Saturday, March 14, 2015
What Makes A Successful Calculus Teaching Program?
In a recent paper appearing in the Notices of the American Mathematical Society, Vol. 62, No. 2, p.144) by David Bressoud and Chris Rasmussen, seven characteristics of successful calculus programs are introduced. This was the outcome of a study undertaken by the Mathematical Association of America, consisting of a national survey in 2010 and subsequent visits to 17 institutions identified as "successful" based on their success in retention and maintenance of "productive disposition"
Retention means keeping students in courses, as opposed to having them withdraw. "Productive disposition" is defined by the authors as:
"habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence, and one's own efficacy."
This is a lot to ask for, given, as the authors observe (ibid.):
"Our survey revealed that Calculus I, as taught in our colleges and universities, is extremely efficient at lowering student confidence, enjoyment of mathematics, and desire to continue in a field that requires further mathematics."
Wow! That sounds almost as depressing as the effects of Common Core Algebra II on HS students, e.g.
But, as they also noted, "the institutions selected bucked this trend".
So what were they doing right that the others weren't, or that the others might have selectively ignored? They give the characteristic of the successful calculus programs as follows:
1. Regular use of local data to guide curricular and structural modifications.
This basically means that the calculus program isn't " set in stone" and that faculty continuously tweak it to enable better outcomes. In this case also, a bad semester isn't simply dismissed as an anomaly but examined in the larger context of what went wrong.
2. Attention to the effectiveness of placement procedures.
This means paying attention to those allowed to take Calculus I, especially in terms of satisfying pre-requisites. (Those not qualified are placed in programs to deal with their special needs.)
3. Coordination of instruction, including building communities of practice.
This implies each section of Calculus I is coordinated in terms of teaching approach, with minimal variation, i.e. no "freelancing". It also means much tighter coordination of instruction for graduate teaching assistants.
4. Construction of challenging and engaging courses.
Thus, successful programs didn't merely base courses on textbooks alone, or only used limited texts. They opted for texts (and selected problems) that requires students to delve into concepts and to work on modeling type problems. In my own calculus teaching experience, practical applications of differentiation and integration played a major role - and this often included astronomy problems such as calculating areas of orbital sectors for different planets as traced out between different times. The point was to challenge students beyond the bounds of their textbooks (with ordinary abstract problems)
5. Use of student-centered pedagogies and active learning strategies.
This entails implementing active learning strategies that force students to "engage mathematical ideas and confront their own misconceptions." This is critical since "few students know how to study and most take very passive roles when attending lectures. The point is students need to be actively involved in their own education and "have opportunities to apply what they've learned to different settings".
6. Effective training of graduate teaching assistants.
This pretty well goes without saying. Unless the section TAs are competent, it will defeat the thrust of the whole program. This is especially true given TAs play an important role at all universities with doctoral programs. In this case, "the most successful universities have extensive programs for training, monitoring and supporting TAs."
7. Proactive student support services - including fostering student academic and social integration.
Thus, successful programs encouraged positive student-faculty exchanges and community as opposed to students feeling isolated. Enriching educational experiences became a primary objective with "extensive student-faculty interaction characterizing both the teaching and learning of math inside and outside the classroom."
In addition, the authors noted a "variety of programs to support at-risk students". This often included supplemental instruction in pre-calculus topics and other "fall back" courses, i.e. for students who discover on their first exam that they're in trouble with calculus.
One of the most notable differences found was between the selected Ph.D. universities and all others. In the former, much less use was made of lectures and more use made of students working together, holding discussions and making presentations. Some of the findings in terms of proportions of final grades earned are shown in Fig. 1 below:
Note in particular from the above, the higher success of the case study doctoral universities in terms of Bs and Cs, as well as the lower withdrawal (W) rates, and the lower Ds, Fs by comparison with all other Ph.D. universities.