The ``Calculus Reform'' movement sweeping the nation has arrived in Cornell! This semester (Spring 95) two special sections of 112 will be offered, with enrollment limited to 20 students per section.
Is this some kind of ``experiment''?
Calculus reform is not an experiment but a broad movement across the country, based on the consensus that how we teach calculus (and mathematics more generally) should be modified to make for a more effective learning process.
Far from being ``experimental'', at many universities, calculus reform has become the norm. For example, most calculus taught at Ithaca College is ``projects-based'' (see below). At New Mexico State University, 80 percent of calculus students are doing projects in their calculus courses.
Will these special sections be totally different from the ``regular'' 112 sections?
No. The basic syllabus in these sections will be the same as in the ``regular'' 112 sections. The same text (James Stewart's Calculus) will be used.
Even the regular sections have modified the old syllabus, which was loaded with a very large number of topics, leaving little time to cover the topics in much depth. This in part reflects responsiveness to students' comments on course evaluation forms; e.g. ``It would be nice to step back from the syllabus and really see what we were doing.'' and ``I think that the course is a bit overloaded. The course [covers] a lot of material in very little depth. I would much prefer less material but in more depth''
Ok, how will these sections be different then?
First, the special sections will take the idea of fewer topics, each covered in more depth, farther than the regular 112 sections -- e.g., fewer formulas to memorize.
This will be done by means of in-class Activities in groups, as well as several (3-4) Projects to be worked on outside of class, in consultation with the instructors. Our basic text will be supplemented by handouts which will introduce activities and projects.
Will this be more fun and interesting?
Yes! Students report, and surveys document, more involvement, interest, and enthusiasm by students who take projects-based calculus.
Have you ever wondered why a sailboat can sail in a direction perpendicular to the wind, or how it can sail upwind? You will be able to learn about this when we study vectors. And how can we use infinite series (and differential equations) to tell us about the right levels of medical doses and safe time intervals between doses? You'll get hands-on experience with that application when we study series.
Try your hands at the Houdini's Escape project when we study
volumes. And when we cover Taylor Series, a topic which has
intimidated many a calculus student, you'll get to play a
mathematician working for Project SETI (Search for Extra-
Terrestrial Intelligence) in the Pi in the Sky project, devising efficient algorithms to compute pi to more decimal places than ever before, in order to compare these with signals from a distant source in the galaxy.
In Tripple Trouble, you are the captain of the Starship Exitprize, which has been invaded by tripples. Help decipher the cryptic report of Spook the Vulgar, then decide whether to use radiation from the ship's engine, as suggested by Scooter, or to use McCool's drug to cut down the tripples' growth rates. You'll also participate in the Integration Olympiads and The World Series.
This sounds like a lot of fun, but what about grades?
Instead of three prelims and a final (the 3rd prelim just before the final), there will be ``one and a half'' prelims -- a ``nuts and bolts'' test of your ability to perform basic computations, and a midterm -- plus a final exam. Hence, exam scores will play a much smaller role in determining your grade.
If you would like to work in groups or you prefer classes having less pressure of prelims, you should consider enrolling in one of these special sections.
Studies have documented that in projects-based calculus courses, students gain a deeper understanding of the material from their hands-on, personal involvement with the material, and often receive higher grades, on average, for these reasons. Similarly documented were positive correlations between having taken projects-based calculus and success in future engineering courses.
Professors who have taught projects-based calculus have also commented that on a student's record, a student having taken an ordinary calculus course is not nearly as striking as one who had participated, while still a calculus student, in a group which produced an Analysis and Report for a client (e.g. report for the Town Council on the Happy Valley Pond's contamination in Save the Perch).
Rather than lecturing from the textbook and then responding to your
questions, your instructor will combine some lecturing with being your
``coach'' as you tackle, either individually or in teams, problems
which let you explore the material in an applied setting.
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