College Algebra … an Archeological Study

As we make real progress on improving mathematics education in colleges, shown especially in developmental mathematics, our attention is going to focus on college algebra and the “STEM Path”.  Of course, the name “college algebra” is given to a variety of courses, some of which serve a pre-calculus purpose (and some do not).  For years, I have thought of the name (college algebra) as a statement of “not being remedial”.

Could be that I was wrong about that.  During some recent searching, I came across a paper that Jeff Suzuki gave a few years ago.  Most of that talk is available at https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxqZWZmc3V6dWtpcHJvamVjdHxneDo2MWI5YWE4YzU2MDM1MmY3; if you have trouble with that link, search for “Jeff Suzuki Project” to get a list of his presentations.

Assuming that the content of that history is essentially correct, here is a brief statement of what college algebra is today:

College algebra is a collection of mathematical topics for general education, taken in place of calculus.

Some of the information in the Suzuki paper is in the form of book references to the 19th century.  This led to a book, possibly the first, to use “College Algebra” in the title — George Wentworth’s “A College Algebra” (1888); a later edition (1902) is available at https://archive.org/stream/acollegealgebra07wentgoog#page/n12/mode/2up .  In the same period, Webster Wells authored “University Algebra” (1879) and “College Algebra” (1890); see the 1879 text at http://books.google.com/books?id=uKZXAAAAYAAJ&pg=PR7&source=gbs_selected_pages&cad=2#v=onepage&q&f=false

These courses were taught as universities (Harvard, Yale, Princeton, Bowdoin, etc) reduced their mathematics requirements.  The college algebra course was not designed to prepare students for calculus.

These early college algebra books did not contain some current topics (factoring and graphing, for example).  The addition of graphing (including properties of functions) is related to calculus preparation; factoring is generally not so related.  Overall, the current college algebra course is clearly a descendent of this earlier course.

One of my current projects is to study the math courses required before calculus in my state (Michigan); Michigan does not have a system for higher education, which results in diversity in mathematics — college algebra, precalculus, and other courses are used.  However, the overall approach (in Michigan and elsewhere) is to consider these as being an equivalence or subsets; either the college algebra course(s) equate to the pre-calculus course(s) OR the college algebra course is a prerequisite to pre-calculus (that is very rare in Michigan).

Therefore, I believe that this is our current method of preparing students for calculus:

After establishing that the student does not need further remediation on high school mathematics, the student enrolls in an antiquated general education math course with a few valid preparatory topics, with the unreasonable hope that this will prepare them for calculus.

Much of our apparent curricular dependency (stuff in college algebra that is needed for calculus) seems to be an artificially created dependency — we need this radical simplification because that technique is needed for a few problems in calculus, and those problems were created in calculus to show why we needed radical simplification; we need this multi-step factoring topic in college algebra because we have created a set of problems in calculus that require creative factoring.

I encourage us all to study the “Mathematical Sciences in 2025” (available at http://www.nap.edu/catalog/15269/the-mathematical-sciences-in-2025 ).  Some parts of our curriculum are archeological artifacts from the 19th century, and some parts date from the mid-20th century.  Very little of our curriculum reflects either current needs of client disciplines; not much more of it reflects the needs of mathematical sciences.

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