Doing the Scholarship of Teaching and Learning in Mathematics

Doing the Scholarship of Teaching and Learning in Mathematics

Jacqueline M. Dewar
Curtis D. Bennett
Series: MAA Notes
Volume: 83
Copyright Date: 2015
Edition: 1
Pages: 227
  • Cite this Item
  • Book Info
    Doing the Scholarship of Teaching and Learning in Mathematics
    Book Description:

    The Scholarship of Teaching and Learning (SoTL) movement encourages faculty to view teaching “problems" as invitations to conduct scholarly investigations. In this growing field of inquiry faculty bring their disciplinary knowledge and teaching experience to bear on questions of teaching and learning. They systematically gather evidence to develop and support their conclusions. The results are to be peer reviewed and made public for others to build on. This Notes volume is written expressly for collegiate mathematics faculty who want to know more about conducting scholarly investigations into their teaching and their students’ learning. Envisioned and edited by two mathematics faculty, the volume serves as a how-to guide for doing SoTL in mathematics.

    eISBN: 978-1-61444-318-6
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-xii)
  3. Foreword
    (pp. xiii-xiv)
    David M. Bressoud

    In our progression as teachers of mathematics, first comes good teaching. This includes learning how to build rapport with one’s students and to motivate them by finding what is exciting and sharing it. It entails seeking ways to challenge, encourage, and support them. That is a powerful start, but, eventually, a good teacher is not content with attentive faces and good teaching evaluations. Eventually, a really good teacher realizes that many of his or her students are having difficulty with fundamental concepts that had been so clearly explained and seemingly firmly fixed in their minds but then somehow were lost....

  4. Preface
    (pp. xv-xvi)
    Jacqueline M. Dewar and Curtis D. Bennett
  5. Part I. Getting Started in SoTL as a Mathematician
    • 1 Understanding SoTL and Its Potential Benefits
      (pp. 3-12)
      Jacqueline M. Dewar and Curtis D. Bennett

      Scholarship of teaching and learning (SoTL) is a scholarly activity whose history is generally not well known to teaching or research mathematicians. Many activities are labeled SoTL, some appropriately and others not. In light of this, Chapter 1 has several goals. It aims to inform the reader about the origins of the scholarship of teaching and learning, the efforts to forge connections between SoTL and academic disciplines, and the emergence of SoTL within mathematics. It attempts to set SoTL apart from good teaching, scholarly teaching, and, to the extent possible, research in undergraduate mathematics education (RUME). The chapter addresses the...

    • 2 Initiating a SoTL Investigation
      (pp. 13-18)
      Jacqueline M. Dewar and Curtis D. Bennett

      In Chapter 1 we defined SoTL as

      the intellectual work that faculty members do when they use their disciplinary knowledge (in our case, mathematics) to investigate a question about their students’ learning (and their teaching), submit their findings to peer review, and make them public for others to build upon.

      This chapter considers questions and situations that might prompt a SoTL study. It presents a taxonomy of SoTL questions derived from the work of Carnegie scholars that can be useful in guiding the development of a project. We discuss how disciplinary knowledge can be brought to bear on framing SoTL...

    • 3 Gathering and Analyzing Evidence
      (pp. 19-44)
      Jacqueline M. Dewar

      SoTL involves the systematic investigation of a question we have about student learning and we look for answers in evidence generated by students. After framing a researchable question, we have to gather and analyze evidence. So this chapter examines some basic considerations of research design, such as whether, and how, to gather quantitative data, qualitative data, or both. It is likely that one or more of the types of evidence discussed in this chapter will be unfamiliar to mathematicians. Many of them were new to Curtis Bennett and me as well, when we began doing SoTL. In this chapter I...

    • 4 Resources for Pursuing SoTL and Going Public
      (pp. 45-48)
      Jacqueline M. Dewar

      This chapter, which closes Part I, offers additional resources and advice for completing a SoTL project. These include the need to obtain human subjects clearance in order to publish the results of the study, why it is a good idea to find collaborators for doing SoTL, and where to find them. Suggestions are offered for other sources of support and possible venues for dissemination. As in the previous chapters, the work of the authors in Part II provides examples.

      At the outset of a SoTL investigation, if the goal is to publish the results, then human subjects issues will arise,...

  6. Part II. Illustrations of SoTLWork in Mathematics
    • Theme 1:: Experiments with Approaches to Teaching
      • 5 Assessing the Effectiveness of Classroom Visual Cues
        (pp. 51-58)
        Gretchen Rimmasch and Jim Brandt

        This chapter illuminates some of the research design issues discussed in Chapter 3. It shows how the authors developed and piloted a novel intervention, visual cues, during one semester and fully implemented and assessed it in another. The methodology involved two sections of the same course, taught by the same instructor, one as an experimental group and the other as control group. Because using visual cues to assist with some computational skills was specific and limited in scope, many of the concerns mentioned about using control groups in Chapter 3 did not arise. The study involved similar interventions with visual...

