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.

At the next stage, we become reflective teachers. We try to understand what went wrong, how we might reach more of our students more effectively. We seek advice from more experienced colleagues, learn about other approaches to the teaching of a given topic, and experiment within our own classrooms. Reflective teachers are constantly learning about teaching, adjusting their courses, seeking to do even better at challenging, encouraging, and supporting their students.

There is a third stage: scholarly teaching. A reflective teacher might discover an approach to a lesson or a course that really works. They want to share it. A scholarly teacher seeks to back this up with evidence that it is working and has the potential to work for others. More than that, a scholarly teacher wants to understand why it works. No one else is going to pick up your insights and implement them precisely the way you did. A scholarly teacher tries to identify the critical core of what makes this approach work, so that those who would adopt it know what is essential and what can be adapted.

There is another motivation for scholarly teaching. It comes when nothing seems to work. Scholarly teaching can arise from the decision to confront pedagogical or curricular difficulties as an intellectual problem worthy of full attack. This involves studying what actually happens in the classroom and exploring why students are having trouble.

Editors' Commentary

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 the two.

Introduction

How often, when thinking about a course you teach, have you wondered what would be the outcome on student learning if you changed some aspect? After making a change, how do you investigate whether or not it improved student understanding and performance? What follows is my tale of researching a change I made in my teaching in a History of Mathematics course.

I hold a Ph.D. in mathematics with a concentration in teaching collegiate mathematics from Western Michigan University. The degree gives me a background in Research in Undergraduate Mathematics Education (RUME), in which researchers apply standard educational research techniques to investigate “the nature of mathematical thinking, teaching, and learning” and try “to use such understandings to improve mathematics instruction” at the collegiate level (Schoenfeld, 2000, p. 641). RUME is an acknowledged research discipline in mathematics with established research procedures and terminology. Scholarship of Teaching and Learning (SoTL), as defined in Chapter 1, is “the intellectual work that faculty members do when they use their disciplinary knowledge … to investigate a question about their students' learning (and their own teaching), submit their findings to peer review, and make them public for others in the academy to build upon.” Clearly SoTL and RUME are related by their concern with investigating student learning. My mathematics education training and my experience with SoTL allow me to comment on their similarities and differences.

Editors' Commentary

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 SoTL. This chapter underscores the usefulness of observation and data collection on two levels. In aiming to teach his students the value of observation and data collection, the author discovers that this is exactly what he must do as their teacher – observe and collect data. The author writes in an engaging style and with passion about his journey to the discovery that the scholarship of teaching and learning enables him to understand what is happening in his classroom.

Introduction

My title is a bit Homeric, which is perhaps a little highbrow for me, so I thought to follow it with a quote from a t-shirt. I saw the above quote in 2006, written on a t-shirt worn by a young man walking across the Charles Bridge in Prague. If we attempt to decipher its literal meaning, we see that it falls somewhere between puzzling and incoherent. It is for this reason that it seems an apt expression of the sentiments of a young American traveling in Europe, particularly one who finds himself in Prague; it expresses, in a humorous way I think, a sense of massive confusion about who and where he is, about here and there, and about time. Prague frequently has this effect on young Americans.

Introduction

In Chapter 1 we defined SoTL as

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 research questions. We describe how literature searches can inform SoTL studies and give suggestions for conducting a search. The chapter includes illustrative examples and points to additional examples in Part II.

A Typical Starting Point

In one of the formative articles of the scholarship of teaching and learning movement in the United States, Randy Bass (1999) discussed the different reactions that “teaching problems” and “research problems” typically garner from faculty members, with the latter engendering far more positive interest and reaction. He posited that one of the tenets of SoTL is that a teaching problem should be viewed as an invitation to a scholarly investigation, similar to how most faculty members view a research problem.

Here is a problem that any teacher can relate to:

My students aren't as prepared for class as I would like them to be.

An attempt to fix the problem might lead to the following sequence of thoughts or actions.

1. • What if I give my students reading assignments in the textbook? (Few will actually read and those who do won't read carefully enough.)

2. • What if I give them reading questions for the assigned reading? (They may read just enough to answer the questions.)

3. • What if I also ask them to generate their own questions after reading? (I probably won't be satisfied with the questions they ask.)

