G: Opportunities and Challenges for Institutional Transformation in College Mathematics
G: Opportunities and Challenges for Institutional Transformation in College Mathematics
TITLE: Features of Successful Calculus Programs at Five Doctoral Degree Granting Institutions
PRESENTERS: Chris Rasmussen, San Diego State University
Calculus is typically the first undergraduate mathematics course for science, technology, engineering and mathematics (STEM) majors. Indeed, each fall approximately 300,000 college or university students, most of them in their first post-secondary year, take a course in differential calculus (Blair, Kirkman, & Maxwell, 2012). This course is also a well-known bottleneck, blocking large numbers of students from continuing to pursue their interest in a STEM major. The role of calculus in disengaging students from a STEM related major are complex, but include lectures that are uninspiring or unimaginative and an over-stuffed curriculum taught at too fast a pace (Seymour & Hewitt, 1997). While reasons that students give for disengaging from a STEM major are fairly well documented (e.g., Kuh et al., 2008), characteristics of calculus programs that are more successful in keeping students engaged in their STEM-related major are less well understood. In this presentation, I report on findings from a large scale, five-year, national study of Calculus I programs that addresses the pressing need to better understand characteristics of successful calculus programs.
The goals of this five-year project include to improve our understanding of the demographics of students who enroll in calculus, to measure the impact of the various characteristics of calculus classes that are believed to influence student success, and to conduct explanatory case study analyses of exemplary programs to identify why and how these programs succeed. The project was conducted in two phases. In Phase 1, surveys were sent to a stratified random sample of students and their instructors at the beginning and the end of Calculus I. The surveys were restricted to the calculus course designed to prepare students for the study of engineering or the mathematical or physical sciences. Surveys were designed to gain an overview of the various calculus programs nationwide, and to determine which institutions had more successful calculus programs. Success was defined by a combination of student variables measured in the student and instructor surveys: persistence in calculus
as marked by stated intention to take Calculus II (a proxy for persistence in a STEM major); affective changes, including enjoyment of math, confidence in mathematical ability, interest to continue studying math; and passing rates. In Phase 2 of the project, we conducted explanatory case studies at 18 different post-secondary institutions, including community colleges through research universities.
In this report, I present findings from our case study analyses at the five research universities that were identified in Phase 1 as having more successful calculus programs. Understanding the features that characterize exemplary calculus programs at research universities is particularly important because these institutions produce the majority of STEM graduates. The five selected research institutions included two large public universities, one large private university, one public technical institute and one private technical institute. At each of these five institutions, we conducted three-day site visits to learn about contextual aspects related to why and how these institutions are producing students who are successful in calculus. During these site visits, we conducted over 90 hour-long interviews with students, instructors and administrators; we observed classes; and we collected exams, course materials and homework.
Cross-case analysis of the five selected research institutions led to the identification of following seven features that contribute to the success of their calculus program: (1) Coordination of Calculus I, (2) Attending to local data, (3) Substantive graduate teaching assistant training programs, (4) Active learning, (5) Rigorous courses, (6) Wellrun learning centers, and (7) Thoughtful placement systems.
In the presentation, I will briefly describe each of the seven features and then provide more detail on one of the more unexpected features, namely the coordination of Calculus I. The fact that all five of the more successful calculus programs at doctoral degree-granting institutions had someone whose official job included coordinating the different calculus sections was surprising and particularly noteworthy. In the presentation, I will articulate the role that the calculus coordinator played in creating and sustaining a community of practice (Wenger, 1998) around the joint enterprise of teaching and learning calculus. In addition to helping to foster a community of practice, the calculus coordinator functioned as a “choice architect” (Thaler & Sunstein, 2000). The notion of a choice architect is adapted from economics to illuminate the unique and influential role that a calculus coordinator can have in creating and sustaining a successful calculus program. In totality, these seven common features of successful calculus programs offer a model for other institutions that want to improve the success of their calculus program.
