Magister Educationis - MEd (Mathematics)

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An analysis of Grade 12 national examinations marking memoranda on the topic of measurement in Mathematical Literacy using a mathematical modelling framework.
(University of the Western Cape, 2017) Bali, Mbulelo; Mbekwa, M.
The research study conducted an in-depth analysis of the national marking memoranda on the topic of measurement in Mathematical Literacy. The object of analysis was the grade 12 national examinations. The purpose of Mathematical Literacy, according to the Department of Basic Education (DBE), is to equip learners with competencies that will enable them to use elementary mathematical concepts and skills to make sense of, participate in and contribute to the twenty-first century world characterised by numbers, numerically based arguments and data represented and misrepresented in a number of ways. With such competencies learners will in future become responsible individuals, contributing workers and participative critical citizens on social and political issues.
A case study of how learners apply a Grade 10 study skills module in a mathematics class
(University of the Western Cape, 2016) Arnold, Feeroezah; Julie, C.; Mbekwa, Monde
A qualitative case study was used to investigate how learners apply a study skills guide during the teaching of mathematics content in a Grade 10 class. A great amount of research and money is continually spent focussing on improving mathematics performance throughout the world. Performance of our learners in South Africa is of concern to the government as well as educators. Researchers agree that many learners lack effective study skills, which is the reason for their poor performance in mathematics. This study intended to infuse study skills in mathematics lessons as an intervention. The study skills intervention sessions were done over a period of 6 weeks. These study skills were infused in topics of the mathematics curriculum which was done in the previous quarter of the school program. Data was collected through interviews, journal entries and a questionnaire. The interviews were done before study skills instruction while the questionnaire was administered after completion of the sessions. Journal entries were completed during the 6 week instruction period by learners. It was found that some learners used the study guide as intended whilst others did not. Furthermore there was improvement in learners' scores for the topics focused on at the end of the study compared to the scores for similar topics in a school-based test written about two months before the intervention. It is concluded that the infusion of study skills in lessons has the potential for improving achievement in high-stakes mathematics examinations.
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.
Conceptions of conservation of energy among grade seven learners in two cape town schools
(University of Western Cape, 2021) Okoroh, Nwakaego Esther Malin; Ogunniyi, M.B.
The clamour in the country about the poor performance of learners in the area of physical science is a concern and this problem had been attributed to different facets of learning which include the amendment of curriculum over the years. But my question is; can the curriculum amendment succeed without effective teaching approaches? This poignant question formed the central concern for this investigation. This study examined two cohorts of grade seven learners’ conceptions of conservation of energy using a Dialogical Argumentation Instructional Model (DAIM) as well as the Traditional Lecture Method (TLM). The study involved 48 learners selected from two public schools in Cape Town. Using a quasi-experimental (Non-equivalent groups) design, the study examined the two groups from different schools (24 learners in each). It exposed one group to the Traditional Lecture Method (TLM) and the other group to a Dialogical Argumentation Instructional Model (DAIM) which was based on two argumentation frameworks– Toulmin’s Argumentation Pattern (TAP) and Contiguity Argumentation Theory (CAT).
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.