4. • How can I get them to ask better questions? (What do I mean by better questions?)

5. • What kind of questions are they asking now?

Introduction

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 issue of evaluating and valuing this work for tenure and promotion, a matter of great concern for junior faculty members. It closes with a brief discussion of the benefits of SoTL, a topic that we revisit in the Epilogue, Chapter 20, where we present a synthesis of the benefits our authors experienced from participating in SoTL.

The Origins of SoTL in Higher Education

In 1990, Ernest Boyer, President of the Carnegie Foundation for the Advancement of Teaching, introduced the expression “scholarship of teaching” into the vocabulary of higher education. His book, Scholarship Reconsidered (Boyer, 1990), called for colleges and universities to embrace a broader vision of scholarship in order to tap the full range of faculty talents across their entire careers and to foster vital connections between academic institutions and their surrounding communities. Boyer argued for the recognition of four types of scholarship: discovery, application, integration, and teaching. The scholarship of discovery refers to what is traditionally called research in most disciplines. The scholarship of application, now frequently called scholarship of engagement, refers to applying knowledge to consequential problems, often conducted with and for community partners. The scholarship of integration makes connections between disciplines. More and more, interdisciplinary work is being recognized as essential to solving complex real world problems. These scholarships may have different interpretations depending on the discipline and type of institution. For example, for engineers, consulting work is often considered scholarship of application.

Editors' Commentary

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 cues in two different settings (first in remedial math, then in calculus). For calculus, the authors discovered that they had to alter their rubric to capture the information they wanted.

Introduction

The large number of students who must take remedial mathematics courses is a problem for many colleges and universities. The courses must be staffed, and students who place into remedial courses are less likely to successfully complete a degree (Attewell, Lavin, Domina, & Levey, 2006). Remediation has been a problem for decades (see, for instance, Handel & Williams, 2011; Patterson & Sallee, 1986; Weiss & Nguyen, 1998). In many lower division mathematics courses the focus of instruction is often on procedural skills. Students should view these courses as an opportunity to improve their skills, but they often see them as hurdles that do not count towards degree completion. The material in remedial courses is often familiar to students, which can make it more difficult for students to expend the time and effort required to correct previous misconceptions. Conversations about our frustrations with these courses led us to consider what we could do to be more effective in teaching procedural skills. The resulting investigation took the form of a What works? study.

We began with an intermediate algebra course, as it involves procedural skills that students have encountered previously. In investigating a What works? question, there are many possible approaches (Patterson & Sallee, 1986).

Editors' Commentary

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.

The Backstory

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 not just assigned readings but reading questions (RQs) as well. We explain why we decided to investigate their use and what it was that we wanted to know, at first.

The process of reading a mathematical text and understanding it is complicated and difficult (Konior, 1993; Reiter, 1998). It is an acquired skill that few, if any, come by naturally. However, it is one that mathematicians must learn. Mathematics conferences and pedagogical publications often contain ideas on how to get, or teach, students to read mathematics (Amick, 1997; Gold, 1998; King, 2001; Ratliff, 1998; Reiter, 1998; Taalman, 1998), and there are hundreds of references on how to help students improve their critical reading skills (Bratina & Lipkin, 2003). The goal is for students to become independent learners capable of teaching themselves, perhaps the ultimate goal of any liberal education program.

If we as teachers are convinced of the need to get students to read a mathematical text, we should then be concerned with determining what our students are gaining, and not gaining, from this task. If our strategies are not leading to desired outcomes, then we should rethink them. This observation led us to collaborate on a SoTL project during the 2005-2006 academic year that focused on student reading.

Introduction

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 write about these methods from our experience in learning to use them.

Triangulating Data

A SoTL researcher should develop a plan for systematically collecting multiple types of evidence. A diversity of evidence can help the researcher to form a convincing picture of student learning (Wiggins, 1998). This approach is called triangulation of the data. According to Webb, Campbell, Schwartz, and Sechrest (as cited in Shavelson & Towne, 2002, p. 64): “When a hypothesis can survive the confrontation of a series of complementary methods of testing, it contains a degree of validity unattainable by one tested within the more constricted framework of a single method.” In other words, claims or explanations supported by several types of evidence-for example, student work samples, interviews, and retention rates-are considered to be more accurate. This will be an asset if the work is submitted for publication in a peer-reviewed journal. We turn now to a discussion of the difficulties in approaching SoTL as standard educational research.