Blair, R., Kirkman, E.E., & Maxwell, J.W. (2012), Statistical abstract of undergraduate programs in the mathematical sciences in the United States. Conference Board of the Mathematical Sciences. American Mathematical Society, Providence, RI.
Kuh, G., Cruce, T., Shoup, R., Kinzie, J., and Gonyea, R. (2008). Unmasking the effects of student engagement on first-year college grades and persistence. The Journal of Higher Education, 79 (5), 540-563.
Seymour, E. & Hewitt, N. M. (1997). Talking about leaving: Why undergraduate leave the sciences. Boulder, CO: Westview Press.
Thaler, R. H., & Sunstein, C. R. (2008). Nudge: Improving decisions about health, wealth, and happiness. Yale University Press.
Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge, UK: Cambridge University Press.
TITLE: Characteristics of Successful Programs in College Calculus at Four Two-Year Colleges
PRESENTERS: Vilma Mesa, University of MIchigan
Calculus I is a gateway course for students interested in science, technology, engineering and math [STEM] fields. Thus, retaining students in Calculus I and improving the teaching-learning environment becomes an issue of national importance. Public two-year colleges, also known as community colleges, play a key role, accounting for 46% of total U.S. mathematics enrollments and 20% of all Calculus I enrollments in 2010 (Blair, Kirkman & Maxwell, 2013).
As part of the NSF-supported Characteristics of Successful Programs in College Calculus research project (MAA, 2013) we studied four two-year public colleges, which were identified from a national survey as having successful Calculus I programs. Success was defined by a combination of student variables: persistence in calculus as marked by stated intention to take Calculus II (a proxy for persistence in a STEM major); affective changes, including enjoyment of math, confidence in mathematical ability, interest to continue studying math; and passing rates. The four selected institutions include two small colleges (enrollment <5,000) (one rural one, located in a city), a midsize urban college, and a large suburban college (enrollment > 10000). We conducted nearly 40 interviews with faculty, students, administrators and staff; 10 classroom observations; and focus groups with over 150 students. In addition we collected syllabi, homework assignments, quizzes, exams and projects
used by the calculus instructors.
In this presentation, I address the following question: “What are the features that participants identify as being directly associated with the success of their calculus program at the selected two-year institutions identified as successful?” We identified seven themes with our analyses: (1) High Quality Instructors, (2) Faculty Autonomy and Administrative Trust in the teaching of calculus, (3) Attention to Placement, (4) Support for students’ social and academic well-being, (5) Transfer Policies, (6) Informal Instructional Support, (7) Assessment and Data Collection. In the presentation I will discuss each of these themes. Here I highlight the first theme, High Quality Instructors, and the third theme, Attention to Placement.
Instructors at these institutions were described as caring, knowledgeable, available and approachable, and as having high expectations for developing conceptual understanding in addition to procedural competency. Such appraisal was also confirmed through our analysis of exams they gave their students and of tasks they used for teaching and through our analysis of the national survey data collected prior to the visits to the colleges. The teachers in these institutions assign more complex exams than what was observed in an analysis of exams of 150 institutions (of all types) in the national survey. In classrooms, instructors used challenging tasks and continuously asked students to participate in the resolution of the problems.
These institutions were also very intentional in their process for establishing adequate placement. They implemented student-oriented rather than institution-oriented policies. That is, they took many steps to ensure that their students were in the correct course: in-house-designed placement tests, commercially available tests, in-class tests on the first day of class, and administrative overrides of registration to switch students who need to change classes. In addition, both administrators and faculty were closely engaged in placing the students in the adequate course. Moreover, in two of the institutions, faculty were proud of the preparatory courses offered at the college and made sure that their students took those courses rather than placing directly from outside. These themes, collectively, reveal elements that are in place to assist students in integrating socially and academically in these campuses. Such integration influences students’ choice to stay in college (Kuh et al, 2008; Tinto, 1975, 1988). These institutions have intentional processes to make sure that students stay: from validating students as learners in the classrooms (Rendon, 2006), to making sure that placement and transfer policies are clear, to offering spaces for them to study and to connect to faculty. When instructors ask challenging questions in class and in exams, and give students confidence that they can master the material, they give students a strong basis to pursue further work. By encouraging students to take the preparatory courses in the college, the departments can create common experiences, foster use of rigorous language, set up expectations and create a community of learners ready for calculus. Such a community fosters social and academic integration. The implications we derive from this work relate to the role of mathematics instruction in fostering academic and social integration, and the ways in which placement can support students in their goals.
