1,720,975 research outputs found
Exploring in-service Zimbabwean mathematics teachers’ preparedness to incorporate ethnomathematics approaches to geometry teaching and learning.
Get PDFDoctoral Degree. University of KwaZulu-Natal, Edgewood.Geometry teachers and learners in Zimbabwe come from a wide range of cultural and social backgrounds. This provides opportunities and challenges in the teaching and learning of geometry. The wide variety of cultural and social backgrounds that the learners bring into the geometry classroom point towards the teachers’ use of learners’ prior knowledge and other cultural experiences as well as activities to improve their performance. The integration of ethnomathematics approaches into the teaching of geometry is beneficial for pedagogical purposes, specifically for improving learners’ performance in geometry. This study explored in-service mathematics teachers’ preparedness to integrate ethnomathematics approaches into the teaching and learning of geometry.
The research was grounded, hypothetically, in social constructivism views of mathematics teaching and learning. Using a pragmatist research paradigm, this convergent parallel mixed methods study involved a questionnaire and focus group discussions with forty second year in-service teachers enrolled in a three-year Bachelor of Science Education Honours program. Proportional stratified random sampling was employed to select the participating teachers for the questionnaire, whilst research based recruitment was used for the focus group discussions. The forty teachers who were involved in the completion of the questionnaires formed the five focus groups.
Data was analysed in an endeavour to determine the teacher’s training on geometry and ethnomathematics approaches. Further, teachers’ views towards the integration of ethnomathematics approaches and challenges faced on the integration of ethnomathematics approaches into the teaching of geometry were also analysed. Inductive data analysis and interpretive data analysis were employed in this study for qualitative and quantitative data analysis respectively. Findings show that both traditional and learner-centred approaches were used by their lecturers during their teacher training period. The approaches that were used during their training were the same that they were using in schools to teach geometry. Findings also show that some of the teachers were not adequately trained to teach geometry. Teachers indicated that they did not do any specific course on ethnomathematics approaches and on how to integrate it into the teaching of geometry. The study also reveals that most of the teachers were of the view that ethnomathematics approaches should be integrated into the teaching of geometry because of the various benefits associated with its use. The study reveals that some of the teachers are using the principles of ethnomathematics approaches such as teaching geometry that builds on learners’ prior knowledge, background and the role that learners’ cultural background as well as the environment play during their learning. However, teachers face various challenges in the integration of ethnomathematics approaches into the teaching of geometry, such as, lack of resources, cultural diversity, lack of geometrical content knowledge, lack of knowledge on ethnomathematics approaches and resistance to change by both teachers and learners.
The role of teachers in the integration of ethnomathematics approaches into the teaching of geometry is of great significance. It is suggested that the government should take greater responsibility to involve the teachers in syllabus development with clear goals and content, develop teachers’ capacity in integrating ethnomathematics approaches when teaching and provide teaching and learning resources for successful integration
An investigation of secondary school mathematics teachers’ knowledge and utilization of their students’ learning styles.
