Modules or Clumps in Developmental Math?

A lot of people are talking about modules in developmental mathematics as part of an effort to ‘fix’ our programs.  Of course, the word ‘modules’ has implications that sometimes are not meant … so I was inspired when I saw somebody refer to them as ‘clumps or modules’. 

The word ‘module’ carries connotations, and also has a denotation.   You might be surprised to learn that ‘module’ does not have a denotation (definition) relative to the practice of clustering learning outcomes into small pieces (‘clumps’), nor with process of assigning a subset of ‘clumps’ to a given student.  Most dictionaries will not give an educational meaning to ‘module’.  What we are doing here is describing by metaphor — “this is like modules in electronics where sub-systems are replaced as a unit”. 

Which leads in to the connotations.  When we think about ‘modules’, we usually have positive images — easy, efficient, better.  “Modules” has a scientific sound, as if describing by metaphor automatically assigns a scientific basis.  I suspect many people think that ‘modules’ means that we are meeting students’ needs, and that the program is individualized.  Some people believe that ‘modules’ mean that students spend more time actively doing ‘mathematics’.

Using modules does not mean anything more than using ‘clumps’ would mean.  Of course, a particular implementation of clumps (or modules) might mean a great deal of good stuff.  Too often, using ‘modules’ means that we focus on the delivery system to the exclusion of critical analysis of the content (beyond creating clumps).

In practice, there usually is one difference between using ‘clumps’ and using ‘modules’.  With ‘modules’, there is not (normally) any summative assessment at the end of a ‘course’.  This means that there is no need, from the student’s point of view, to integrate knowledge and understand how parts fit together.  “Connections”, in a modular math environment, is limited to those that can be developed within a single module.  “Clumps” might share this property, but ‘modules’ almost always do.

As mathematicians, we have shared values — reasoning, application, relationships, representations, and even creativity.  Whether you call them ‘modules’ or ‘clumps’, do our values come through?  This really is important; imagine a freshman writing class where students learned about components of writing in isolation, and never had the opportunity to develop a position or argument.  Like writing, the purpose of mathematics is centered on communication.  Let’s build courses where our values are accessible to students.

 
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