The development of the number concept in Grade R: a case study of a school in the Wellington area
(University of the Western Cape, 2014) Le Grange, Lynn Louise; Hartley, M S
Systemic evaluation undertaken by the Department of Basic Education as part of the Literacy and Numeracy Strategy 2006 – 2016 posed a serious challenge in South African schools. The numeracy and mathematics results in 2009 stated that 35% of learners in Grade 3 achieved the required level of competence in Mathematics. This has, however, improved to 48.3% in 2010 but dropped to 47.6% in 2011. The development of early number concept in countries such as the Netherlands, Singapore and Helsinki has shown that early intervention is essential for reaching mathematical success in schooling. The Curriculum and Assessment Policy Statement (CAPS) integrates the three learning programmes: Literacy, Numeracy and Life Skills for Grade R into a daily programme of activities. Within this daily programme it specifies that 35% of each day must be used towards Numeracy. The Grade R method of teaching emphasizes the fact that teaching must take place informally but planned formally. The purpose of this study is to examine how early mathematics is taught in an integrated and informal setting to improve number concept. The theoretical framework underpinning this study is based on the constructivist views of Piaget and Vygotsky and how these theories lay the foundation for the development of number concept in Grade R. Number skills to develop number concept were identified in nine lessons to underpin the content area 1, Numbers, Operations and Relationships as determined by the Grade R Mathematics Curriculum and Assessment Policy Statement (CAPS). The methodology employed to answer the research question were video-recordings, observations and interviews. The findings identified number skills such as emergent number concepts: distinguishing numerosity, imitating resultative counting and symbolizing by using fingers as well as growing number concepts: discovering different meanings of numbers, oral counting, one- to- one correspondence, rote counting, perceptual subitising, resultative counting, representing and symbolizing numbers, ordinality, place value, emergent object-based counting and calculating and golden moments. The discussion of the findings focused on the CAPS content area and how these number skills were used to achieve the demands of the content area 1. The major findings of this study presented a case of the utilization of number skills to achieve the development of number concept in Grade R, how mathematics should be made fun, and how incidental learning, “golden moments” can be used to introduce key mathematical concepts informally. This study has implications for teachers of Grade R and for the training of pre-service Grade R teachers at tertiary level.
The effect of an argumentation instructional model on pre-service teachers' ability to implement a science-IK curriculum
(University of the Western Cape, 2013) Siseho, Simasiku Charles; Ogunniyi, Meshach B.; NULL
This study investigated the effect of an Argumentation Instructional Model (AIM) on the preservice teachers‘ ability to implement a Science-IK Curriculum in selected South African schools. I examined what instructional practices the pre-service teachers engage in when they introduce scientific explanation and whether those practices influence learners‘ ability to construct scientific explanations during a natural science unit of a South African school curriculum. My study began with a pilot study of 16 pre-service science teachers who completed a B.Ed university module, Science for Teaching, which included an IK component. Data collection for main study took place from 2010 to 2011, and used questionnaires, face-to-face and reflective interview protocols, case studies, lesson plans and classroom observation schedules. I took videos and audios of each of the pre-service teacher‘s enactment of the focal lesson on argumentation and then coded the videotape for different instructional practices. The study investigated firstly, what currently informed teachers‘ thinking, knowledge and action of IK. Secondly, the research questioned how teachers interpreted and implemented IK in the science classroom. A sample of the three pre-service teachers were followed into their classrooms to investigate how they specifically implemented Learning Outcome Three using argumentation instruction as a mode of instruction and what approaches relevant to the inclusion of IK were developed. The study found that the three pre-service teachers used three very different approaches through which IK was brought in the science curriculum. An assimilationist approach, that brings IK into science by seeking how best IK fits into science. A segregationist approach that holds IK side-by-side with scientific knowledge. Lastly, an integrationist approach makes connections between IK and science. The approaches developed by the pre-service teachers were found to be informed by their biographies, values, cultural backgrounds and worldviews. Meticulously, the study explored how shifts were being made from a theoretical phase at the university where the pre-service teachers engaged IK to an actual phase of implementation in their school science classrooms. Finally, I attempted to explain why the pre-service teachers interpreted and implemented IK in the way they did.
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.
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.
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.
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.
Effects of a dialogical argumentation instructional model on science teachers’ understanding of capacitors in selected Western Cape schools
(University of the Western Cape, 2015) Goodman, Lynn; Fakudze, C.; Ogunniyi, Meshach B.