Blair, R., Kirkman, E. E., & Maxwell, J. W. (2013). Statistical abstract of undergraduate programs in the mathematical sciences in the United States. Fall 2010 CBMS Survey. Washington D.C.: American Mathematical Society.
Cohen, A. M. & Brawer, F. B. (2003). The American Community College (4th ed.). San Francisco: Jossey-Bass
Kuh, G. D. (2008). High impact educational practices: What they are, who has access to them, and why they matter. Washington, D.C.: American Association of Colleges & Universities.
Mathematical Association of America. (2013). Characteristics of Successful Programs in College Calculus. Retrieved from http://www.maa.org/programs/faculty-and-departments/curriculum-development-resources/characteristics-of-successful-programs-in-college-calculus.
Rendon, L. (2006). Reconceptualizing success for underserved students in higher education. Response paper for NPEC National Post-secondary Education Cooperative. NPEC National Post-secondary Education Cooperative. Retrieved from http://nces.ed.gov/npec/pdf/resp_Rendon.pdf.
Tinto, V. (1975). Dropout from higher education: A theoretical synthesis of recent research. Review of Educational Research, 45(1), 89-125.
Tinto, V. (1988). Stages of student departure: Reflections on the longitudinal character of student leaving. The Journal of Higher Education, 59(4), 438-455.
TITLE: Supporting Mathematics Instructors’ Adoption of Inquiry-Based Learning (IBL): Lessons from Professional Development Workshops
PRESENTERS: Charles Hayward, University of Colorado at Boulder
Mathematics is essential for success in STEM fields. Studies have linked students’ persistence in STEM majors to differences in instructional methods (Seymour & Hewitt, 1997; Freeman, et al., 2014), specifically for their Calculus courses (Ellis, Kelton, & Rasmussen, 2014). However, relatively few students experience high-impact educational practices that require students to interact with each other about substantive content (Kuh, 2008). Any effort to transform undergraduate STEM education and increase the use of research-based high-impact practices hinges on individual instructors changing and adopting these strategies. Professional development workshops can help support individuals in making these transitions.
This report discusses how faculty development workshops have helped instructors adopt Inquiry-Based Learning (IBL) methods in college mathematics. IBL is a spectrum of teaching methods that share the spirit of student inquiry through deep engagement with mathematics and collaboration with peers (Yoshinobu & Jones, 2013). Students learn through analyzing ill-defined problems and constructing and evaluating arguments (Prince & Felder, 2007; Savin-Baden & Major, 2004). IBL strategies in college mathematics courses are associated with affective gains and greater persistence with math majors for female students, and improved grades lowperforming students. (Laursen, Hassi, Kogan, & Weston, 2014).
I focus on survey and interview findings from a series of annual, week-long workshops featuring invited talks, collaborative work time, and panel discussions designed to support instructors in implementing IBL in their own classrooms. The workshops served 167 instructors from various institutions around the U.S. and Canada. Each year, participants were invited to complete pre-workshop, post-workshop, and one-year follow-up surveys. I use survey findings from 139 participants for which follow-up data are currently available, and interviews from a subset of 16 participants from the first two workshops, to identify professional development practices that have been effective in shifting mathematics instructors toward IBL pedagogies. These practices include communication of inclusive definitions of IBL, supports for implementation, frequent follow-up and inclusion in the broader IBL community. These components have contributed to successful workshops; so far, 58% or participants have reported implementing IBL methods in their classrooms in the first year following the workshop.
