Saturday, June 30, 2018

Departmental Turnaround: The Case of San Diego State University

By David Bressoud

You can now follow me on Twitter @dbressoud

Paul Zorn and I have just published a special issue of PRIMUS on Improving the Teaching and Learning of Calculus (Bressoud & Zorn, 2018) . It contains eight articles that should be of interest to anyone who is discontented with the current state of calculus instruction at their institution. Four of these articles present case studies of universities that have made significant changes within the past few years: San Diego State University (SDSU), the University of Illinois-Chicago, Colorado State University, and the University of Hartford. The most extensive revamping occurred at San Diego State University, which is where I am focusing below.

MAA’s national study of calculus instruction, Characteristics of Successful Programs in College Calculus (CSPCC) , identified seven practices (Bressoud & Rasmussen, 2015; see the Appendix for descriptions) that we observed in the most effective programs. A few years ago, San Diego State University, facing unacceptably high failure rates and low persistence rates in its Precalculus through Calculus II sequence, decided to work on all seven areas. The result has been a dramatic improvement in these courses. Naneh Apkarian, who was a doctoral student in mathematics education within the mathematics department during this process, is the lead author on this account (Apkarian et al., 2018) .

Figure 1: The landmark Hepner Hall at San Diego State University.

With roughly 30,000 undergraduates, San Diego State University is a large public university, part of the California State University System, and chronically underfunded. It is a Hispanic-Serving Institution where 84% of students are on some form of financial aid. Science, technology, engineering, and mathematics (STEM) majors account for 10% of bachelor’s degrees. The mainstream precalculus and single variable calculus courses enroll about 1,500 students each fall. The Department of Mathematics and Statistics consists of 17 faculty in pure and applied mathematics, seven in statistics, and six in mathematics education.

Michael O’Sullivan was appointed chair of the department in 2014. He made it his mission to revamp lower-division mathematics instruction. The effort began that fall with the creation of a Calculus Task Force charged with proposing a system for coordinating the courses in the Precalculus to Calculus II sequence (P2C2). As Rasmussen and Ellis (2015) have documented, one of the most important characteristics of successful P2C2 programs is coordination of the essential elements of each course including policies, learning objectives, and exams and their scoring rubrics. Coordination also involves regular communication among those teaching different sections. At San Diego State University, total autonomy—to the point where different instructors were using different textbooks, homework systems, and even course content—had been the rule.

As the department expanded its data collection beyond simple pass rates, they discovered that only 17% of those who began with Precalculus successfully completed Calculus II, only 10% within the standard three semesters. This made mathematics faculty aware that something was seriously wrong and needed to change.

Because the discontinuation of large lectures was not financially feasible, the implementation of active learning to address this completion rate was concentrated in breakout sections led by Graduate Teaching Assistants (GTAs). The chair successfully lobbied to increase breakout sections from one to two hours per week and managed to reduce the size of most of these sections.

The chair also tied into a university initiative, Building on Excellence, to fund a new Mathematics Learning Center within the library building, directed by the office of the Dean of Science—ensuring its continued funding—but led by the department. The static 40-question placement exam was replaced by ALEKS Placement, Preparation, and Learning, with the license paid by the California State University System and student payments of $20 per proctored exam.

While these contributions were serendipitous, I have found that—particularly in situations of tightly constrained budgets—deans and provosts are keen to direct resources toward strategic initiatives with the potential for high impact. I have frequently encountered deans who asserted that if only the department would come forward with a well-thought-out and cost-effective plan for improving student outcomes, the money could be found to fund it.

As the authors reported, the effort at revision was successful because of the attention paid to opening and maintaining communication channels with stakeholders in this process (see Figure 2).

Figure 2: Significant communication channels between the mathematics department and various administrative programs as they relate to the seven targeted program features. Source: Apkarian et al. 2018, p. 540.

The result is a calculus program of which the department is justly proud, as reflected in this video. Students find the new Math Learning Center particularly helpful because its work is tightly connected to what is happening in all sections of each course.

The Department of Mathematics and Statistics at San Diego State University is a good example of how a program can be transformed. Its story illustrates the role of leadership from the department chair, buy-in and effort from a core of committed faculty, and strong two-way communication with all of the stakeholders.

  • Apkarian, N., Bowers, J., O’Sullivan, M., and Rasmussen, C. (2018). A Case study of change in the teaching and learning of Precalculus to Calculus 2: what we are doing with what we have. PRIMUS. 28:6, 528-549, DOI: 10.1080/10511970.2017.1388319
  • Bressoud, D., and Rasmussen, C. (2015). Seven characteristics of successful calculus programs. AMS Notices. 62:2, 144–146.
  • Bressoud, D. and Zorn, P. (2018). Improving the Teaching and Learning of Calculus. PRIMUS vol. 28.
  • Rasmussen, C., and Ellis, J. (2015). Calculus coordination at PhD-granting universities: more than just using the same syllabus, textbook, and final exam. In Bressoud, Mesa, and Rasmussen (Eds.), Insight and Recommendations from the MAA National Study of College Calculus. MAA Notes #84. Washington, DC: MAA Press. 

