The Doom of Developmental Mathematics

At the recent AMATYC conference, I gave my final presentation at a national conference.  That session seemed helpful to those attending, and I plan to create a video to post here for others who may wish to experience that presentation.  However, it is critical that we understand why traditional developmental mathematics is doomed.

This doom has two primary sources, one objective and one subjective.  The objective doom is our historical ties to grade levels in K-12 mathematics of a prior era; the subjective doom is the perception that we have created an exponential decay function experienced by our students which prevents them from completing their degree.  These ‘dooms’ of developmental mathematics can not be removed by debate nor by data.  That does not mean our work will end; we can create a model which avoids these dooms … and (more importantly) works for our students.

First, the objective doom:  historical ties to grade levels in K-12 mathematics.  The traditional developmental mathematics courses were created as clones of high school courses — 8th grade math copied as pre-algebra or basic math, 9th grade Algebra I copied as our ‘beginning algebra’, 11th grade Algebra II copied as our ‘intermediate algebra’ with some copying 6th-7th grade math as ‘arithmetic.  All this copying was based on facts from the 1960’s: not all students completed Algebra II in high school, and we needed to get them ready for college algebra.

The result is a sequence of courses prior to college mathematics which exhibits the exponential decay function property … no matter how high the pass rate in a given course, the net result of the sequence is that only a small minority can finish.   Even ignoring that, we have a curriculum which is inconsistent with current course taking patterns in high school; we are not serving current needs — the ‘need’ is an image from 50 years ago.  This doom, this conflict with reality, is as obvious as it is deterministic.

Second, the subjective doom: developmental mathematics prevents students from completing their degrees.  Why is this ‘subjective’ when we have seen data supporting it?  Perhaps it would be more accurate to say that this is a hypotheses which has not yet been statistically supported by data.  The data used to support this viewpoint uses observed correlations to support a conclusion — a large portion of non-degree-completers did not complete their developmental math courses, therefore the developmental math courses caused the non-completions.

Nobody has (yet) shown that removing the ‘dev math barrier’ results in a significant increase in degree completion.  Yes, there have been reports that removing dev math results in more students completing a  college math course.  By itself, that is a small improvement.  We don’t know if more students are completing degrees … or if we are just changing which courses students complete on their way to non-degree status.

The fact that this is an unproven hypotheses does not matter for our purposes.  For our purposes, the doom is present regardless of evidence:  our presidents and provosts and chancellors generally accept this conjecture as ‘the truth’.  We would need years of effort to counter this subjective truth; we lack the time.  Once accepted, this conjecture causes a failure in the patience circuits.  We have passed the tipping point, and few of our collegiate leaders support traditional developmental mathematics.

How do we avoid the dooms?

  1. Replace traditional developmental math courses with new courses which do not clone K-12 mathematics
  2. Avoid the word “algebra” in all course titles (ALL … including college level)
  3. Avoid the words “developmental” and “remedial” when describing our work; perhaps use the label “pre-college mathematics”
  4. Allow no more than two pre-college courses at any institution
  5. Establish placement processes which allow at least 90% of all students to reach their college math course with one year

It is my view that traditional developmental math courses will NOT survive; within 5 to 7 years, they will be eliminated … either by our planning or by external directives.  We can not escape the doom of dev math.  However, we can greatly help our students by re-creating pre-college math courses which provide modern content in an efficient curriculum.

If we fail to create a new curriculum, stand-alone dev math courses will become extinct.  Is that what we want?  I hope not!

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2 Comments

  • By Ed Laughbaum, November 14, 2017 @ 11:07 am

    Hi Jack,

    While I do not disagree with your observations, I have two other thoughts. One is that politicians got in the way, and the other is that developmental math continues to rely on the unconnected topics-based approach. Further, adding the glitz of the Internet cannot possibly improve learning because the content is still topics based. The glitz gets the attention of the students, but not to the math – mainly just the glitz. My focus has been on teaching math using function as a connective theme. To find out why this is important, please Google “laughbaum.6” to get to my academic home page. Of course, the solution to learning algebra is not just daily connections through function representation and behaviors, but also using pattern building, visualization, … found on my academic page.

    Ed

  • By Jack Rotman, November 14, 2017 @ 12:47 pm

    Thanks, Ed. I actually mentioned your ‘time for a change’ opinion piece (1993 I believe) in my last presentation.
    I agree with your two observations, though we may disagree on how foundational those problems are (especially the politicians … their involvement is a consequence, not a root problem). The anti-connection topic approach is a bigger problem, though not a ‘doom’ on its own; after all, we do the same thing in pre-calculus (in general).

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