Get PDFDoctoral Degree. University of KwaZulu-Natal, Durban.This study explores secondary school mathematics teachers’ knowledge of students’ learning styles and how they used the knowledge when they were teaching mathematics. The study went further to explore barriers which the mathematics teachers faced when they were teaching their students according to the students’ learning styles. The study was a qualitative exploratory interpretive case study of thirty-four secondary school mathematics teachers from ten secondary schools. It was carried out in the Makoni District of Manicaland Province in Zimbabwe. The schools were selected using stratified random sampling. Stratified random sampling was used as a way of making sure that schools from different responsible authorities were represented in the study. Mathematics teachers were purposefully selected since the researcher sought data on the mathematics teachers’ knowledge of students’ learning styles and how they used the knowledge in mathematics teaching. All the mathematics teachers at the selected schools took part in the study. The study was done in three phases. A phase addressed one research question. The results of the study revealed that the mathematics teachers had basic knowledge of students’ learning styles. The teachers thought that teaching students according to their learning styles had more benefits than problems. The mathematics teachers varied their teaching strategies when they were teaching mathematics. They sometimes tried to meet the demands of their students’ learning styles. However, some of the students’ learning styles were not catered for by the teachers. The teachers did not use standard tools to assess the learning styles of their students. A number of barriers impinged on the mathematics teachers as they individualised their teaching strategies in order to meet the demands of their students’ learning styles. The barriers were classified into the following categories: teacher related barriers, student related barriers, curriculum related barriers and socio-economic barriers. The researcher recommended that the mathematics teachers be in-serviced so that they could overcome the barriers that impinged on their use of students’ learning styles when teaching mathematics. Besides attending to in-service courses, the teachers could form clubs, panels and associations so that they could share ideas on how best they could assist their students to learn. It was also important for the teachers to avoid competing with each other and collaborate for the benefit of all their students despite the different learning styles that the students had. The researcher also recommended that the teachers consider the learning styles of all their students when they teach mathematics. Their lesson plans and delivery of lessons had to be determined by the learning styles of their students. The researcher also found it important for the teachers themselves to know their own learning styles so that their teaching strategies were not controlled by their learning styles but by the learning styles of their students. The researcher also recommended further studies on the same topic but to be carried out in a different setting. The researcher expressed interest, in future, to carry out a study to find the proportions of learners with particular learning styles in a normal class. Recommendations were also made on the need to carry out studies to establish the relationship between differences in learning styles and the performance of the students. There was also need to find out how factors like gender and age affect learning styles.List of Publications arising from this thesis on page v
Investigation of the South African public TVET colleges’ engineering official mathematics curriculum for entry level artisans.
Get PDFDoctoral Degree. University of KwaZulu-Natal, Durban.One of the main objectives of any mathematics curriculum is to equip students with the
necessary thinking skills for real-world problems. As the world evolves every day of our lives,
so do the people living in it. Hence, the same exceptional functioning curriculum used in
previous years is highly possible to be dysfunctional in the current days. Therefore, time and
again curriculum evaluation is essential for both Basic and Higher education. However, before
the actual curriculum evaluation, one should identify or develop suitable evaluation tool/s. In
that regard, this study focused on the evaluation of the public Technical and Vocational
Education and Training (TVET) colleges’ mathematics curriculum from N1 to N2. Initially,
the intention of the current study was to collect data across all KwaZulu-Natal TVET Colleges,
which was unsuccessful due to a lack of cooperation from some of the TVET colleges’
gatekeepers. The study was only able to access the eMnambithi TVET College data set, where
47 students participated. Two aspects were evaluated, namely, the participating students’
attainment of the curriculum objectives and the ability of the curriculum to equip students with
high order thinking skills (HOTS). The Tyler’s objective model was adopted to evaluate the
effectiveness of the curriculum to train students for the attainment of the curriculum’s
objectives. That was done using the pre- and post-assessments method as stated by the pioneer
of that model. The results indicated that the curriculum was most likely to be incapable of
equipping the students for the attainment of its own objectives. Further on, this study used the
Susceptible-Infected-Recovered (SIR) model to develop a new model called the Susceptible Vaccinated-Healthy-Infected-Recovered (SVHIR) model. The SVHIR model was used to
evaluate the effectiveness of the curriculum to equip students with HOTS. Also, the results
obtained from the SVHIR model indicated that the curriculum was most likely to be incapable
of equipping the students with HOTS. It was also found that the students’ ability to attain the
curriculum objectives and their HOTS have a strong linear relationship. The latter implied that
fully equipping students with HOTS should enable them to better attain the curriculum
objectives. The convenience sampling supports the need to conduct a future study that covers
all the TVET colleges that did not respond to the researcher’s request for access on time.
Further pursuance will give more clarity and findings that may or may not differ that much
with the ones of this reported study
An APOS exploration of conceptual understanding of the chain rule in calculus by first year engineering students.