Challenges that Educational Research Design Presents for SoTL

Designing an educational research study can pose a number of challenges to faculty members interested in SoTL. Many of the same challenges confront mathematics education research at all levels. In response to a query from the NSF, and with its funding, the American Statistical Association held a series of workshops for statisticians and mathematics education researchers to discuss whether the statistics community could “offer any contributions to improving the quality of mathematics education research” (Working Group on Statistics in Mathematics Education Research, 2007, p. 1).

Introduction

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.

Human Subjects Considerations

At the outset of a SoTL investigation, if the goal is to publish the results, then human subjects issues will arise, which will be unfamiliar to many mathematicians. According to United States Federal Guidelines, a human subject is a person about whom an investigator (whether professional or student) conducting research obtains data through intervention or interaction with the individual or identifiable private information (32 CFR 219.102.f). Because of past abuses of human subjects in medical trials in populations such as prisoners or minorities in the armed forces, the federal government has developed procedures requiring informed consent for human subjects research (U.S. Department of Health and Human Services, n.d.). Special rules for obtaining informed consent apply to any subject under the age of 18, a situation that can be encountered in SoTL studies of first-year college courses.

Because SoTL publications may involve making the work of our students public, we must follow institutional guidelines for working with human subjects. Most colleges and universities have a committee or group, often called an Institutional Review Board (IRB) or a Human Subjects Review Board, charged with ensuring that the federal guidelines are observed.

Human subjects researchers are expected to inform their subjects of the risks of their involvement in the study and obtain written consent for their participation. Studies that involve little or no physical or emotional risk to the subject, and will not reveal anything about the subject's behavior that would be damaging if it became public, may be exempted from obtaining written consent.

Editors' Commentary

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 share the results of this work was submitted to the NSF.

Introduction

Through the efforts of the Carnegie Foundation and others, many faculty are introduced to SoTL through conferences, workshops at their institution, colleagues, or journal articles devoted to SoTL (Hutchings, 2010). As discussed in this volume, these activities have struck a chord with, and given voice to, the scholarly and intellectual interests of many faculty in higher education. The growth of SoTL has provided validation and motivation for faculty to develop SoTL projects. In this chapter, we describe a different introduction to SoTL, one that is more unintentional and less self-conscious. We will discuss how a small group of faculty faced with an instructional problem gradually adopted an increasingly scholarly approach to addressing it. Instead of scholars creating solutions to problems, in this case a problem created scholars.

We were all exposed to SoTL work early in our careers. We mostly set it aside as we pursued our teaching. We rediscovered it when the need arose, and we wanted to stand on the shoulders of those who had attempted to address the problems we encountered. We believe that our experience can be instructive for those who are new to SoTL and for those who have had some involvement with it.

Editors' Commentary

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.

Introduction

The relationship between successful mathematics course completion and degree attainment in higher education is significant (Adelman, 2006, 2009). Hence, the low graduation rates in higher education institutions (Callan, 2008) indicate a need for a more effective and engaging mathematics curriculum. In addition, as more mathematically underprepared students enter higher education (Parsad & Lewis, 2003), engaging students and increasing retention rates in mathematics courses become greater challenges. Low completion rates in general education mathematics courses at Metropolitan State University, a comprehensive public university in St. Paul, Minnesota, led to an investigation of how civic engagement could be used in a statistics course to increase retention and students' interest and confidence in their ability to do mathematics.

Metropolitan State University is an urban institution serving the Twin Cities of Minnesota. The student population is the most diverse in the higher education system in Minnesota. Students of color make up 34% of its student body. The university was founded on principles of connecting higher education with surrounding communities. The idea to incorporate community-based projects into an introductory statistics course emerged as a result of the university's founding principles and also from attending the 2006 SENCER Summer Institute. SENCER, which stands for Science Education for New Civic Engagements and Responsibilities, is an NSF-funded curriculum and dissemination project. It aims to improve collegiate instruction in STEM fields by promoting the teaching of science and mathematics through complex, real world problems.