EXAMINING STUDENT AGENCY IN AN ACTIVE-LEARNING BUSINESS CALCULUS COURSE By ...

442 Pages·2017·7.92 MB·English

by  Abigail Higgins

EXAMINING STUDENT AGENCY IN AN ACTIVE-LEARNING BUSINESS CALCULUS COURSE

By
ABIGAIL L. HIGGINS

A dissertation submitted in partial fulfillment of
the requirements for the degree of

DOCTOR OF PHILOSOPHY

WASHINGTON STATE UNIVERSITY
Department of Mathematics and Statistics

JULY 2017

Ó Copyright by ABIGAIL L. HIGGINS, 2017
All Rights Reserved
Ó Copyright by ABIGAIL L. HIGGINS, 2017
All Rights Reserved
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To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of ABIGAIL L. HIGGINS
find it satisfactory and recommend that it be accepted.

__________________________________
Shiv Smith Karunakaran, Ph.D., Co-Chair

__________________________________
Libby Knott, Ph.D., Co-Chair

__________________________________
Sandra Cooper, Ph.D.

__________________________________
Molly Kelton, Ph.D.
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ACKNOWLEDGMENT
This project was not the result of a single individual’s work. Rather, it was facilitated by many
different influencing and supporting characters. Each person in this section contributed to this journey in
significant ways. Without any one of the following people, this project would not have been completed.
To Dr. Powell: You were my teacher for twelve years and the first person I knew who had earned
a Ph.D. Thank you for your unending kindness and support. Long after I moved away, you remained
eager to hear about my studies. As I have transitioned from student to teacher, your constant patience with
my gross lack of preparation astounds me. You taught me to love the piano and how intricately music,
science, and history are intertwined. I think about you every day and I wish you were here to see me
finish this thing – I know you’d be proud. I hope the kindness you showed to me extends from me to my
students; you are an inspiration.
My officemates, Cameron, Spencer, and Ian: Thank you for putting up with my constant
distractions. Your patience with my frustrations is remarkable. I laughed more in Neill 318 than I ever
have in any room. Grad school also made me cry in there, but thankfully I had you guys.
To the developers of and contributors to Habitica: Your application was one of the most
practically helpful influences on this project; thank you!
To my mathematics professors at Walla Walla University: Collectively, you inspired me to
pursue an academic career. Dr. Thompson and Dr. Wiggins, your kindness, your compassion, and your
valuable mentorship were incredibly influential. I cannot effectively articulate the effect you have had on
me. Thank you for believing in me even when I did not feel believable. I hope I can impact students like
you have.
To my family: Thank you for supporting my academic pursuits. To my father, Ron Higgins:
Thank you for instilling a love of mathematics in me. You taught me to foster an inquisitive mind and you
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believed in me. Thank you for contributing to my mathematical confidence. To my mother, Deborah
Higgins: Thank you for feeding me, clothing me, and caring for me, despite my ungratefulness. You
supported me in the most literal sense; thank you. To my brother, Nate Higgins: your indomitable spirit
was the most poignant inspiration for this project. I wanted to give up so many times. You never gave up.
Thank you for demonstrating the power of determination.
To Anya Rasmussen: You are a dear friend, without whom I certainly would not be completing
this now. I will never be able to repay your unending kindness. You continued to care for me, despite my
own shortcomings. You and your family have had a tremendous impact on the person I am today. Thank
you.
To the Thiel family: Your kindness will stay with me my whole life. The community you created
for me made a deep impression on who I am today. Thank you, Shelley, for supporting me, mentoring
me, listening to me, and caring for me. Your impact is indescribable. Arthur, you and I always had
wonderful conversations about mathematics. You undoubtedly influenced on the field I pursued. Thank
you for your conversation, your advice, and your kindness. Cedric, you are the best analog of a little
brother. Thank you for your humor, your wit, and your patience. Lastly, Tiffany Kim, you were my
kindred spirit through many, many years. Your friendship had a profound impact on me. Thank you for
listening, for being kind, and for being there.
To my future employer, California Maritime Academy: You provided the ultimate motivation to
complete my dissertation! Thank you for giving me a chance. I am excited to be part of your community,
to interact with students in a meaningful way, and to contribute to your wonderfully unique institution.
To Wyatt Brege: I am consistently amazed by your thoughtfulness, unique perspective, and
kindness. Your presence in my life enriches in my view of the world; you make me more well-rounded.
The ways in which you supported me near the end of this project were especially meaningful. I am
thrilled to continue our adventures, even if they are in California.
To my committee, thank you for your guidance. Libby: You inspired me to pursue a degree in
mathematics education. Thank you for introducing me to this field. I would never have even started a
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Ph.D. in mathematics education without you. Sandy: Your support for me as an instructor and as a student
was incredibly meaningful. I feel confident as I transition to my next position that I will effectively
instruct post-secondary mathematics courses. Your dedicated work as Associate Chair gave me
opportunities to develop my instructional practices. Additionally, your experience provides a necessary
and unique insight into this project. Thank you for contributing to this study. Molly: I want to be you. I’m
swept off my feet by your vocabulary during our meetings. Thank you for supporting me through this
project. You convinced me this was possible and that I would be proud of my accomplishments. Lastly,
Shiv: This project would not have even begun without your guidance. Whenever I try to thank you, you
always attempt to brush it off as exclusively my accomplishment. Guess who doesn’t get a rebuttal now? I
am not embarrassed of this project only because I trust the feedback that you have given. I will forever be
grateful for your invaluable direction and mentorship. I am proud to be your first student. I cannot begin
to describe how you have impacted my academic trajectory. Thank you for teaching me to not hate
research. Thank you for listening to my unending questions.
My participants, Christina and Jacob, contributed immensely to the execution of this project.
Thank you so much for your time; working with you both was wonderful.
To all my former teachers: Thank you for work. Each one of you influenced the kind of instructor
I am today. To my former students: Every one of you contributed to this project; thank you for your
patience with me.
This project is dedicated to my future students. I hope what I have learned from this study
translates into observable kindness and consideration in the classroom.
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EXAMINING STUDENT AGENCY IN AN ACTIVE-LEARNING BUSINESS CALCULUS COURSE
Abstract
by Abigail L. Higgins, Ph.D.
Washington State University
July 2017

