twenty one secondary schools in Zimbabwe (N=734) targeting sixteen year old learners.Comparisons are made with twenty eight other countries.Factor analysis and descriptive statistics has been used to make comparisons of Zimbabwean and international trends.The Zimbabwean sample generally showed a mismatch between their expectations and realities of the science education curriculum. Results suggested that Science education was largely irrelevant to their needs and interests. Many out-of-class experiences were not explored in science classes. However, the sensitivity of learners to significant issues around their lives, such as AIDS and other diseases showed in their wish to research to cure those infected.The newly found voice of the learners will provide new insights on how to improve science education in Zimbabwe in such a way that it is able to meet the hopes, aspirations and the perceived interests, needs and priorities of the learners. Rapid developments in mundane applications of science and technology require that the curriculum negotiates a level that empowers learners to cope with a technologically driven world.For the development of capabilities to understand and use science and technology, either in daily life or study at higher levels the science education debate must periodically consider needs, views and concerns of the learners themselves among other stakeholders.
Effects of an argumentation-based instruction on grade 10 learners' understanding of the causes of pollution at a river site
(University of the Western Cape, 2011) Magerman, Ruben Clive; Ogunniyi, Meshach B.; Langenhoven, Keith; School of Science and Mathematics Education; Faculty of Arts
This study was based on the Science and Indigenous Knowledge Systems Project (SIKSP) at the School of Science and Mathematics Education, University of the Western Cape. The project seeks to enhance educators' understanding of and ability to implement a Science-IKS curriculum (Ogunniyi, 2007) through using the theoretical framework of argumentation (Toulmin Argument Pattern) to the extent that learners would value the significance of both worldviews. This study sought to find the effects of an Argumentation-Based Instruction on grade 10 learners' understanding of the causes of pollution at a river site. Since the integration of Science and IKS are envisaged by Curriculum 2005 (C2005), two theoretical argumentation constructs have been used namely, Toulmin's (1958) Argumentation Pattern (TAP) and Ogunniyi's (1995) Contiguity Argumentation Theory (CAT).
Fitted numerical methods to solve differential models describing unsteady magneto-hydrodynamic flow
(2011) Buzuzi, George; Patidar, Kailash C.
In this thesis, we consider some nonlinear differential models that govern unsteady magneto-hydrodynamic convective flow and mass transfer of viscous, incompressible,electrically conducting fluid past a porous plate with/without heat sources. The study focusses on the effect of a combination of a number of physical parameters (e.g., chemical reaction, suction, radiation, soret effect,thermophoresis and radiation absorption) which play vital role in these models.Non dimensionalization of these models gives us sets of differential equations. Reliable solutions of such differential equations can-not be obtained by standard numerical techniques. We therefore resorted to the use of the singular perturbation approaches. To proceed, each of these model problems is discretized in time by using a suitable time-stepping method and then by using a fitted operator finite difference method in spatial direction. The combined methods are then analyzed for stability and convergence. Aiming to study the robustness of the proposed numerical schemes with respect to change in the values of the key parame- ters, we present extensive numerical simulations for each of these models. Finally, we confirm theoretical results through a set of specificc numerical experiments.
The effect of an argumentation-based instructional approach on Grade 3 learners' understanding of river pollution
(University of the Western Cape, 2012) Philander, Lorraine; Ogunniyi, Meshach B.; NULL
The research reported in this paper involves the use of dialogical argumentation in scientific context with 7-9 year olds as part of teaching and learning in primary classrooms. To develop an understanding of scientific concepts, four suitable collaborative activities on river pollution were used as a stimulus to effectively engage learners in scientific reasoning and use evidence for decision-making through cognitive harmonization. The research, involved four groups of five children each. Data were collected through analysis of children’s Water Pollution Questionnaire (WPQ), classroom observation, documentation of field notes, conversations and focus group interviews. The study found that all groups were able to engage in the activities to some extent, but that good quality argumentation develops when children are familiar with working in this manner. This study sought to investigate the opportunities, possibilities and challenges associated with a dialogical argumentation teaching and learning approach in a primary school science class A mapping technique was used to analyze the children’s discussions and identify the quality of their different “levels” of argument. This study confirmed that an argumentation based instruction was an effective way of enhancing learners’ understanding of river pollution. The learners’ listening skills improved tremendously and they were actively involve during discussions and provided claims with valid grounds or reasons. They were also very enthusiastic and challenged each other’s claims during these argumentation lessons, but most of all was the enjoyment that was visible on their young faces. Further research needs to be carried out over a longer period to determine the effectiveness of an argumentation based instruction.