This study investigated 1) the conceptions on capacitors held by a group teachers in the Western Cape; 2) the effect of a dialogical argumentation instructional model on the teachers’ conceptions on the capacitor; and 3) the teachers’ perceptions on the implementation of this instructional model. The theoretical framework of the study was based on Toulmin’s Argumentation Pattern (TAP) and Ogunniyi’s Contiguity Argumentation Theory (CAT). The objective was to retrain science teachers in their awareness and understanding of the Nature of Science and Indigenous Knowledge Systems thereby enhancing their ability and efficacy in integrating science and Indigenous Knowledge Systems. The study involved workshop activities that included the teachers’ Reflective Diary, interview sessions, and video-taped lesson observations. The study adopted a Case Study approach and the data was analysed both quantitatively and qualitatively. The findings of the study showed that: 1) the teachers held varying conceptions of the capacitor; 2) the teachers’ conceptions of the capacitor improved after being exposed to the Dialogical Argumentation Instructional Model and 3) the teachers were dominantly in favour of the Dialogical Argumentation Instruction Model as a teaching method to be introduced at schools. The implications of the findings for school science and pedagogy were highlighted for closer observation.
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).
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.
Effects of dialogical argumentation instruction on grade 10 learners’ understanding of concepts of chemical equations
(University of the Western Cape, 2014) George, Frikkie; Ogunniyi, Meshach B.
This study explored the dialogical argumentation instruction approach to determine whether it enhanced grade ten learners‟ understanding of the chemical equation concept. Toulmin‟s argumentation pattern and the contiguity argumentation theory underpin this study and was used to construct the dialogical argumentation instruction methodology, which was used as the intervention strategy. Information and communication technology and computer-assisted learning were used as contextual environment for this study. This study is located in the interpretive paradigm and the data was collected and analysed using both qualitative and quantitative methods based on a quasi-experimental research design model. A survey questionnaire, open-end and fixed choice questionnaires and a chemistry achievement test was used to collect data from a high school in the Western Cape Province
Effects of using a dialogical argumentation instructional model to teach grade 11 learners some concepts of sound by means of indigenous musical instruments
(UWC, 2012) Angaama, Daniel Angwe; Ogunniyi, Meshach B.
Two grade 11 classes of two high schools in Cape Town were taught some concepts of sound by means of indigenous musical instruments. The purpose was to find out the relative effects (or none) of two instructional strategies. Toulmin (1958)’s Argumentation Pattern, Ogunniyi (1997)’s Contiguity Argumentation Theory and Reiner et al. (2000)’s Substance Schema formed the theoretical framework. A pre-post-test quasi-experimental design was employed and data collated using questionnaires, a sound conceptual test, argumentation worksheets, and classroom observation schedules. One teacher taught the experimental group using dialogical argumentation while another teacher taught the comparative group using lecturedemonstration method, coupled with the use of ICTs for duration of four weeks. Data were analysed using a mixed (quantitative and qualitative) methods approach. The findings revealed that many the learners held some scientifically valid conceptions of sound prior to formal instruction. However, the learners also held many scientifically invalid conceptions in relation to the speed of sound in air, sound propagation, and sound produced by stringed instruments. The alternative conceptions of learners in the C group remained largely unchanged after instruction, while those of the E group changed appreciably, but not completely. The E group learners changed the alternative conceptions that were worked into structured argumentation activities better than those which were not. Also, the learners in both groups seemed to hold indigenous beliefs in relation to sound which did not seem to change after instruction. Most learners had a positive attitude towards the use of indigenous knowledge in the science class. No significant difference was found between male and female learners with respect to conceptual understanding of sound, indigenous beliefs, and interest in the integration of science and indigenous knowledge.
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.
Exploring the effect of a Dialogical Argumentation Instructional Model in enhancing grade two learners' understanding of the day and night cycle
(University of the Western Cape, 2016) February, Florence; Fakudze, C.; Ogunniyi, Meshach B.
