The First Two Years of College Mathematics: Reflections and Highlights from the CBMS Forum

By Diana White, Contributing Editor, University of Colorado Denver

In early October, approximately 150 educators and policy makers gathered together in Reston, Virginia for the fifth Conference Board of the Mathematical Sciences (CBMS) Forum entitled The First Two Years of College Mathematics: Building for Student Success. Participants came from almost every state in the country and represented higher education institutions ranging from two-year colleges to top-ranked research universities. We spent two days reflecting, learning, and in some cases planning how to improve the last year of high school mathematics and the first two years of college mathematics.

As is often my reaction at these types of conferences, I found the two days both sobering and energizing — sobering because of the sometimes harsh realities and challenges we face, energizing because of the good work participants report on and the many people gathered together who care so passionately and who dedicate so much of their time and energy to moving us forward. For those who could not join us in Virginia, this blog post will present a few key highlights from the Forum, in an effort to open a broader conversation about the future of the first two years of collegiate mathematics instruction.

The Forum began by emphasizing many ways in which the mathematical sciences are thriving. The National Research Council report Mathematical Sciences in 2025 notes that there have been many major research advances, both theoretical and in high-impact applications, with clear benefits to other STEM areas and to the nation. As the foundation of many recent STEM advances, the role of the mathematical sciences has expanded.

This creates a need to revisit many aspects of our mathematical training of students to ensure that we are meeting the needs of our diverse constituents.  In addition, the overall student success rates in mathematics are concerning. The President’s Council of Advisors on Science and Technology (PCAST) report Engage to Excel: Producing One Million Additional College Graduates with Degrees in STEM notes that “Reducing or eliminating the mathematics preparation gap is one of the most urgent challenges — and promising opportunities — in preparing the workforce of the 21st century.” PCAST considers the situation so dire that they suggest an experiment in which faculty from mathematics-intensive disciplines such as physics, engineering, and computer science design and teach college mathematics courses.  The PCAST report has received a lot of attention from the mathematical community, see the blog post from David Bressoud for some historical context and the summary response from the Joint Policy Board for Mathematics.  The full response is here.

Multiple speakers at the Forum called on the mathematical community to wake up and heed the call for change this proposal implies.  They called for a broadening of localized efforts to respond, while taking note of illuminating data and promising programs that may make this possible.   Speakers at the Forum emphasized that we do not lack demonstrably successful and promising programs to meet many of the challenges the first two years of college mathematics present.  However, widespread adoption of these programs has lagged.

STEM Careers: Building for Success in Calculus

The Characteristics of Successful Programs in College Calculus study from the Mathematical Association of America provides a large-scale, evidence-based understanding of who takes calculus, why they take it, and what happens in the course.

Students come out of calculus courses with greatly decreased confidence and frustration at their lack of understanding. Further, many students who initially declare or express interest in Science, Technology, Engineering, and Mathematics (STEM) majors change their mind in calculus class. The lack of persistence in STEM trajectories is sufficiently dire that we can currently view a moderate decrease in overall student interest in pursuing a STEM career after taking calculus as a success.

However discouraging this may seem, it is also encouraging that we now have such extensive data, as it allows the mathematical community to transition from small scale studies and so-called autobiographical reasoning — based on personal experience at our own institutions or throughout our own careers — to evidence-based reasoning from a large scale study.

Affecting Student Success in General Education Mathematics

As noted by Tony Bryk, President of the Carnegie Foundation for the Advancement of Teaching, “developmental mathematics is where aspirations go to die”.  Yet the vast majority of first year community college students require some form of developmental education. Lack of student success in these developmental mathematics courses often hampers degree completion, as less than half successfully go on to complete a transfer level mathematics course (defined as a course that meets the general education mathematics requirement at a four year institution).  The likelihood of persisting to successful completion of a transfer level course decreases drastically as the number of developmental courses needed as a prerequisite to a transfer level course increase, dropping to approximately 10% for those needing three or more developmental courses.

The New Mathways Project, an initiative of the Dana Center and the Texas Association of Community Colleges, is thus far showing remarkable results in both decreasing the time required for students to be ready for a transfer level course, as well as the success rates in such courses.  It consists of three primary pathways — the statistics pathway, the quantitative pathway, and the STEM pathway.

The statistics pathway, known as Statway, prepares students in disciplines such as nursing, social work, and criminal justice for the college level statistics course their disciplines require. Now in its fourth year of implementation, it has a success rate (defined as earning a C or better in a college level statistics course within two years) of approximately 50%, as opposed to approximately 15% for those in a comparison group.

Results in the other pathways are also promising, and scale-up efforts are in place.  The New Mathways Project is now being implemented in additional states, including my own state of Colorado, with optimism based on solid data that it will positively affect degree completion.

Moving Forward

This blog post cannot possibly do justice to the scope of topics addressed throughout the two days. For example, I have not addressed the Common Core and secondary to post-secondary articulation, faculty instructional approaches, diversity and gender concerns, or the reality of the fiscal challenges associated with these efforts. The complete list of abstracts, many of which contain the corresponding slides, give a sense of the scope of the Forum.

There remain many challenges related to entry-level mathematics, and to put the importance in context, the mathematics community would be wise to keep in mind that the number of students taking these courses, including the calculus sequence, by far eclipses the number of mathematics majors.  College mathematics instructors would benefit from increasing their awareness of the extensive developments related to curriculum and teaching, especially at this lower level.  Several Forum speakers also noted that the reward structure for mathematicians in academia, especially those at research universities, is another obstacle that we need to address to further increase participation, especially amongst active research mathematicians.

The intensive two days ended with a final challenge.  Noting that the Forum would be a failure if participants only used what we learned as information for ourselves, we were encouraged to talk broadly with colleagues about what we learned and more broadly about the first two years of college mathematics education.  Toward this end, I presented a summary of this meeting to our undergraduate committee, and I am going to share a copy of Mathematical Sciences in 2025 with both my department chair and dean. It doesn’t feel like much, but it’s a start. This blog entry is also a contribution to that discussion, and an attempt to reach out to colleagues beyond my institution.

What are your thoughts about the issues the Forum addressed? How can we improve the first few years of undergraduate mathematics instruction, either locally or nationally? What do you view as the barriers to wider implementation of programs with demonstrated success? What are you willing to do to contribute to this effort?

I encourage readers to contribute to this discussion in the comments section and/or under the announcement for it on the AMS Facebook page.

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1 Response to The First Two Years of College Mathematics: Reflections and Highlights from the CBMS Forum

  1. Avatar Albert says:

    Since the meetings described here, the TPSEMath report has appeared: Transforming Post-Secondary Education in Mathematics: A National Discussion. It contains recommendations resulting from a meeting in Austin 20-22 June 2014. http://www.tpsemath.org/meeting1

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