Get PDFThesis (Ph.D.)-University of KwaZulu-Natal, Edgewood, 2011.The main issue in this study is how students conceptualise mathematical learning in the context of calculus with specific reference to the chain rule. The study focuses on how students use the chain rule in finding derivatives of composite functions (including trigonometric ones). The study was based on the APOS (Action-Process-Objects-Schema) approach in exploring conceptual understanding displayed by first year University of Technology students in learning the chain rule in calculus.
The study consisted of two phases, both using a qualitative approach. Phase 1 was the pilot study which involved collection of data via questionnaires which were administered to 23 previous semester students of known ability, willing to participate in the study. The questionnaire was then administered to 30 volunteering first year students in Phase 2. A structured way to describe an individual student's understanding of the chain rule was developed and applied to analyzing the evolution of that understanding for each of the 30 first year students. Various methods of data collection were used namely: (1) classroom observations, (2) open-ended questionnaire, (3) semi-structured and unstructured interviews, (4) video-recordings, and (5) written class work, tests and exercises.
The research done indicates that it is essential for instructional design to accommodate multiple ways of function representation to enable students to make connections and have a deeper understanding of the concept of the chain rule. Learning activities should include tasks that demand all three techniques, Straight form technique, Link form technique and Leibniz form technique, to cater for the variation in learner preferences. It is believed that the APOS paradigm using selected activities brought the students to the point of being better able to understand the chain rule and informed the teaching strategies for this concept.
In this way, it is believed that this conceptualization will enable the formulation of schema of the chain rule which can be applied to a wider range of contexts in calculus. There is a need to establish a conceptual basis that allows construction of a schema of the chain rule. The understanding of the concept with skills can then be augmented by instructional design based on the modified genetic decomposition. This will then subject students to a better understanding of the chain rule and hence more of calculus and its applications
An exploration of the design and development of a semi-integrated curriculum for a mathematical literacy course offered in a B-Ed. programme at a South African university.
Get PDFDoctor of Philosophy in Education Studies. University of KwaZulu-Natal, Edgewood 2016.An exploration of the design and development of a Semi-Integrated Curriculum conceptualized for the Mathematical Literacy module, offered as part of the Bachelor of Education course, was conducted at the University of Zululand, South Africa. The research focussed on exploring the feasibility and sustainability of integrating various curriculum elements, namely: context, content, and a set of predetermined essential skills and concepts. The research further explored the effectiveness of consolidating essential skills and concepts prior to the introduction of context-based problems. The appropriate level at which those elements should be integrated was also investigated. Another significant objective of the study was to explore the extent to which Higher Order Thinking Skills could be developed and sustained by a curricular innovation such as the Semi-Integrated Curriculum.
The mathematical-literacy-related competency levels attained at school by first-year students in the Faculty of Education and reinforced by the first-year university mathematical literacy module, were of concern to the faculty. A need for significantly improving the mathematical literacy competency levels of students across majors was therefore the principal rationale of this research. Non-science major students made up a large portion of the Faculty of Education’s student population. Ensuring a satisfactory level of mathematical literacy in the student teachers across the faculty was thus imperative.
Based on a qualitative research paradigm, this research used a case-study research method that involved a single case study with multiple units of analysis. The research was guided by the overarching research question related to the design and development of a Semi-Integrated Curriculum, the answer to which was constructed by the five sub-questions that were simultaneously answered. Ten student participants were selected from the first-year mathematical literacy student cohort. These students were taken through a series of specially designed mathematical literacy teaching and learning sessions. The content matter taught was designed according to the Semi-Integrated Curriculum format. A pre-test administered prior to the contact sessions and a post-test administered after the contact sessions indicated levels of attainment and the influence the curricular intervention had had on the participants’ mathematical performance. The post-test also incorporated tasks that were designed to measure the levels of attainment of Higher Order Thinking Skills. Data collected included semi-structured interviews with the
participants conducted before and after the contact sessions; and an interview with the Head of Department. Sources of data collected also included informal working of participants gathered during contact sessions, curriculum materials published by the faculty, and relevant literature. Examination, test and assignment papers were also analysed to assess the level at which the current curriculum functioned and to explore the improvements needed.