Over the last 15 years the Department of Education has rolled out various projects in an attempt to improve Mathematics and Science results and to increase the amount of learners who exit their schooling with those subjects. The 2010 - 2014 matric results show a decrease in the number of students who exiting with Science. One of the factors that might influence the learners' decision to do science can be ascribed to the methodologies that the teachers are using to teach Science. In response to the latter, this study investigated the cognitive shifts of grade two learners' conceptual knowledge of the day and night cycle after being exposed to a Dialogical Argumentation Based Instructional Model. The Contiguity Argumentation Theory (CAT) and Toulmin's Argumentation Pattern (TAP) were used as a framework to capture and interrogate learners' arguments with argumentation frames developed to categorize the learners’ argument responses. Analytical approaches were used to assess learners' argumentation skills along four stages namely intra-argumentation, inter-argumentation, whole class discussion and trans-argumentation. The study employed both quantitative and qualitative methods. The data was collected from grade 2 learners in a primary school in Cape Town, Western Cape Province in the form of a pre-post questionnaire, focus group interviews and classroom observation. The major findings of this study indicated that ● The Dialogical Argumentation Instructional model can assist learners to develop argumentative skills. ● The grade two learners in this study had alternative conceptions regarding the day and night cycle which is not scientifically valid. ● The views that learners hold are egocentric. ● DAIM is an effective teaching strategy to help learners to eliminate the misconceptions This study has shown that the Dialogical Argumentation Instructional Model (DAIM) seems to be effective in enhancing the learners’ understanding of the day and night cycle.
The impact of using technology through cooperative learning on learners’ performance on grade 11 circle geometry
(University of the Western Cape, 2020) Shonhiwa, William; Govender, Rajendran
Euclidean geometry was recently re-introduced as a compulsory topic in the Mathematics Curriculum for learners in the Further Education and Training (FET) band in 2012. The diagnostic analysis reports on the National Senior Certificate (NSC) Mathematics Paper 2 examinations since 2014 has repeatedly expressed concern of the poor performance of leaners in proof and reasoning items linked to circle geometry. Various efforts have been made to examine the composition of the curriculum to find ways of motivating learners in the study of circle geometry and enhancing their performance but not much has been realized. The use of technology or cooperative learning approaches for the teaching of geometry is beneficial for pedagogical purposes, particularly for improving learners’ performance in geometry. Hence, this study investigated the impact of using technology through cooperative learning on learners’ performance on grade circle 11 geometry. It was thus an attempt to focus on blending these two teaching methods with an emphasis on the use of technology. The research took place at a Khayelitsha school and the scope of technology was limited to using a mathematical computer programme called Heymath.
Implementing an intentional teaching model to investigate grade 9 learners’ ways of working with rational algebraic fractions
(University of the Western Cape, 2019) Maphini, Nwabisa Vivian; Mbekwa, Monde; Julie, Cyril
In South Africa it is widely known that most learners struggle with mathematics. The results for mathematics are poor. The department of basic education offers a number of intervention programmes to assist learners in mathematics but the problem still persists. Algebra is the most basic and important topic in mathematics as it becomes an element in almost all the other topics in mathematics curriculum. Algebraic fractions in particular are a challenge for most leaners. Research shows that learners commit a number of errors when they work with algebraic fractions. The study investigated the implementation of an intentional teaching model into grade 9 mathematics learners’ ways of working with rational algebraic fractions. An intentional teaching model is a teaching strategy which emphasizes teaching intentions or teaching objectives are brought to the fore during a lesson, the model emphasizes the use of spiral revision and assessment for learning. Ways of working in this study refers to the way in which learners deal with algebraic fractions when they simplify them including the errors they commit from the misconceptions they have about aspects of working with fractions. The study was conducted in a group of grade 9 mathematics learners at Gugulethu High school, which is located in Guguletu, a township in the Western Cape Province of South Africa. The study is premised on a qualitative research paradigm which focuses on studying situations in their natural settings and applying an interpretive perspective. Data was collected by means of observation and video recording of lessons while learners were engaged in working with algebraic fractions. Learners’ written work was analysed as part of the data collection. The results of the study show that leaners commit a number of errors when they manipulate algebraic fractions. Among other errors are: (i) Cancellation errors which had the highest frequency of occurrence (ii) Defractionalisation (iii) No recognition of the common factor and (iv)Exponential laws error. It was found that the learners’ ways of working with algebraic fractions are mostly characterised by their misunderstanding of exponential laws and difficulty in working with fractions needing the use of factorisation to simplify and find the lowest or highest common denominator during addition or subtraction. The results of the study also reveal that learners struggle to articulate extensively or in detail what they are actually doing as they simplify rational algebraic fraction.

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