I frame these components with a three-stage theory of change in human systems (Lewin, 1947), as adapted by Paulsen and Feldman (1995) to model instructor change. In the first stage, unfreezing, instructors become motivated to make a change. I will argue that communicating broad, inclusive definitions of IBL helps instructors with the “safety” criterion of the first stage, as they allow instructors to “envision ways to change that will produce results that reestablish his or her positive self-image without feeling any loss of integrity or identity” (Paulsen & Feldman, 1995, p. 12). Interview participants commented on the “spectrum of IBL” and one described how this “was kind of a big moment for me because it made it seem less scary.”
The workshops, to varying degrees, have also helped support participants with the second stage, changing, when they implement their new learning. We observed that workshops provided participants with how-to knowledge about implementing IBL in their own classrooms, and participants reported increased knowledge and skills following the workshops. While there were common elements across the workshops, each one featured its own blend of invited talks, panel discussion, video observations, discussions of readings and collaborative work time with colleagues. Based on participants’ comments, workshop features that appear to have particularly supported participants’ learning include discussions with experienced IBL implementers, modeling of IBL teaching methods, and informal interactions and networking with other participants.
The third stage, refreezing, helps to reconfirm new behaviors and sustain the change. Our data suggest that this is supported by two components of the workshops, frequent follow-up and inclusion in the broader IBL community. For the third workshop, organizers engaged participants in frequent email mentoring through a group email list and individual messages. Many of the participants (62%) have been active on the list, and have used it to provide encouragement and address challenges they faced. Participants in this workshop reported significantly higher implementation rates than the first two cohorts. Participants from all three workshops were encouraged to join the broader IBL mathematics community through IBL-focused conferences and networking with other IBL instructors, and some reported doing so. These two components provide opportunities for colleagues to help reinforce and confirm the instructor’s decision to implement IBL methods. While these findings do not directly address institutional and national contexts, they do provide insight into ways to support individual instructors in incorporating new research-based teaching strategies. This is an important, and necessary, component of broader institutional transformation efforts.
Ellis, J., Kelton, M. L., & Rasmussen, C. (2014, March). Student perceptions of pedagogy and associated persistence in calculus. ZDM: The International Journal on Mathematics Education , 1-13.
Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., et al. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences , 201319030.
Kuh, G. (2008). High-impact educational practices: What they are, who has access to them, and why they matter. Washington D.C.: AAC&U.
Laursen, S. L., Hassi, M.-L., Kogan, M., & Weston, T. J. (2014). Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution study. Journal of Research in Mathematics Education , in press.
Lewin, K. (1947). Group decision and social change. Readings in social psychology , 3, 197-211.
Paulsen, M. B., & Feldman, K. A. (1995). Taking Teaching Seriously: Meeting the Challenge of Instructional Improvement. ASHE-ERIC Higher Education Report No. 2, 1995. Washington D.C.: ERIC Clearinghouse on Higher Education.
Prince, M., & Felder, R. (2007). The many facets of inductive teaching and learning. Journal of College Science Teaching , 36(5), 14-20.
Savin-Baden, M., & Major, C. H. (2004). Foundation of problem-based learning. Maidenhead, UK: Open University Press.
Seymour, E., & Hewitt, N. M. (1997). Talking about leaving: Why undergraduates leave the sciences. Boulder, CO: Westview Press.
Yoshinobu, S., & Jones, M. (2013). An overview of inquiry-based learning in mathematics. Wiley Encyclopedia of Operations Research and Management Science , 1-11.
TITLE: Experiments in Educational Transformation: Departmental Contexts and Strategies for Implementing Inquiry-Based Learning in College Mathematics
PRESENTERS: Sandra Laursen, University of Colorado Boulder
Ample research evidence supports the use of student-centered teaching approaches to improve student educational outcomes in science, technology, engineering and mathematics (STEM) disciplines. The bottleneck in actually making these improvements on a national scale is not a lack of well-developed classroom approaches from which to choose; rather, slow faculty uptake of proven teaching methods limits large-scale implementation and institutional commitment to these approaches. That is, “The problem in STEM education lies less in not knowing what works and more in getting people to use proven techniques” (Fairweather, 2008, p. 28).
