Are Modules the Answer for Developmental Mathematics?

The number of institutions implementing modules in developmental mathematics continues to increase, which I expect to continue for another year or two.  Over the next 5 years, I expect most of these institutions to shift to other models and solutions for their developmental mathematics programs.  Perhaps you can think of some reasons why colleges would try modules now and then replace modules.

Our context for this problem is complex, with multiple expectations for developmental mathematics and multiple measures of current problems.  Modules are appealing because of the clear connection between a modular design and some measures of current problems — low pass rates and low completion rates in particular.  For a change to survive in a longer term, the methodology needs to address enough of the basic problems to be sustainable.

When we started the New Life project in the Developmental Mathematics Committee of AMATYC, we asked a set of national leaders in the field to identify the basic problems they saw.  In analyzing that input (done via email, primarily), the problems could be clustered in a few basic categories:

The content of developmental mathematics courses is not appropriate for the majority of students.

The typical sequence of courses has too many steps for students to complete in a reasonable amount of time.

The learning methods emphasized in most programs were not effective, and do not reflect the accumulated wisdom about learning and cognition.

Faculty, especially in developmental mathematics, were professionally inactive and they tended to be isolated.

Faculty were not using professional development opportunities, both due to lack of information and due to lack of institutional support.

Modules are often selected based on rationale of content and sequence.  However, when we look deeper at the content problem, the issue is a very basic one: the typical developmental mathematics sequence emphasizes symbolic procedures presented in isolation from both applications and other mathematics.  In other words, completing a developmental math course typically does not result in a significant increase in the mathematical capabilities of students … the learning was of the type that is quickly forgotten.

One reason, then, that modules will tend to be a short-term process is that the design does not generally address basic content problems.   A modular program makes it easier for students to complete; a consequence of this is that the content is deliberately compartmentalized and isolated.  Module 4 is independent of Module 3; the learning is not connected, nor is there (normally) a cumulative assessment at the end of a sequence (like a final exam). 

I am hoping that you are thinking … “Wait a minute, modules can do more — the learning can be connected, and we can have a cumulative assessment”.  Great, good job thinking critically.  However, every single modular implementation I am reading about focuses on the independence of the modules, and none have a ‘final exam’.  Some colleges will eventually try to address this problem.  The challenge is that doing so is fairly difficult, and will tend to increase cost.  [You might have noticed that cost was not a general problem as identified by leaders in the profession.]

The learning methods are also a problem in the typical modular design.  Modules have a high probability of using online homework systems; these systems tend to be limited to symbolic procedures.  More fundamentally, though, I see modular programs as missing the learning power of groups and language.  Modular programs tend to be individual-based; social settings, such as small group work, are either difficult to manage or just plain impossible.  Language (meaning speaking and writing) are often quite limited; as in traditional developmental programs, modules tend to emphasize the correctness of answers as a measure of learning … as opposed to quality of work, written explanations, or spoken explanations.  Therefore, I generally expect that modular programs will result in levels of learning that are statistically equal to the programs they replace; this (if true) is enough of reason for colleges to leave the module design in a few years.

Some modular designs have addressed some of the problems related to faculty … at the point of implementation, and in limited areas.  Not enough for long-term viability.  We, the faculty in developmental mathematics, have much to do.  The overwhelming majority of us are not engaged in any professional activity (beyond a few hours of work per year at our own campus); we generally do not attend conferences, we don’t join AMATYC and state affiliates; we don’t read professional journals, let alone publish in them.  We need to develop a deeper understanding of our profession; in particular, we need to be proficient in analyzing learning mathematics as a matter of mathematics and of cognition.  We need both deeper toolsets and the knowledge about best uses for those tools.  None of the modular designs I read about have a long-term strategy for supporting faculty.

The designs I often call “the emerging models” all deal with multiple problem areas, resulting in long-term viability.  The emerging models (AMATYC New Life, Carnegie Pathways, Dana Center Mathways) address content, sequence, learning, and faculty issues.  Over the next few years, you will begin hearing of institutions who had implemented modules switching to one of these emerging models.  We all are committed to helping our students, and these models provide a better solution.

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