Saving Mathematics, part I

Because ‘developmental mathematics’ has been so much in the spotlight, we tend to treat the remainder of mathematics in the first two years as a stable curriculum with the presumption that it serves needs appropriately.  I suggest that the problems in ‘regular’ college mathematics are more significant than the problems in developmental mathematics.  #STEM_Path #MathProfess

We have indications that pre-calculus is not effective preparation for calculus (see David Bressoud’s note on “The Pitfalls of Precalculus” at http://launchings.blogspot.com/2014/10/the-pitfalls-of-precalculus.html).  The large data set used provides strong evidence for the fallacy of pre-calculus; the history of that course also suggests that it is ill-served for the purpose (see Jeff Suzuki’s talk “College Algebra in the Nineteenth Century” at https://sites.google.com/site/jeffsuzukiproject/presentations) .

The calculus sequence remains unchanged in any fundamental way over the past half-century, in spite of the changing needs of the client disciplines (engineering, biology in particular).  I believe that our calculus sequence is both inefficient and lacking.  In particular, our obsession with symbolic methods and the special tools that accompany them results in students who complete calculus but lack the abilities to do the work expected in their field (outside of mathematics or within).

So, just for fun, think about this unifying view of mathematics in the first two years.

Pre-college mathematics: 2 courses, at most

• Mathematical Literacy (prerequisite: basic numeracy)
• Algebraic Literacy (prerequisite: some basic algebra, or Math Literacy course)

College mathematics:  5 courses, at most

• Reformed Precalculus (one semester only)  (prerequisite: Algebraic Literacy, or intermediate algebra,, or ACT Math 19 or equivalent)
• Calculus and Modeling I (symbolic and numeric methods of derivatives, integration)
• Calculus and Modeling II (symbolic and numeric methods of multi-variable calculus)
• Linear Algebra and Modeling (symbolic and numeric methods, including high-level matrix procedures with technology)
• Intro to Differential Equations and Modeling (symbolic and numeric methods)

The current curriculum, over the same range, involves 3 to 5 pre-college courses and then from 6 to 9 college courses. The weight of this inefficiency will eventually be our undoing.

By itself, this inefficiency is not strong enough to be a strong risk to mathematics in the short term.  However, our client disciplines are not happy with our work … in many cases, they are teaching the ‘mathematics’ needed for their programs.  In general, those disciplines are focusing on modeling using numeric methods (MatLab, Mathematica, etc); symbolic methods are only used to a limited extent.

Our revised curriculum must be focused on good mathematics, central concepts, theory, and connections … implemented based on sound understanding of learning theory and diverse pedagogy.  The current pre-calculus course(s) offer a good example of what NOT to do — we focus on individual topics, procedures, limited connections, and artificially difficult problems. The capabilities needed for calculus are much more related to a sound conceptual basis along with procedural flexibility.  Take a look at the MAA Calculus Concepts Readiness material (http://www.maa.org/press/periodicals/maa-focus/maa-updates-its-test-for-calculus-readiness) .

We can continue offering the same college mathematics courses that the grandparents of our students took; OR, we can take steps to save mathematics.

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2 Comments

• 

  By Laura Bracken, December 7, 2015 @ 9:22 pm

  One on colleagues has been reading the CUPM document on the calculus sequence. He summarizes it this way: semester 1. – focus by thinking about the biologists (less integration). Semester 2– focus by thinking about the chemists (some multi-variable for pchem, no sequences and series). Semester 3 — think about the majors, the engineers, and the cscience. it isn’t that one group of students is more important — it is just a useful way to start the necessary conversations.

• 

  By Jack Rotman, December 9, 2015 @ 7:40 am

  Sounds like an interesting way to start a conversation!!

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