When we embarked on Project CALC, we weren't at all sure that a reformed calculus course should have a textbook. Weren't those thousand-page monsters more of a problem than a solution? For a generation or more, everyone teaching calculus collaborated in demanding (or writing) textbooks that would help our students pretend to learn mathematics by memorizing rules for moving symbols in response to set types of problems -- “template exercises” -- that have no relationship to mathematics as practiced by anyone else. We had an unspoken contract with the students that we would pretend to teach if they would pretend to learn. The primary aid we provided for carrying out their end of the bargain was a book in which the words did not have to be read. It was sufficient to match each exercise to a “fully worked out example” that would reveal the sequence of symbol manipulations sufficient for getting the answer in the back of the book.
As the Project CALC development progressed -- and as we observed students learning to solve substantial problems -- we found ourselves writing more and more background information for which there was not enough time in the classroom. As we wrote, we rediscovered the proper role of the textbook as a source of information. But to serve that role, the book has to be read. In mathematics, it has to be read with pencil and paper at hand -- and now a graphing tool as well -- responding to frequent challenges. It is not enough to read through pages of carefully reasoned material, dutifully agreeing with the author, and then expect to be able to do as the author did. Given our students' general lack of intrinsic interest in the course, we had to present new information in engaging contexts. Thus was born The Calculus Reader.
Alas, it was not to be. Word came back from the publisher's representatives trying to interest faculty in preliminary editions of the Reader that, if the book signaled “read” on the cover, faculty would not even look inside, let alone consider adoption. So our labor of love has appeared under a new title that is less scary to our colleagues.
That still leaves the problem of how we get students to read about mathematics when they never had to do that before. The problem is not unlike getting them to write about mathematics when they never had to do that before. Many others have addressed the latter issue with various approaches -- some quite successful -- to Writing Across the Curriculum. I have written elsewhere of having to invent Reading Across the Curriculum -- possibly a harder task, because no one wants to admit that otherwise qualified college students can't read.
Well, in fact, they can read -- and write -- but someone has to teach them how. Lacking freshman reading courses analogous to our ubiquitous writing courses, we have to do it ourselves. Our first step has been to do reading exercises in the classroom. For example, early in the course we might assign small groups to read two pages of text to each other, working the exercises as they go, with an expectation of being called on to report before the period is over. Under supervision -- and with an appropriate reward or penalty -- students find they can read a well-written book. Once they believe it is possible, it is possible. They continue to need incentives, such as pop quizzes focused directly on reading assignments. If they continue to use their new-found ability throughout the course, then our textbooks can serve their intended purpose -- the same purpose books have served since Gutenberg.
The payoff for teaching students to read is that we can stop worrying about covering the syllabus -- properly the students' job -- and concentrate instead on uncovering it.
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Send comments to the author <das@math.duke.edu>Last modified: May 15, 1997