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How to cite this thesis Surname, Initial(s). (2012) Title of the thesis or dissertation. [Unpublished]: University of Johannesburg. EXPLORING LEARNING AND TEACHING STYLES OF MATHEMATICS AT AN URBAN UNIVERSITY IN SOUTH AFRICA BY: SANGHEE CHO A THESIS SUBMITTED TO THE FACULTY OF EDUCATION, DEPARTMENT OF MATHEMATICS, SCIENCE, TECHNOLOGY, UNIVERSITY OF JOHANNESBURG, SOUTH AFIRCA, IN FULFILMENT OF THE REQURIEMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY SUPERVISOR: PROFESSOR KAKOMA LUNETA JOHANNESBURG JANUARY 2016 DECLARATION I declare that this research report is my own, unaided work.
It is being submitted for the Doctor of Philosophy at the University of Johannesburg, South Africa. It has not been submitted before for any degree or examination in any other university. Signature 31st day of January, 2016 ii | P a g e DEDICATION This thesis is the completion of a prolonged, protracted and huge effort to acquire this qualification. With this reason and many others, I am ever thankful to the Lord Almighty; who granted me his wonderful grace so that I could successfully complete these studies.
iii | P a g e ACKNOWLEDGEMENTS First and foremost, I would like to thank God who cared for me and empowered me not only with this thesis but also throughout all the days of my life. I would like to express my sincere thank to my Supervisor, Prof. Luneta for his help from the proposal stage to final submission. I am deeply indebted to him for his invaluable guidance, support, and patience throughout this project.
Best wishes for him every success in his life and work through Christ. I also love to thank my husband, Christiaan. His love, patience, understanding and emotional support helped me through many difficulties. Without him, I would never be where I am now.
There are many people to whom I owe a debt of gratitude. I am deeply grateful to the members of the faculty of Mathematics and Education for their assistance and support. Above all, none of this would have been possible without prayer supports from whom I love; UBF members both in South Africa and South Korea, my parent, my parents-in- law and my friends. Great thanks to all of them with sincere love.
I dedicate this thesis to the LORD with my life. iv | P a g e ABSTRACT A conventional lecture course may be helpful to efficiently disseminate a huge body of content to a large number of students. However, it is possible for students to become passive recipients of knowledge. As a result, the traditional lectures can often produce undergraduates without the skills needed for professional success.
One of the recent reforms in mathematics education was the movement towards a student-centered instructional approach. Within this perspective, differences of students can be considered as resources for effective learning and teaching mathematics and learning and teaching style have been given great attention. There has been much debate about the relationship between, and effectiveness of learning styles and teaching styles. Regardless of the inconsistent results from two constructs, there are many benefits for being aware of learning and teaching styles.
It can lead to the improvement of various areas of learning and teaching; provision for different views of learning and teaching; aid for the learning process or enhancement of lecturer training, development and assessment. Considering the diversity of students’ backgrounds and abilities in South Africa, an awareness of the value of learning and teaching style will be helpful for more balanced instruction. This study sought to weigh the extent to which such a vision exists in the reality of teaching and learning at university, within the context of the relationships between learning and teaching styles. The learning styles of students and the teaching styles of lecturers in mathematics class were examined at an urban South African university.
An explanatory sequential mixed-methods approach was used to identify the prominent learning and teaching styles; and to provide different views of learning and teaching for a balanced instructional approach. The sequential explanatory mixed-methods design called for an initially round of quantitative data collection, which was followed by a qualitative bout of data collection. v|Page The quantitative and qualitative analysis shed some light on the relationship between learning and teaching styles for developing balanced instruction to enhance students with multidisciplinary skills. These analyses also provide a view based on learning- conducive environment where lecturers and students perform the integrated mathematics tasks.
From three phases (quantitative, qualitative and integrated analysis), two ways to promote a balanced instructional approach were obtained. Firstly, mathematical tasks should be authentic and meaningful. Given that most courses related to science and mathematics are favourable to ‘intuitive’ students, authentic problems linked to everyday life motivate students, especially the majority of ‘sensing’ students. Using authentic and real-world examples is considered as essential to mathematically empower students with multidisciplinary skills.
Secondly, students are to be familiar with abstract and conceptual-oriented problems in a holistic way. Formal education engages in a logically ordered sequential progression from concept to concept, which is favourable to ‘sequential’ students. Yet concrete aspects in handling the corresponding abstract objects in a holistic way are highly valued in any academic field. In a sense, students should be able to perceive and manipulate concepts and methods through a visual image in both sequential and global way.