Appendix: Seven Characteristics of Successful Programs in College Calculus
  1. Local Data. Regular collection and use of local data to guide program modifications as part of continual improvement efforts.
  2. Placement. Effective procedures for placing students appropriately into their first Precalculus to Calculus II (P2C2) course (both initial placement and re-placing students after the term begins).
  3. Coordination System. A coordination system for instruction that (i) makes use of a uniform textbook and assessments and (ii) goes beyond uniform curricular elements to include regular P2C2 instructor meetings in development of de facto communities of practice.
  4. Course Content. Course content that challenges and engages students with mathematics.
  5. Active Pedagogy. The use and support of student-centered pedagogies, including active learning strategies.
  6. GTA Preparation & Development. Robust teaching development programs for teaching assistants.
  7. Student Support Service. Proactive student support services (e.g., tutoring centers, services for first-generation students) that foster students’ academic and social integration

Friday, June 1, 2018

Explosive Growth of Advanced Undergraduate Statistics

By David Bressoud

You can now follow me on Twitter @dbressoud

The 2015 CBMS Survey is now available. Last month I reported on Trends in Mathematics Majors. This month I am looking at what has happened to enrollments in particular mathematics courses. The column has three section: Enrollments by Category, where we see that the fastest growing category is Advanced Undergraduate Statistics; Calculus Enrollments, noting that the growth here is almost exclusively within the research universities where it is tied to the strong growth in engineering enrollments; and Dual Enrollment, where the story is about the dramatic increase in four-year institutions now offering dual enrollment courses.

Enrollments by Category
The first graph (Figure 1) shows strong growth in course enrollments in 4-year undergraduate programs, exceeding 2.5 million for the first time. This is certainly tied to the rampant growth in the number of prospective STEM majors (Figure 2). The number of prospective engineering majors grew from 108,000 in 2005 to 156,000 in 2010, peaking at 194,000 in 2015. Over the same period, prospective physical science majors grew from 30,000 to 40,000. Students entering with the intention of majoring in the mathematical sciences grew from 10,000 to 16,000.
Figure 1: Undergraduate enrollments by course category in mathematics and statistics departments at 4-year institutions.
Intro Level includes College Algebra and Precalculus; Calculus Level includes sophomore courses in linear algebra and differential equations.

Figure 2: Number of entering full-time first-year students at 4-year institutions intending to major in five core STEM disciplines.
Data from The American Freshman, published by the Higher Education Research Institute.

The most remarkable growth among categories of courses was for Advanced Statistics, any course beyond a first college-level statistics course, almost doubling from 60,000 in 2010 to 110,000 in 2015. This is in line with the growth in the number of Bachelor’s degrees awarded in Statistics, from 858 in 2010 to 1509 in 2015. Figure 3 shows that this growth has occurred primarily within departments of statistics, although there has also been strong growth at Bachelor’s level colleges and a remarkable turnaround in Master’s granting universities.

Figure 3: Enrollments in Advanced Undergraduate Statistics by type of department.
Departments of mathematics are characterized by the highest degree offered by the department.

Calculus Enrollments 

Calculus enrollments have also seen strong growth, driven by increases in prospective STEM majors (Figure 4). The MAA Progress through Calculus study found that for mainstream Calculus I, fall enrollments account for about 60% of all mainstream Calculus I enrollments throughout the year, while fall Calculus II enrollments account for about 40% of all Calculus II enrollments. Thus, about 550,000 students study Calculus I each year at a post-secondary institution. This compares with roughly 800,000 students who study calculus in high school each year (NCES data).

Figure 4: Fall term mainstream calculus enrollments (meaning that they lead to the usual upper division mathematical sciences courses), combined from all 2- and 4-year institutions.

Supporting the claim that most of the growth in calculus enrollments can be attributed to the growth in prospective engineering majors, Figures 5–7 show that the increase in calculus enrollments has occurred at the universities that also offer a PhD in mathematics, predominantly the large research universities.

Figure 5: Fall enrollments in mainstream Calculus I, by type of institution.
Figure 6: Fall enrollments in mainstream Calculus II, by type of institution.
Figure 7: Fall enrollments in mainstream Calculus III&IV, by type of institution.

The connection to engineering is reinforced by an interesting though not surprising observation. In 2005, I plotted the number of prospective engineering majors against the total number of students enrolled in all mainstream calculus classes (single and multi-variable) in PhD-granting departments (Figure 8). The correlation, at slightly over two students enrolled in the fall for each engineering major is remarkably tight, with a Pearson r=0.99.

Figure 8: Number of entering freshman intending to major in Engineering against total fall enrollment in all mainstream calculus (single and multi-variable).
Pearson’s r = 0.99.

The 2010 and 2015 data do not come close to fitting this line. It overestimates calculus enrollments by about 35%. Fitting a line to the data from 1995 to 2015 yields the graph in Figure 9. The multiplier effect of each prospective engineer has dropped to a little over 1, evidence that whereas an engineering major would, in the past, study single or multi-variable calculus in two fall terms, they now usually take calculus in only one fall term.

Figure 9: Number of entering freshman intending to major in Engineering against total fall enrollment in all mainstream calculus (single and multi-variable).
Pearson’s r = 0.97.

Dual Enrollment

CBMS began tracking dual enrollment in 2005, courses offered by a 2- or 4-year college, taught in a high school by a high school teacher, but carrying both high school and college credit. In 2005, 50% of 2-year departments, but only 14% of 4-year departments offered dual enrollment courses in mathematics. By 2015, these percentages had climbed to 63% at 2-year institutions and 26% at 4-year institutions. We conclude this column with Figures 10 and 11, showing the number of fall enrollments in the four most common dual enrollment courses: College Algebra, Precalculus, Calculus I, and Statistics.

Figure 10: Fall term dual enrollment at 2-year colleges.
Figure 11: Fall term dual enrollment at 4-year institutions.