Excerpts from transcripts of interviews and faculty curriculum documents were thematically analysed to determine initial categories which were later reduced to themes and concepts. The analysis focussed on deriving a broad understanding of the purpose with which the mathematical literacy course currently functioned, and possible changes in the formulation the purpose itself. The analysis also focussed on the formulation of a set of aspects that characterized the Semi-Integrated Curriculum. The influence of Higher Order Thinking Skills and their sustainability were also aspects that were scrutinised. The effect of a Semi-Integrated Curriculum on the development of mathematical-literacy-related competencies and Higher Order Thinking Skills were explored, in accordance with the conceptual framework that envisaged significant levels of attainment in such aspects of learning. Pre-test and post-test scripts were also analysed to ascertain the levels of attainment of mathematical literacy competencies, and the extent to which Higher Order Thinking Skills were fostered and sustained.
The results indicated that a focussed curricular intervention such as the Semi-Integrated Curriculum does have an effect on the general mathematical-literacy-related competencies. However, major changes in the levels of attainment could not be established. The development and sustainability of Higher Order Thinking Skills were also noticed at a relatively low level despite instances of satisfactory performances from participants that were noteworthy. However, significant changes in the approach to learning and the influence that a curricular focus on Higher Order Thinking Skills can have on learning were remarkable. Participants developed noticeable positive changes in their mathematical learning approach that placed a heavy emphasis on conceptual mastery as opposed to procedural focus; which in turn led to changes in the attainment of Higher Order Thinking Skills. The significance of this research is, therefore, that curricular interventions focussing on consolidation of Essential Skills and Concepts prior to the introduction of context-based problems, in a mathematical literacy context, underpinned by an emphasis on Higher Order Thinking Skills, do produce positive changes in mathematical literacy competencies
Exploring university students' mental constructions of the limit concept in relation to sequences and series.
Get PDFDoctoral Degree. University of KwaZulu-Natal, Durban.The present thesis refers to some first semester calculus 1 university students’ mental constructions of the limit concept in relation to sequences and series. A plethora of research on the limit concept is available and suggests that the concept is on record of being difficult for students to learn and comprehend. However, in Zimbabwe, there is inadequate research on mental constructions made by students of the limit concept in relation to sequences and series. This research aims at filling this gap in the literature. This study utilized the Action-Process-Object-Schema (APOS) theory in exploring conceptual appreciative displayed by students when dealing with limits of sequences and series. The study proposes the genetic decompositions on how students might construct the mental constructions in learning the sequences and series through the use of Activities-Classroom discussions –Exercises (ACE). Collection of data was done by the use of a methodology that used practical teaching. All the thirty students who took calculus 1 accepted to participate in this study and answered the limit test questions. The students’ written responses were analyzed using APOS theory. Ten students were selected for interviews through purposive sampling. Two declined to take part leaving eight to take part in the process. The APOS theory was used to analyze the interview results. The revision of preliminary genetic decomposition was done basing on the analyzed data. The instructional method employed, facilitated the appreciation of the limit concept in relation to sequences and series by the students. Nearly all students showed that they operated at the Action level, a good number showed that they operated at least at the Process level and more than half of the students showed that they operated at the Object level. Three out eight interviewed students indicated that the managed to operate at the Schema level on some of the test questions. However, there is need for the establishment of a conceptual basis that promotes and allows the construction of the limit concept schema in relation to sequences and series. Furthermore, interviewed students’ responses paralleled the chronological improvement of the limit concept as reported in literature. Historical analysis of the development of concepts needs to be reflected upon when preparing and designing instruction. This would help the lecturer to foresee the challenges that lay ahead and address students’ difficulties during the learning process. The implementation of APOS Theory is recommended for the learning of other mathematical aspects, which cause difficulties in students’ learning. Moreover, other constructivist learning methods can be fused together with the APOS Theory to obtain improved results on students’ performance in mathematics.List of Figures on page v
An APOS Analysis of Natural Science Students' Understanding of Integration.
