About 6 months ago, I got invited to give one of two plenary addresses at the upcoming 2014 Kansas City Math Expo, which will occur in three short weeks. My Saturday talk at the conference is titled “Calculus 2020: A vision for the future.”
One can’t have a vision for the future without an appreciation for the past, so I’ve been doing some reading about the history of calculus instruction generally, and the calculus reform movement in particular. It’s been fascinating. Two MAA publications have been immensely helpful: “Catalyzing a National Community for Reform: NSF Awards 1987-1995” and “Assessing Calculus Reform Efforts”, published in 1997 and 1994, respectively, together provide an insightful history of a wide range of developments.
1987 was a seminal year in the history of calculus instruction (and the year I graduated from high school, sigh). The Tulane Conference that kicked off calculus reform was in January 1986, and between 1987 and 1995, the NSF awarded $44M in grants to over 350 institutions to impact calculus instruction as part of the “reform” movement. These grants had a huge impact. In the former of the two books noted above, the editor (William E. Haver) writes that “Calculus: A Pump, not a Filter sums up the desire of mathematicians that calculus be valuable to students in pursuing their educational and career goals, not a barrier to success. Courses and materials developed under the aegis of calculus reform emphasize direct experience with methods and processes of inquiry. Students learn mathematics by doing mathematics, by applying mathematical tools to significant and engaging problems, by working with other students, and by writing about their work. The use of modern technology adds visual and numeric perspectives to the usual algebraic perspective.”
Later in the volume (still writing in 1997), Haver writes that “calculus students today are making extensive use of modern technology; regularly completing long-term assignments; and frequently participating actively as members of study groups and activity teams. Ten years ago these activities were virtually unheard of in college mathematics classes.”
Looking back over the span of the last almost 30 years, it’s evident that the calculus reform movement has had a profound impact on collegiate mathematics instruction. At conferences, in journals, on the NExTList, and with my GVSU colleagues, I am constantly seeing instructional work that reflects the influence of this movement, and certainly not just in calculus.
And yet, some other recent information on calculus instruction is making me wonder if important parts of the reform movement haven’t fully taken root, including those regarding “direct experience with methods and processes of inquiry” and “learn[ing] by doing mathematics … [and] working with other students.”
To see why I’m feeling this way, consider two quotes from David Bressoud’s ongoing “Characteristics of Successful Programs in College Calculus” study:
– “Most instructors see themselves as fairly traditional. They view lecture as the best way to teach students and believe that procedural fluency precedes conceptual understanding.”
– “The emphasis in exams is on computational technique, but almost all instructors have some points devoted to graphical interpretation of central ideas, and most include some complex or unfamiliar problems as well as proofs or justifications.”
(Both quotes are from a post on “The Calculus I Instructor“; you can see a wide range of posts and information related to the project at http://www.maa.org/cspcc/.)
In the near future, I’ll share some thoughts about the Calculus Concept Inventory, and with it some recent work about the considerable impact of “interactive engagement” as an instruction style over “traditional” (i.e. “lecture”) instruction, along with some further reflections on the statements that “most instructors see themselves as fairly traditional” and “they view lecture as the best way to teach students.”
For now, coming up on 30 years since the calculus reform movement started, I’d say to our community: giant steps of progress, still considerable room for growth.
