The Influence of Teaching Instruction and Learning Styles on Mathematics Anxiety in the Developmental Mathematics Classroom Sun Young Ban Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2019 © 2019 Sun Young Ban All Rights Reserved ABSTRACT The Influence of Teaching Instruction and Learning Styles on Mathematics Anxiety in the Developmental Mathematics Classroom Sun Young Ban In the US, an estimated 25% of four-year college students and up to 80% of community college students suffer from a moderate to high degree of mathematics anxiety (MA) (Chang & Beilock, 2016). Many scholars have noted that mathematics anxiety can be regarded as a significant factor in determining a student's achievement and mathematics related jobs. In the existing literature body, many researchers noted that MA may stem from teaching methods that are more conventional and rule-bounded such as lecture-style classroom models. On the other hand, MA can be mitigated by inquiry-based learning classroom models where students construct knowledge through inquiry, communication, critical thinking, and group work. However, the current literature has not built the connection between different teaching styles and students' individual differences with respect to MA. The individual differences are associated with the personality of the learner, learning styles, learning speed, and needs and interests of the learner. Depending on a student's learning style and a compatible teaching style, the student may actively participate in their own learning with less mathematics anxiety. Thus, the purpose of this study is to determine the influence of different teaching styles on MA, when interacted with Kolb’s and Gregorc’s (1984) four different learning and thinking styles. The research questions investigated in this study are: 1) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on students’ mathematics anxiety levels over a fifteen-week semester of a college-level remedial mathematics course?; 2) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on mathematics anxiety levels for students with different learning and thinking styles (as defined by Kolb’s and Gregorc’s learning styles) over a fifteen-week semester?; and 3) What aspects of instructional approaches (LCM and IBL) do students with different learning and thinking styles report as being related to mathematics anxiety? The abbreviated version of the mathematics anxiety rating scale (A-MARS), Kolb’s learning styles inventory, Gregorc’s thinking styles, and Written questionnaire were used to measure students’ MA levels and identify their learning and thinking styles. The results provided evidence that IBL instruction is beneficial for the students with MA, especially with mathematics test anxiety and mathematics course anxiety. Only numerical task anxiety was not significant. Thus, student-centered learning pedagogies turned out to be an effective and engaging method for lowering MA. However, there was no evidence to support the overall relationship between the constructs of learning and thinking styles and MA levels, above and beyond the instructional approaches. Classifying students according to learning and thinking styles did not influence students’ MA levels in this study over the 15 academic weeks. Moreover, after a 15 academic weeks, students in both LCM and IBL classes responded positively to key components of LCM and IBL classroom models. This implies that both LCM and IBL approaches still are important models regardless of students’ MA level. TABLE OF CONTENTS LIST OF TABLES ........................................................................................................... vi LIST OF FIGURES ....................................................................................................... viii CHAPTER I: INTRODUCTION .................................................................................... 1 NEED FOR STUDY ............................................................................................................. 1 PURPOSE OF STUDY ......................................................................................................... 5 PROCEDURE ..................................................................................................................... 7 CHAPTER II: LITERATURE REVIEW ................................................................... 16 MATHEMATICS ANXIETY ............................................................................................... 17 Anxiety in a Mathematics Classroom ....................................................................... 17 Mathematics Anxiety and Yerkes-Dodson Law ....................................................... 18 Factors of Mathematics Anxiety ............................................................................... 19 Individual’s Influence on Mathematics Anxiety................................................... 20 Cognitive Processing ........................................................................................ 21 Self-efficacy. ..................................................................................................... 21 Prior Negative Experience ................................................................................ 22 Teachers’ Influence on Mathematics Anxiety ...................................................... 23 Teachers’ Instruction ........................................................................................ 23 Teachers’ Beliefs and Attitudes ........................................................................ 24 Societal Influence on Mathematics Anxiety ......................................................... 25 Socio-Economic Status (SES)........................................................................... 25 Gender Stereotype ............................................................................................. 27 INFLUENCE OF LEARNING THEORIES ON TEACHING INSTRUCTIONS ............................... 27 i Teacher-Centered Instruction under Behaviorism ................................................ 28 Lecture Method in Mathematics Classroom ..................................................... 29 Lecture Method and Mathematics Anxiety....................................................... 31 Student-Centered Instruction under Constructivism. ............................................ 34 Inquiry-Based Learning in Mathematics Classroom ........................................ 35 Inquiry-Based Learning and Mathematics Anxiety .......................................... 40 INDIVIDUAL DIFFERENCE ............................................................................................... 43 Learning Styles and Mathematics Anxiety. .............................................................. 44 Teaching Strategy with Learning Styles. .................................................................. 46 LEARNING STYLE MODEL .............................................................................................. 47 Kolb’s Learning Styles ......................................................................................... 48 Kolb's Experiential Learning Cycle .................................................................. 48 Kolb's Learning Styles. ..................................................................................... 50 Gregorc's Thinking Styles Model ..................................................................... 51 Rationale for Using Kolb’s Learning Styles and Gregorc's Thinking Styles ... 53 CHAPTER III: METHODOLOGY .............................................................................. 60 RESEARCH CONTEXT ..................................................................................................... 61 Urban Community College (UCC) ........................................................................... 61 Rationale of Choosing MAT 56 ................................................................................ 63 Course Descriptions .................................................................................................. 63 RESEARCH DESIGN ........................................................................................................ 64 Study Participants ..................................................................................................... 64 Instruments ................................................................................................................ 65 ii Abbreviated Mathematics Anxiety Rating Scale (A-MARS) ............................... 66 Learning Style Inventory (LSI) (Kolb, 1984) ....................................................... 67 Gregorc's Thinking Styles (GTS) (Gregorc's 1984) ............................................. 67 Data Collection ......................................................................................................... 68 Pre-Survey............................................................................................................. 68 Field Notes ............................................................................................................ 69 Post-survey ............................................................................................................ 69 Written Survey 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