Is Calculus Instruction Changing (or Curriculum)?

In our applications for living course, we are finishing our work with statistics.  One situation involves students deciding which situation is likely to involve statistical significance:.

Rolling a die 40 times and getting 5 threes             OR

Rolling a die 400 times and getting 25 threes

This is a tricky thing, as students often focus on the sample size only.  Although this problem presents situations where the larger number is connected with significance, there is no general pattern that says ‘larger sample sizes means significance.’

Within our curriculum, developmental mathematics has dominated the news and much of our work for a long time.  There definitely is a larger sample size; is there a difference in statistical significance between developmental math and calculus courses?  In a basic way, yes, there is — developmental math serves a large group of students with multiple academic problems, while calculus serves a group of students with general academic success.  A 60% pass rate in calculus is not good, and is statistically significant given that most students in the calculus courses are expecting a high grade (while developmental math students often expect low grades).

You can try this as I did — search for ‘reform in calculus college’ or similar terms.  Most of the results of this search will be historical artifacts from the 1980’s and early 1990’s.  What’s with that??

I think we have fallen into the large number fallacy — a larger sample size indicates significance (dev math), instead of analyzing each situation separately.  We should be able to expect an 80% pass rate in calculus 1, given the academic skills of students who typically enroll in that course.  My own college gets about 60% pass, and this seems pretty normal.

For programs which require a 4-semester sequence (Calc I – II – III plus diff eq), a 60% pass rate means that a maximum of 13% will ever complete the sequence.  The likely values are far less — some portion of students are lost between courses even after passing.  I suspect that observed values will be between 5 and 10% — which, coincidentally, is the same range as a developmental math sequence.  [These low values are the result of ‘exponential attrition.]

Recently, I did learn of some work of our friends in the MAA on calculus.  It’s not on reform; rather, their focus is to analyze data to identify what we are doing and what is more successful — the Characteristics of Successful Programs in College Calculus (CSPCC) project.  The web page for their work is http://www.maa.org/programs/faculty-and-departments/curriculum-development-resources/characteristics-of-successful-programs-in-college-calculus

David Bressoud is a lead ‘PI’ on this work; he’s written a few articles about their work for the MAA Newsletter, so you may have seen those if you belong to the MAA.  The web site (above) has links to those articles, as well as papers written about their work.

One of the co-PI for the work is Vilma Mesa, who has done quite a bit of work on community college mathematics.  Dr. Mesa did a session at our recent MichMATYC conference on some of the data from community colleges for the CSPCC work, including the contrast between homework and exams in terms of assessment level … and an analysis of prompt types and expected response types (verbal, symbolic, graphic, or multiple).

I encourage you to read the material on the CSPCC web site.

The larger question is this:  Are we doing anything of substance to make basic improvements in calculus?  Or, is our ‘best shot’ using Mathematica and/or MatLab with our students?  I hope that is not the case.

If you are doing some reform in calculus, I hope that you will share your work — the good and not so good.  “Developmental Math” should not be having all the fun!!

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