      • 6 (Re)discovering SoTL Through a Fundamental Challenge: Helping Students Transition to College Calculus
        (pp. 59-66)
        Rann Bar-On, Jack Bookman, Benjamin Cooke, Donna Hall and Sarah Schott

        In this chapter Rann Bar-On, Jack Bookman, Benjamin Cooke, Donna Hall, and Sarah Schott describe how one faculty member’s attempt to improve student success in a special freshmen calculus sequence for underprepared students evolved into scholarship of teaching and learning. Key to this progression was collaboration with academic support professionals and non-tenure track faculty. Thoughtful discussions, a few trial interventions, and examining the research literature enabled the group to move from reflection and experimentation to scholarly teaching and then to the scholarship of teaching and learning. After several years of collaborative effort, a grant application to further develop, study, and...

      • 7 A Quantitative and Qualitative Comparison of Homework Structures in a Multivariable Calculus Class
        (pp. 67-76)
        Lynn Gieger, John Nardo, Karen Schmeichel and Leah Zinner

        This chapter describes the work of an interdisciplinary team, Lynn Gieger (Mathematics Education), John Nardo (Mathematics and Computer Science), Karen Schmeichel (Biology), and Leah Zinner (Psychology), to improve the effectiveness of homework in a multivariate calculus class by using an online homework system. Although at the beginning of the investigation, the majority of the team members were not very familiar with qualitative methods, they found the qualitative data particularly useful for providing context and depth to the mixed quantitative results they obtained. Their study highlights the merit of a mixed method approach, particularly when statistically significant results are not obtained...

      • 8 Playing Games to Teach Mathematics
        (pp. 77-86)
        Edwin Herman

        Edwin Herman’s project was prompted by a desire to incorporate games as a learning device. This chapter details how the project unfolded in stages, because as he gathered evidence he kept refining his question. The first time he gathered evidence regarding whether the students enjoyed the activity. Next, he sought evidence of learning. Because of his knowledge of statistical methods he relied mostly on quantitative evidence. During the last iteration of the course, he became more interested in why game play might be having an effect, leading him to consider qualitative measures. Even readers having neither the interest nor the...

      • 9 Investigating How Students’ Linking Historical Events to Developments in Mathematics Changed Engagement in a History of Mathematics Course
        (pp. 87-96)
        Pam Crawford

        The author of this chapter, Pam Crawford, holds a doctorate in mathematics with a concentration in teaching collegiate mathematics. The dissertation she wrote gave her experience in conducting research in undergraduate mathematics education (RUME). More recently, she participated in her university’s SoTL scholars program, undertaking an investigation prompted by frustrations encountered repeatedly when teaching a history of mathematics course. The mathematics majors in the course were reluctant to engage in historical thinking. She tried an intervention and describes how her study of its effect is an example of SoTL (and not RUME) work, thereby illuminating some of the distinctions between...

    • Theme 2:: Crafting Learning Experiences around Real-World Data or Civic Engagement
      • 10 Using SoTL to Assess the Outcomes of Teaching Statistics Through Civic Engagement
        (pp. 99-106)
        Cindy Kaus

        In this chapter Cindy Kaus discusses a SoTL project that grew out of her involvement with a national initiative to incorporate civic engagement into the teaching of science and mathematics. She called upon SoTL to provide assessment for the effectiveness of her course redesign. The chapter considers a common problem in doing SoTL, namely encountering difficulties in getting comparison data from control groups taught by other faculty members even when they are willing to assist. The author also describes the professional connections and benefits that accrued to her from employing SoTL to investigate student learning.

        The relationship between successful mathematics...

      • 11 A Pedagogical Odyssey
        (pp. 107-116)
        Michael C. Burke

        Michael Burke’s odyssey in this inspirational chapter could be characterized as a “vision of the possible” investigation, initiated because he wanted to try something unusual. He began with a desire to help his students gain a deeper understanding of the concept of a function. He also wanted them to encounter genuine applications of mathematics, ones that were truly interdisciplinary. He thought that asking his students to write about this would help them clarify their thinking. As his experiment unfolded, to understand what was happening and to refine what he was trying to achieve, he first used reflective practice, and later...

      • 12 Presenting Evidence for the Field That Invented the Randomized Clinical Trial
        (pp. 117-124)
        John Holcomb

        In this chapter John Holcomb raises difficult questions about the ethics of experimental design when investigating questions about student learning, which led him to forego the traditional approach of using a control group. This decision resulted in difficulties with getting his work published in statistics education journals, despite the work having received extremely positive feedback at conferences. He also discusses the meaning of reliability and validity in measurement and provides an example of a simple scheme for analyzing open-ended responses to surveys.

        My SoTL study involved developing data analysis group projects for an introductory statistics course that required students to...

    • Theme 3:: Using Assigned Reading Questions to Explore Student Understanding
      • 13 Conceptual or Computational? Making Sense of Reading Questions in an Inverted Statistics Course
        (pp. 127-136)
        Derek Bruff

        In this chapter Derek Bruff describes his project, trying to get students to read a mathematics textbook more effectively. His report discusses working with existing data, identifying patterns within qualitative data, and trying to approximate a control group experiment within a single course. He also obtained a surprising result that has implications for the teaching of conceptual and computational material in statistics courses. He tells us that his overall plan was inspired by a SoTL project by Axtell and Turner (2006), who have a chapter on that work in this book (Chapter 14). This illustrates a key tenet of SoTL...