Preferred contexts of Korean youth for the learning of school mathematics (grades 8-10)
(2012) Kim, Sun Hi; Julie, Cyril; Holtman, Lorna; Mbekwa, Monde
This study investigated real life situations which learners in South Korea grade 8-10 learners would prefer to be used in school mathematics.This thesis is based on the ROSMEII (Relevance of School Mathematics ducation) questionnaires and interviews, which was used to examine the preferred mathematical learning contexts for South Korean grade 8-10 learners. The study investigates the affective factors that pupils perceive to be of possible relevance for the learning and teaching of mathematic; and is aimed at providing data that might form part of a basis for a local theory of the mathematics curriculum. The standardized ROSMEII survey questionnaire of 23closeended items that relate to some aspects of mathematics on a 4-point Likert-type scale was administered to Korean grade 8-10 learners at the end of compulsory schooling, and mainly 14 to 16 year old cohorts. The data for this study were collected from a sample of 1839 learners drawn from 26 South Korean schools in the year 2009. Interviews were conducted to gauge the pupils‘ preference of the ROSMEII questionnaire contexts and used to validate learners‘ responses. In analyzing their responses, it became clear that, on the average, views expressed were common to all groups of pupils in South Korea (whether male or female, or from the metropolitan, city, or countryside). The clusters of the most preferred mathematical learning contexts are linked to youth culture, which learners are usually and easily engaged with in one way or another. These clusters include the sports, leisure and recreation cluster; planning a journey/popular youth culture cluster the technology cluster; the making of computer games, storing music and videos on CD‘s and Ipods. The lowest preferred mathematical learning contexts are: an agricultural cluster which focuses on agricultural matters and traditional games (yut). In conclusion, this study suggests that teachers should use contexts that increase learners‘ interest in classroom activities. Therefore mathematics curricula and textbooks which are appropriate to this context must be provided in order to provide more efficient mathematics education. It is imperative that the Korean school system must develop a particular program for nurturing learners‘ mathematical power. Furthermore, mathematics education policy makers must reconsider whether the current education system is appropriate, and also listen to learners‘ preferences when designing appropriate mathematics curriculum and textbooks.
Effects of a dialogical argumentation based instruction on grade 9 learners’ conceptions of a meteorological concept: cold fronts in the Western Cape, South Africa
(University of Western Cape, 2012) Riffel, Alvin Daniel; Ogunniyi, M.B.
This study looks at the effects of a dialogical argumentation instructional model (DAIM) on grade 9 learners understanding of selected meteorological concepts: Cold fronts in the Western Cape of South Africa. Using a quasi-experimental research design model, the study employed both quantitative and qualitative (so-called ‘mixed methods’) to collect data in a public secondary school in Cape Town, in the Western Cape Province. A survey questionnaire on attitudes and perceptions towards high school as well as conceptions of weather was administered before the main study to give the researcher baseline information and to develop pilot instruments to use in the main study. The study employed a dialogical instructional model (DAIM) with an experimental group of learners exposed to the intervention, and recorded differences from a control group which had no intervention. Learners from the two groups were exposed to a meteorological literacy test evaluation before and after the DAIM intervention. The results from the two groups were then compared and analysed according to the two theoretical frameworks that underpin the study namely: Toulmin’s Argumentation Pattern - TAP (Toulmin, 1958) and Contiguity Argumentation Theory - CAT (Ogunniyi, 1997). Further analyses were conducted on learners’ beliefs and indigenous knowledge, according to their conceptual understanding of weather related concepts used in the current NCS (National Curriculum Statement). After completing the study some interesting findings were made and based on these findings certain recommendations were suggested on how to implement a DAIM-model into classroom teaching using Indigenous Knowledge (IK). These recommendations are suggestions to plot the way towards developing a science–IK curriculum for the Natural Sciences subjects in South African schools.
The contexts which Namibian learners in grades 8 to 10 prefer to use in mathematics
(University of the Western Cape, 2012) Shifula, Loide Ndahafa; Julie, Cyril; Mbekwa, Monde; NULL
One of the key ideas in the research on mathematics education is that the mathematical knowledge that learners acquire is strongly tied to the particular situation in which it is learnt. This study investigated the contexts that learners in grades eight, nine and ten prefer to deal with in the learning of mathematics based on their personal, social, societal, cultural and contextual concerns or affinities. The study is situated in the large-scale project called the Relevance of School Mathematics Education II (ROSMEII), which is concerned with the application and the use of mathematical knowledge and processes in real life situations. It is based on a survey of learners from ten (10) secondary schools in the Oshana and Khomas regions of Namibia. The ten schools that were sampled represent the spectrum of schools in Namibia in both urban and semi-urban areas. The Rasch model of data analysis is employed to provide some insight into the contextual situations learners would like to deal with in their mathematical learning. The data obtained for this study was analysed using the WINSTEPS Version 3.65.0 suite of computer programs. The current study arises from a concern about the absence of the voices of learners in the contextual situations in mathematics selected by adults such as mathematics teachers, inspectorates and curriculum and materials developers. The assumption is that the inclusion of learners’ insights into mathematics curricular might enhance mathematical learning. The study reveals that school children have an intrinsic desire to learn about mathematical issues embedded in real-life contexts. Several items which Namibian learners have shown interest in are issues they experience in life out of school which are not directly dealt with in school, such as managing personal and financial affairs, health matters, technology, construction, engineering and government financial matters. However, learners indicated to have a low preference in contexts like lotteries and gambling, national and international politics, cultural products, all kinds of pop music and dancing. This thesis contends that the inclusion of contexts in the mathematics curriculum which are of interest to learners will go a long way in facilitating good performance of learners in mathematics.

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