Modules in Developemtnal Mathematics — pro and con
I am hearing about colleges either adopting or considering modules in their developmental mathematics program. Sometimes, this is done as part of an ’emporium model’; however, other designs make use of modules. Perhaps it would help to have a brief exploration of the pros and cons of modules.
The word ‘modules’ does not have a uniform meaning for us. In general, a ‘module’ could be another name for a ‘chapter’ — each being a sub-unit within a larger organization of material. However, most uses of the word ‘module’ refer to one of two approaches to content — uniform sequence of modules or customized sequence.
| Uniform Sequence of Modules | Customized Sequence of Modules | |
| What a student does | Every student works through modules | Exit point (ending module) is determined by student program or other criteria |
| Entry point | Often ‘module 1’ for all students | Sometimes customized based on diagnostic testing |
The difference between the two uses can be subtle, such as a case where the customized exit point is the end of a ‘course’ — some modular programs designate ‘modules 5 to 8’ as a course, and that is where the exit point is. Customizing is done by either changing the ending module within a course or changing the entry point (starting module) within the course. Conceptually the contrast for the two designs is important due to the fact that a customized program prevents a summative assessment common for all students.
Over the past several years, I have had discussions with faculty involved in a type of modular program. Via this obviously non-scientific method, I have developed some pros and cons for modularization. Most of these apply to either type (uniform or customized).
|
MODULARIZATION |
Pro | Con |
| Interface to HW systems | Strong | Tends to limit the range |
| Assessment – convenience | Strong | Student work might be hidden |
| Assessment – breadth | Weak (often very procedural, less on application & reasoning) | |
| Assessment – Summative | Uniform: Weak (not normally done)Customized: Very weak | |
| Reduction in time for remediation | Uniform: Good (fewer topics)Customized: Strong | |
| Learning skills for college | Weak (learning is “doing problems”, not studying) | |
| Student motivation | Good for students who “do no like lectures or math classes” | Negative for students who want to see connections |
| Student attendance | Direct connect between attending and progress | Implies that being a student is mostly about being there |
| Faculty workload | More time for 1-to-1 help | Less individual faculty autonomy |
| Faculty motivation | Often high initially | Long-term – tends to decline |
| Content modernized | Could be done | Usually is very traditional |
A modularized approach is usually based on an assumption that the delivery mode is a major source of problems, sometimes stated “we can’t teach this to them the same way they saw it the first time”. I have not seen any evidence of this being true; it’s not that I want to teach them “the same way” (whatever that means) … it’s that this assumption about the delivery mode often precludes examination of larger issues about the curriculum. Modularized tends to reinforce notions that ‘mathematics’ is about knowing the procedures to obtain correct answers to problems (often contrived and overly complex). Our professional standards (such as the AMATYC Beyond Crossroads … see http://beyondcrossroads.amatyc.org/) begin the discussion about mathematics by describing quantitative literacy. This aspect — of modularization tending to limit the mathematics considered — is the largest factor in seeing this approach as being weak and temporary.
The other major area of concern, suggested somewhat in the pros and cons, is the professional status of faculty in developmental mathematics. Administrators and policy makers often do not understand the professional demands of being developmental mathematics faculty; in the modularized approaches, faculty tend to look a lot like tutors. This similarity then suggests to some that faculty are not necessary, and we can provide a larger pool of tutors. Our professional standards call for us to see the work in math classrooms as being rigorous in both mathematics and education. This aspect — the professionalism of faculty — is the most common concern reported by faculty engaged in a modularized program.
Summary:
The attractiveness of modular approaches is easy to understand. However, the typical implementation of modular approaches will reinforce a traditional content with a weaker assessment system combined with a generally lower faculty professionalism. When implemented, modular programs will tend to be temporary solutions. The emerging models — New Life, Carnegie Pathways, Dana Center Mathways — provide a clear alternative to address the problems based on professional standards to create long-term solutions.
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Learning math, Professional Development | Jack Rotman | 
June 28, 2012 11:50 am
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Jack Rotman
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