Acceleration in Developmental Mathematics

Whether it is the recent Achieving the Dream conference, reports from Complete College America, or even education blogs, “acceleration” is a hot topic; acceleration is deemed ‘a good thing’.  Is it?

In physical contexts, acceleration is the second derivative of a position function … the rate of change of the rate of change.  To model acceleration, a valid position function has to be established (along with technical requirements such as continuity).  We can estimate acceleration outside of these limitations by use of numeric methods; however, numeric methods can not yield results appropriate for comparisons of different conditions in a scientific manner.

In education, what is ‘acceleration’?  The applied definition is something like “progression to college mathematics done significantly faster” (usually compared to a tedious sequence of traditional developmental mathematics).  Assessment of acceleration models in education is most often done by anecdote — we now get n% of students through their college course in two semesters, and previously we only got t% through.  This corresponds to the numeric methods for physical situations; are the results valid?

Before we can interpret results from acceleration efforts, we need to have a valid model for position.  We do not currently.  The traditional mathematics curriculum in the first two years is primarily a historical artifact continued though social inertia.  We (mathematicians) have not established what mathematics is required and how this mathematics should be ‘packaged’ into steps; without these steps (courses), we lack valid measurements of progress — which is the heart of the acceleration work.

The AMATYC New Life model (Developmental Mathematics Committee) and the Dana Center (University of Texas – Austin) “New Mathways” provide a consistent message about a package (sequence) that offers a scheme to measure valid progress.  Here is a segment of the New Life vision of the curriculum:

With all of the attention on developmental mathematics, there is a tendency to neglect the critical courses which follow:  pre-calculus needs to be a proven preparation for calculus, college algebra needs to be a proven preparation for other STEM courses, and general education mathematics needs to be proven preparation for other quantitative needs.

Until we tackle this large problem area, acceleration may (or may not) be a waste of effort — getting students to the on-ramp faster does not help if the highway is going in the wrong direction (or if the highway is full of unneeded hazards).  Acceleration efforts make the statement that the college mathematics is both a reliable and a valid position (goal); this statement is questionable.    In this way, I see acceleration as sharing a risk with modularization — they both will tend to entrench existing curricular structures at a time when we need to re-build the structure.

Acceleration is done through a variety of methods, and someday we can determine which method is valid for our position function (curriculum).  Until we get closer to that goal, I would not invest significant resources in acceleration.

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1 Comment

• 

  By Sue J, March 21, 2013 @ 4:32 pm

  I’d be inclined (in that positive-function way) to agree.

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