To lead students to the level where they can make out what they are doing beyond the sequential comprehension, many new attempts would be constructive: open-ended problems and exercises; the overall conceptual framework with visual symbols; presenting problems before offering explanations; deep consideration of the connections between concepts; or contextualised and relevance-tied up concepts. Given that the university students in this study favour to learn mathematics in a collaborative and participatory way (‘collaborative and participant’ learning style); group- based works are advisable and more collaborative-oriented environment might motivate and accommodate more students. Yet many students did not take full responsibility of their learning (‘Dependent’), which was compatible with the fact that most lecturers used vi | P a g e traditional, teacher-centered styles in university settings. The needs to endorse students to be independent were found from both students and lecturers: ‘to work increasingly with less structured teaching materials and with less reliance on lecturers.
To create learning-conducive environment, students should vigorously and reflectively engage in the learning process which leads to active and effective teaching The results of identifying individual learning and teaching style were doubtful in terms of what they produced. It would be appropriate to consider that learning and teaching style are processing states rather fixed traits. They are affected by their affective characteristics, the nature of subject or topics, and their studying methods and educational philosophy. If lecturers use specific methods and aids in certain mathematics classes respectively such as the incessant lecturing, the considerable use of visual representations and giving students many opportunity to discuss could have a great bearing on how students view what they prefer.
Any attempt to implement changes in instructional processes should reckon with the interaction between students’ learning style and lecturers’ teaching style along with affective factors (their belief, emotional factors and attitude). vii | P a g e Table of Contents CHAPTER ONE: INTRODUCTION 1.1 Background to the study 3 1.2 Significance of the study 6 1.4 Purpose of the study 14 1.6 Definition of terms 15 1.8 Structure of the Study 16 CHAPTER TWO: REVIEW OF THE LITERATURE 2.2 Theories of learning and teaching 19 2.1 Behaviourism and Cognitive Learning theory 19 2.3 Learning and teaching style in Constructivism 27 2.3 Style as an central construct for individual development 32 2.1 Style in literature 32 2.2 From ‘Ability and Interest’ to ‘style’ 34 viii | P a g e 2.4 The Learning style 38 2.1 The theoretical development of learning style 38 2.2 Learning style as a characteristics of learners 39 2.3 The classification of learning style 44 2.4 The learning style of cognitive approach to information 48 The dimension of ‘information perception’ 48 The dimension of ‘information input’ 51 The dimension of ‘information understanding’ 52 The dimension of ‘information processing’ 55 The multifaceted dimension 57 2.1 The notion of teaching style 65 2.2 The conceptual base of teaching style 66 2.3 The models of teaching style 68 2.1 Formal – informal teaching style 68 2.2 Intellectual excitement – Interpersonal rapport 70 2.3 Assertive – Suggestive – Collaborative – Facilitative 72 2.4 Didactic – Socratic – Facilitative – Experiential 73 2.6 The Learning and Teaching style with other influential Variables 74 2.7 Conclusion 80 ix | P a g e CHAPTER THREE: RESEARCH METHODOLOGY 3.2 A Research Design and Approach 83 3.4 Mixed Methods Design 86 3.4 Data Analysis and Interpretation 102 3.3 Procedure and Analysis 108 3.8 Summary 109 x|Page CHAPTER FOUR: ANALYSIS AND RESULTS 4.2 Analysis and Results for Research Question 1 110 4.1 Interactive Learning Style (GRSLSS) 110 The Dominant Interactive Learning Style 111 The Interactive Learning Styles Based on Gender 113 The Interactive Learning Styles Based on the Year of Study 114 The Interactive Learning Styles Based on Discipline 116 4.2 The Flexibly Stable Learning Style (ILS) 117 The Dominant Preference 117 The Preferred Combination of Learning Style Modalities 120 The Flexibly Stable Learning Style based on Gender 122 The Flexibly Stable Learning Style based on Discipline 125 4.3 Teaching Styles of Mathematics Lecturers 126 4.3 Analysis and Results for Research Question 2 128 4.1 Emerging concepts and categories 129 4.2 Categories and subcategories 129 4.2 Motivating students’ learning 136 4.4 Participating in the learning process 145 4.5 Flexibility for individual development 152 xi | P a g e 4.4 Analysis and Results for Research Question 3 157 4.1 A mathematics classroom with enhancing active learning 157 4.2 The balanced learning and teaching in mathematics (‘Sequential’ to ‘Global’) 162 4.3 Lecturer-centered teaching style moving towards learner-centered teaching style 165 4.5 Summary 168 CHAPTER FIVE: SUMMARY, IMPLICATIONS, AND RECOMMENDATIONS 5.2 Balanced learning and teaching mathematics 178 5.