      • 14 An Investigation Into the Effectiveness of Pre-Class Reading Questions
        (pp. 137-142)
        Mike Axtell and William Turner

        In this chapter Mike Axtell and William Turner describe how they went about undertaking, as novices, a literature review in mathematics education. Their experience revealed to them the critical role that the literature review can play in refining a SoTL research question and how it can aid in designing a study. Readers may want to contrast their study of reading questions with that written by Derek Bruff in the preceding chapter.

        We begin by providing the background of our investigation. We describe what motivated us to use pre-class reading assignments and how over time we developed a system that involved...

    • Theme 4:: Exploring Student Understanding of the Nature of Mathematics
      • 15 Liberal Arts Mathematics Students’ Beliefs About the Nature of Mathematics: A Case Study in Survey Research
        (pp. 145-156)
        Stephen D. Szydlik

        Stephen Szydlik’s experience teaching a problem-based inquiry seminar for over 10 years led him to question his perceptions about student learning. He lacked empirical evidence about student gains and he couldn’t define what he meant by success in his course. This realization led him to a SoTL investigation that required work and reflection in order to frame a researchable question. Particularly worth noting is his description of how he came to define success in the course based on his desired outcomes. His realization that success meant student progress in the higher order activities inherent in doing mathematics led to a...

      • 16 The Mathematics of Symmetry and Attitudes towards Mathematics
        (pp. 157-170)
        Blake Mellor

        In this chapter Blake Mellor describes a study of student learning in a mathematics for liberal arts course offered as an alternative to the typical quantitative skills course. His approach to getting baseline data for his study was to teach the traditional quantitative skills course first. As a result of pursuing a SoTL investigation over several semesters, he encountered a number of issues with the use of surveys. Awareness of the lessons learned by Mellor will be useful to those beginning in SoTL. The author presents a different perspective on the personal and professional impact of SoTL. For him, SoTL...

      • 17 Mathematics Research Experiences for Preservice Teachers: Investigating the Impact on Their Beliefs
        (pp. 171-180)
        Wendy A. O’Hanlon, David D. Barker, Cynthia W. Langrall, John A. Dossey, Sharon M. McCrone and Saad I. El-Zanati

        In this chapter a group at Illinois State University describe how they used the scholarship of teaching and learning to investigate whether having preservice teachers participate in a mathematical research experience for undergraduates (REU) program influenced their beliefs about teaching and learning mathematics. Unable to find an appropriate survey instrument, they developed their own. They explain the organization and content of the survey, tell how they piloted and tested it for reliability, and describe how the results are being used to improve the REU program.

        The Scholarship of Teaching and Learning (SoTL) can serve as a critical tool for improving...

    • Theme 5:: Tackling Large Questions
      • 18 The Question of Transfer: Investigating How Mathematics Contributes to a Liberal Education
        (pp. 183-190)
        Curtis D. Bennett and Jacqueline M. Dewar

        An opportunity, not a teaching or learning problem, prompted the investigation in this chapter, where all three types of SoTL questions make an appearance. The authors raise questions about evidence: what to gather and from whom, and how to analyze it. They describe unexpected difficulties they encountered. The study, completed in 2004, continues to offer lessons and open new avenues for the authors, their department, their university, and the discipline, especially related to quantitative literacy and first-year-seminar courses.

        Appropriate transfer of knowledge, even within the same domain and across remarkably similar contexts, has been demonstrated to be very difficult to...

      • 19 Using SoTL Practices to Drive Curriculum Development
        (pp. 191-200)
        Rikki Wagstrom

        In this chapter, RikkiWagstrom describes how she applied SoTL processes to aid in the development and evaluation of a new curriculum that integrated civic issues into a prerequisite course for college algebra. Her experience illustrates how it can take a long time to identify and frame an appropriate research question. She describes searching the literature and tells how it led her to a useful model, one that prompted her to change the site of her investigation and revise her research question. She provides insights into the problems that can arise in finding faculty members to teach experimental and control sections,...

  7. Epilogue
    • 20 Synthesis of the Value and Benefits of SoTL Experienced by the Contributors
      (pp. 203-206)
      Curtis D. Bennett and Jacqueline M. Dewar

      The primary goal for this volume is to provide guidance for mathematics faculty members interested in undertaking a scholarly study of their teaching practice, but a secondary goal is to promote a greater understanding of this work and its value to the mathematics community. In this chapter we reflect on the value of SoTL, generally, and take stock of the outcomes and benefits that accrued to the 25 contributing authors as a result of their scholarly inquiries into teaching and learning.

      In 1999, Lee Shulman, then President of the Carnegie Foundation for the Advancement of Teaching, wrote entertainingly and perceptively...

  8. Index
    (pp. 207-210)