Most studies of this issue have focused on challenges to faculty uptake: the internal and external barriers to pedagogical change among STEM instructors (e.g., Henderson & Dancy, 2007). Early socialization in their discipline develops a values hierarchy that privileges research over teaching; structural issues such as class size and room configuration complicate practical classroom logistics; and instructors fear real or perceived skepticism of students, colleagues, or chairs. Most studies have also focused on individual instructors, for example, their knowledge and choices about instruction (e.g., Walczyk, Ramsey & Zha, 2007). This is logical if we view teacher decision-making as individualized. But STEM instructors are embedded in social systems that influence their thinking in positive and negative ways, especially their discipline and department, and thus we must also understand instructors’ working contexts. In this presentation, we examine departmental activities and contexts
that influence the spread and sustainability of pedagogical change within university mathematics departments.
To examine this issue, we draw upon a study of the implementation of inquiry-based learning in four research mathematics departments with privately funded IBL Mathematics Centers established “to further develop, study, promote and disseminate the use of inquiry-based learning (IBL) approaches in the teaching of mathematics by fostering IBL activities at … prestigious national universities” (EAF, 2007). These leading research departments were expected to have high visibility and influence in their discipline, and were selected in part for their history of engagement in mathematics education. As a group, they present interesting case examples of efforts at institutional transformation, especially given the crucial role of mathematics courses as a gateway to STEM majors and jobs.
These universities are part of a larger mathematics education community surrounding a version of inquiry based learning that stems from collegially shared traditions of Socratic teaching based on the practices of late mathematician R. L. Moore, rather than on the research literature in the learning sciences. However, their teaching practices as observed are largely consistent with modern, research-based approaches to active and collaborative learning. Each campus independently selected and developed its own set of IBL courses, yielding a range of courses targeted to audiences from first-year to senior level, and to mathematics majors, mixed STEM majors, or pre-service K-12 teachers. While the IBL teaching practices used in these courses are broadly consistent across the four campuses, the campuses also show variation in local cultures of how IBL is conceived and executed in the classroom.
This presentation will examine some of the strategies developed by these departments to support IBL instructors and engage colleagues, including formal and informal mentoring, team-teaching, and collegial gatherings, as well as some strategies used to inform colleagues not actively involved in IBL teaching. Interestingly, no department used all of these strategies. A comparative analysis suggests ways in which these strategies may have helped or hindered the spread and sustainability of departmental IBL programs.
In addition to their engagement with regular faculty, some departments involved numerous graduate students as teaching assistants in inquiry-based courses, while others worked with postdoctoral scholars as IBL instructors. Working as instructors in IBL courses proved to be a powerful form of professional development for early-career instructors, many of whom moved on to teaching roles at other institutions, carrying reshaped teaching philosophies and expertise with them, and remaining active in the larger IBL mathematics community. I will briefly describe outcomes for early-career instructors and suggest how this aspect of the Centers’ work offers another potential avenue for transformation of teaching and learning in college mathematics.
Educational Advancement Foundation (EAF) (2007, February). Request for Proposal on Assessment & Evaluation Center for Transforming American Mathematics Education, Inquiry-Based Learning Project in Mathematics.
Fairweather, J. (2008). Linking evidence and promising practices in science, technology, engineering, and mathematics (STEM) undergraduate education: A status report for the National Academies Research Council
Board of Science Education. Retrieved 5/27/14 from http://sites.nationalacademies.org/DBASSE/BOSE/DBASSE_071087.
Henderson, C., & Dancy, M. H. (2007). Barriers to the use of research-based instructional strategies: The influence of both individual and situational characteristics. Physical Review Special Topics-Physics Education Research, 3(2), 020102.
Walczyk, J. J., Ramsay, L., & Zha, P. (2007). Obstacles to instructional innovation according to college science and mathematics faculty. Journal of Research in Science Teaching, 44(1), 85-106.