Get PDFThis article reports on a study which used the APOS (action-process-object-schema) Theory framework and a classification of errors to investigate university students' understanding of the integration concept and its applications. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The relevant rules for finding antiderivatives, the link between derivatives and antiderivatives, interpreting a definite integral as area under the relevant curve and their context-based applications were taught to undergraduate science students. This paper reports on the analysis of two students� responses to questions on integrals and their applications. The findings of this study suggest that those students had difficulty in applying the rules for integrals and their applications, and this was possibly the result of them not having appropriate mental structures at the process, object and schema levels.Este artículo responde a un estudio en el que se utiliza la teoría APOS (acción-proceso-objeto-esquema) y una clasificación de errores para investigar la comprensión del concepto de integral de un conjunto de estudiantes universitarios, y sus aplicaciones. La investigación se llevó a cabo en el Campus Westville de la University of KwaZulu-Natal en Sudáfrica. Las normas relevantes para encontrar anti-derivadas, la relación entre las derivadas y las anti-derivadas, la interpretación de la integral definida como área bajo la curva y las aplicaciones basadas en el contexto fueron enseñadas a los estudiantes de grado de ciencias. Este artículo presenta el análisis de las respuestas de dos estudiantes a preguntas sobre integrales y sus aplicaciones. Los resultados sugieren que los estudiantes tienen dificultades en la aplicación de las normas de integración, y posiblemente este resultado fue motivado por no disponer de estructuras mentales del proceso adecuadas
In-service secondary teachers’ teaching approaches and views towards integrating ethnomathematics approaches into geometry teaching
Get PDFGeometry teaching and learning ought to mirror and embrace the social diversity found in the geometry learning environment as well as the increasingly connected world. For that reason, ethnomathematics approaches that relate geometry teaching and learning to the learners’ cultural experiences and background should be used when teaching geometry. The aim of this study was to find out the teachers’ teaching approaches in geometry as well as their views towards the incorporation of ethnomathematics into the geometry teaching. A convergent mixed methods design was used in this study. Focus group discussions and questionnaires were used as data gathering instruments. The sample comprised of 40 in-service mathematics teachers. Findings show that both teacher-centered and learner-centered approaches were used in geometry teaching and learning. The study also revealed that teachers had the opinion that ethnomathematics approaches should be integrated into geometry teaching. The study recommends that teachers should be trained to use ethnomathematics approaches when teaching geometry
Some findings on the design and implementation of mathematics tutorials at a university
No full textThis paper reports on the design and effectiveness of four tutorial types in the context of first year mathematics tutorials, at a South African university for the period 2003 to 2011. A model for the design of mathematics tutorials was formulated. This model informed the design, implementation and refining of the mathematics tutorials over the nine year period. It was found that mathematics students get greater benefit from tutorials that are more organized and include a completion of homework unit requirement
First-year university students’ understanding of function concepts encountered in Grade 12 Mathematics: a case study
Get PDFThis article focuses on first-year university students’ understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics. In this study three online questions from two firstyear mathematics quizzes at the University of KwaZulu-Natal were analysed. The first question focused on the characteristics of a polynomial function, while the second and third questions focused on the characteristics of trigonometric functions. The characteristics included calculus-related concepts, for example, intervals of increase or decrease, concavity and local extrema. It was found that about a fifth of the participants (n = 557), science students who studied the core mathematics module Introduction to Calculus, had difficulties in answering those calculus-related questions compared to determining the general non-calculus characteristics, for example, the range and domain. The study also found that about a quarter of the participants lacked relational understanding with regard to calculus-related concepts. This study recommends that lecturers need to spend more time on calculus-related concepts of a function that focus on relational understanding
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