The Role of Mathematics in Engineering Practice and in the Formation of Engineers Volume 1 of 2 Eileen Goold B. E., M.Eng. Thesis Submitted for the Award of Doctor of Philosophy National University of Ireland Maynooth Department of Design Innovation June 2012 Head of Department: Dr. Frank Devitt Supervisor: Dr. Frank Devitt TABLE OF CONTENTS Page number LIST OF FIGURES ................................................................................................... VII LIST OF TABLES ...................................................................................................... IX SUMMARY .............................................................................................................. X ACKNOWLEDGEMENTS ......................................................................................... XII DEDICATION ........................................................................................................ XIII CHAPTER 1: INTRODUCTION ................................................................................... 1 1.1 BACKGROUND ........................................................................................................ 1 1.2 MOTIVATION ......................................................................................................... 4 1.3 RESEARCH QUESTIONS .......................................................................................... 5 1.4 SIGNIFICANCE ........................................................................................................ 6 1.5 ORGANISATION OF THESIS ..................................................................................... 6 CHAPTER 2: LITERATURE REVIEW .......................................................................... 11 2.1 INTRODUCTION .................................................................................................... 11 2.2 MATHEMATICS .................................................................................................... 12 2.2.1 What is Mathematics? .................................................................................. 12 2.2.2 Mathematical Thinking ................................................................................. 17 2.2.3 Is Mathematics a Special Subject? ................................................................ 19 2.3 LEARNING MATHEMATICS ................................................................................... 23 2.3.1 Mathematics Learning Theory ...................................................................... 23 2.3.2 Effective Mathematics Teaching................................................................... 25 2.4 ENGINEERING CAREER CHOICE ............................................................................ 31 2.5 MATHEMATICS IN ENGINEERING EDUCATION .................................................... 42 2.6 ENGINEERING PRACTICE ...................................................................................... 50 2.6.1 What is Engineering? .................................................................................... 50 2.6.2 The Engineering Profession ........................................................................... 56 2.7 MATHEMATICS USAGE IN ENGINEERING PRACTICE ............................................ 57 i 2.7.1 Investigating Engineers’ Mathematics Usage .............................................. 58 2.7.2 Summary ....................................................................................................... 68 2.8 SUMMARY ............................................................................................................ 69 CHAPTER 3: RESEARCH DESIGN ............................................................................. 71 3.1 INTRODUCTION .................................................................................................... 71 3.2 BACKGROUND THEORY BASED FRAMEWORK FOR THE RESEARCH DESIGN ........ 72 3.2.1 Measuring Engineers’ Mathematics Usage .................................................. 72 3.2.2 Measuring Engineers’ Feelings about Mathematics .................................... 79 3.3 RESEARCH DESIGN ............................................................................................... 99 3.3.1 Research Frameworks ................................................................................... 99 3.3.2 Data Collection Methodologies .................................................................. 104 3.3.3 Study Population ......................................................................................... 106 3.3.4 Initial Quantitative Phase ........................................................................... 108 3.3.5 Secondary Qualitative Phase ...................................................................... 109 3.3.6 Quality Considerations ................................................................................ 109 3.3.7 Researcher’s Role ........................................................................................ 111 3.3.8 Ethical Considerations ................................................................................. 114 3.4 SUMMARY .......................................................................................................... 115 CHAPTER 4: SURVEY METHODOLOGY AND DATA ANALYSIS ................................. 116 4.1 INTRODUCTION .................................................................................................. 116 4.2 SURVEY POPULATION ........................................................................................ 117 4.2.1 Study Sample............................................................................................... 117 4.3 SURVEY DESIGN ................................................................................................. 120 4.3.1 Biographical Information ............................................................................ 122 4.3.2 Measuring Curriculum Mathematics Usage ............................................... 122 4.3.3 Measuring Thinking Usage and Engaging with Mathematics.................... 127 4.3.4 Survey Support Document .......................................................................... 132 4.4 ADMINISTRATION OF SURVEY ........................................................................... 132 4.5 SURVEY DATA COLLECTION ................................................................................ 133 4.6 SURVEY DATA ANALYSIS..................................................................................... 138 4.7 SUMMARY .......................................................................................................... 141 ii CHAPTER 5: SURVEY FINDINGS ............................................................................ 142 5.1 INTRODUCTION .................................................................................................. 142 5.2 PERCEIVED VALUE OF HIGHER LEVEL LEAVING CERTIFICATE MATHEMATICS IN ENGINEERING PRACTICE .......................................................................................... 145 5.2.1 Engineers’ Work Performance without Higher Level Leaving Certificate Mathematics ........................................................................................................ 145 5.2.2 Impact of Engineering Discipline and Role on Perceived Value of Higher Level Leaving Certificate Mathematics in Engineering Practice .......................... 145 5.3 CURRICULUM MATHEMATICS USAGE IN ENGINEERING PRACTICE ................... 147 5.3.1 Engineers’ Mean Curriculum Mathematics Usage ..................................... 147 5.3.2 Engineers’ Curriculum Mathematics Usage by Domain ............................. 147 5.3.3 Engineers’ Curriculum Mathematics Usage by Academic Level ................. 148 5.3.4 Engineers’ Curriculum Mathematics Usage by Usage Type ....................... 148 5.3.5 Effect of Engineering Discipline and Role on Curriculum Mathematics Usage ............................................................................................................................. 149 5.4 THINKING USAGE IN ENGINEERING PRACTICE ................................................... 152 5.4.1 Engineers’ Mean Thinking Usage ............................................................... 152 5.4.2 Effect of Engineering Discipline and Role on Engineers’ Thinking Usage ... 152 5.4.3 Engineers’ Modes of Thinking ..................................................................... 153 5.4.4 Comparison of Engineers’ Thinking and Curriculum Mathematics Usages 155 5.5 ENGAGING WITH MATHEMATICS IN ENGINEERING PRACTICE .......................... 156 5.5.1 Degree a Specifically Mathematical Approach is Necessary in Engineers’ Work ..................................................................................................................... 156 5.5.2 Degree Engineers Seek a Mathematical Approach .................................... 159 5.5.3 Degree Engineers Enjoy Using Mathematics .............................................. 162 5.5.4 Degree Engineers Feel Confident Dealing with Mathematics .................... 164 5.5.5 Degree Engineers have a Negative Experience when Using Mathematics 169 5.6 SCHOOL MATHEMATICS .................................................................................... 173 5.6.1 Engineers’ Enjoyment of School Mathematics ........................................... 173 5.6.2 Factors Within and Outside of School that Contributed to Engineers’ Interest in and Learning of Mathematics .........................................................................