Modules in Developmental Mathematics

Are modules a good thing in developmental mathematics?  They are certainly popular these days, with quite a few colleges … and some entire state systems … putting their entire developmental math program in modules.

The word ‘modules’ overlaps in meaning with some more generic labels such as ‘chapters’ or ‘units’.  However, the word module implies a planned independence — you install only the modules needed, or only repair the one that is ‘broken’.  In the case of developmental mathematics, one of the benefits attributed to modules is that students only have to study what they ‘need’ (based on some assessment).

The design implies that there are discrete skills necessary, that developmental mathematics is all about students demonstrating accurate procedures in the modules prescribed for them, and that we should not expect any other ‘value added’ for our students.  Briefly, here are arguments against each of these implications.

A number of studies have looked at the actual mathematics used in various occupations.  This list often includes arithmetic skills (especially with percents), some formula work, and a few other items.  Rather than discrete skills, the occupational need is for the problem solving and ‘STEM-like skill set’ (see http://www.insidehighered.com/news/2011/10/20/study-analyzes-science-work-force-through-different-lens for example).  Our 2010 developmental mathematics courses emphasize discrete skills because of history, not because that is what students need.  By constructing a series of independent modules, we are creating a wider gap between our curriculum and the needs of our students. 

Much of the technology behind the current module ‘frenzy’ is heavily procedural, with the main thing being correct answers.  There are two significant shortcomings of this approach.  First, getting a correct answer has only an indirect connection to knowing something; we have all seen students get a ‘correct’ answer with either multiple errors or no comprehension of what they are doing.  Second, procedural details are notorious for being forgotten — the old ‘use it or lose it’ syndrome; if we focus on procedures, we are essentially saying that developmental mathematics has no lasting benefit for the students.  If this is true, we would be more professional to take the student’s money and give them their grade without them going through the game of producing the correct answers for us.

The last implication, that we should not expect any other value-added for our students, goes beyond the prior concern.  Are students in developmental mathematics classes so limited intellectually that we should give up on their capacity to learn mathematics in the academic sense?  By setting the standard so low, we are not only limiting our students — we are actively reinforcing every bad attitude about mathematics.  Many of these attitudes are based on perceptions of mathematics as dealing only with specific procedures and correct answers, coupled with a belief that normal people are not capable of understanding mathematics. 

You may be wondering if I somehow believe that the existing developmental mathematics curriculum is better than what I describe; in general, it is not much better.  There might be a better problem solving component, and a little bit of conceptual understanding.  However, we have inherited a curriculum that has been fixated on algebraic procedures (and a particular collection of procedures). 

No, it is not that modules are breaking something good.  Rather, modules are giving the illusion that we are fixing something because we can point to a change.  Change is not progress, not unless the change results in achieving what the community of professionals sees as something of basic and intrinsic value.  When I have conversations with mathematicians, I do not hear people describe the outcomes of modules as being of value … we value concepts and connections, thinking and problem solving.

Modules are an easy ‘solution’ to the wrong problem, and I suggest to you that modules create additional problems.  Let us not get distracted by the technological appeal of modules; instead, let us look critically at the mathematics we deliver … and how we can actually help our students.

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