Co-Chairs: Shiv Smith Karunakaran and Libby Knott

This study explored student agency in an active-learning business calculus course. The lecture-
style instructional practices typically used in this course at this institution allow few opportunities for
students to interact with their peers, interface with the instructor one-on-one, or do mathematics during
class time. Additionally, this course has focused heavily on procedural content. As an instructor of this
course, I was aware that students perceived the content to be irrelevant and tended to be passive in class. I
wondered how students were responding to these structural elements that they had identified, namely
irrelevant content and lack of opportunity to be active in class. This led me to the concept of agency.
I redesigned this course with the intention of emphasizing real-life applications and creating an
environment that encouraged students to be active. I implemented a pilot version of this course during
Summer 2016 and carried out the final version during Fall 2016. During my main project in Fall 2016, I
selected two participants, Christina and Jacob, as cases within my course. From interviews with these
participants and from classroom data, I identified their goals and associated structural elements. These
goals and structural elements were used to describe how Christina and Jacob responded to structure in my
course, in other words, how they achieved agency in my course.
Major themes from this project include the value of mathematics problems contextualized in real-
life and relatable situations, the ways in which students use interactions during class time to facilitate their
course goals, and the importance of providing opportunities for students to do mathematics during class
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time. This project contributes to the existing literature on mathematics education at the post-secondary
level, in particular the mathematics education of students majoring in non-STEM fields, and specifically
the mathematics education of students majoring in business disciplines. Considering the popularity of
business degrees in the United States, the lack of mathematics education research concerning this student
demographic is concerning. This study aims to expose this gap and encourage further research in these
areas.
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TABLE OF CONTENTS
Page
ACKNOWLEDGMENT .............................................................................................................................. iii
ABSTRACT .................................................................................................................................................. vi
LIST OF FIGURES .................................................................................................................................... xiv
LIST OF TABLES ....................................................................................................................................... xv
CHAPTER 1 RATIONALE ......................................................................................................................... 1
Business Mathematics Education ........................................................................................................... 1
Student Agency ...................................................................................................................................... 3
Learning Perspective .............................................................................................................................. 4
Business calculus instructional design ........................................................................................... 4
Lack of Literature ................................................................................................................................... 7
Research Questions ................................................................................................................................ 7
CHAPTER 2 LITERATURE REVIEW ....................................................................................................... 9
Business Calculus .................................................................................................................................. 9
Agency and Structure ........................................................................................................................... 12
Biesta and Tedder’s conception of structure and agency ............................................................. 13
Ashwin’s conception of structure and agency ............................................................................. 15
Agency in mathematics education research ................................................................................. 16
My conception of structure and agency ....................................................................................... 17
Agency and identity ..................................................................................................................... 19
Agency and learning .................................................................................................................... 19
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Resistive and supportive moves ................................................................................................... 20
Learning Perspective ............................................................................................................................ 21
Sociocultural perspective ............................................................................................................. 21
Community of practice ................................................................................................................. 22
Schooling versus learning and mathematics ................................................................................ 24
Identity and learning .................................................................................................................... 25
Learning and agency .................................................................................................................... 26
Undergraduate Mathematics Classroom Norms .................................................................................. 27
Active-Learning Strategies .................................................................................................................. 28
CHAPTER 3 METHODS ........................................................................................................................... 31
Course Background and Information ................................................................................................... 31
Pilot Work ............................................................................................................................................ 32
Business faculty interview ........................................................................................................... 32
Student interviews ........................................................................................................................ 37
Course coordinator interview ....................................................................................................... 38
Pilot Study .................................................................................................................................... 43
Business Calculus Fall 2016 ................................................................................................................ 54
Course design ............................................................................................................................... 54
Student make-up ........................................................................................................................... 57
Selection of participants ............................................................................................................... 58
Data Collection and Sources ................................................................................................................ 63
Classroom data ............................................................................................................................. 63
Interview data ............................................................................................................................... 64
Analysis ................................................................................................................................................ 66
Analysis of student goals and associated structural elements ...................................................... 66