Why We Have a Major Problem Now: Forty Five Years of Dev Math, Part V

This is the 5th post in a series on “forty five years’ of developmental mathematics, roughly coinciding with my professional experience. The prior 4 posts took us from the early 1970’s to the late 1980’s, with the last post talking about ‘normalizing a bad curriculum’. It’s time to move on to the early 1990s.

When the NCTM released it’s standards in 1989, people teaching developmental mathematics could immediately see the implications for our work. The conceptualization of the dev math curriculum was a one-to-one mapping to 9th to 11th grade mathematics (in ‘the old days’). The NCTM calls for increased attention and decreased attention had a lot of appeal.

During this same time period, the graphing calculator became a reasonable tool for mathematics classrooms; both TI and Casio had good machines, with some design elements driven by what math teachers wanted. [The HP calculators of the time were designed for engineer use, so they seldom had much traction in schools.] These graphing calculators provided a tool that would help teachers implement the NCTM standards.

In the Spring of 1992, Ed Laughbaum had an opinion piece published in the AMATYC journal (called “The AMATYC Review” at that time), with the title A Time for Change in Remedial Mathematics. One of Ed’s main points was:

To change the current pattern of instruction, I propose that teaching methods be changed to support implementation of the graphing calculator into the remedial sequence.

Ed’s article is primarily an agreement with Lynn Arthur Steen that most mathematics remediation is a failure. You might notice that this is the same message being sent in the last 5 years by change agents such as Complete College America. Twenty-five years ago, we were saying it. What happened?

One thing that happened was that I wrote a response, which appeared in the AMATYC Review a year later, with the title “Time, Indeed, for a Change in Developmental Mathematics“. http://files.eric.ed.gov/fulltext/ED373817.pdf This was written just as I was about to become chair of the AMATYC Dev Math Committee (the first time, 1993 to 1997). My response was a little too soft in terms of critiquing our work at the time; I regret that now.

This response was the first time I used the phrase “mathematical literacy”, written in the general sense (not course specific). Sadly, one of the things I said was that graphing calculators should not be used in courses at the beginning algebra level. My position on this changed over the subsequent five years, but my comments resulted in a number of AMATYC members thanking me … they felt supported in doing their traditional courses (which was not my intent).

My conclusion in that article had this:

The basic issue facing mathematics educators today is how to integrate the various forces attempting to drive our mathematics curriculum. The solution involves dialogue and consensus building. Institutions such as AMATYC provide a needed forum and structure for this work. As we work together, our theories and standards will converge, resulting in changes in our curriculum which will certainly integrate technology in many ways.

It’s clear that this change process did not occur … in spite of the NCTM standards resonating with our own interests as shown in the first AMATYC Standards (“Crossroads”). What happened?

Our collective resistance to the graphing calculator is the primary reason that we did not make any progress when there was another opportunity. Partially, this was due to the overwhelming resistance to calculators at the college math level (college algebra, pre-calculus) … and much of this still exists today. The fact that students could not use numeric methods in the next course meant that our use of those methods in developmental mathematics was a possible risk to our students.

In some ways, the content of our courses became ‘locked in’ by 1990. We resisted professional calls for numeric methods, we collectively ignored the NCTM standards; we even ignored most of our own AMATYC standards (which were being written during the early 1990s). From 1995 to 2010, fewer natural opportunities for change would arise. Our default support for an antiquated curriculum is exactly why dev math was an easy target for policy makers and change agents in 2012 … 20 years after the early 1990s.

We are facing a similar call for change today. The Common Vision suggests that our courses emphasize numeric methods alongside symbolic ones, as well as suggesting that our teaching methods change. This is the danger of ‘pathways’ … that only non-STEM students get a modern course with numeric & symbolic methods; STEM students are required to survive a series of courses overly focused on symbolic methods with little emphasis on reasoning, and far too little emphasis on connections between concepts. “Right Answer” still is the goal in these courses, which is the wrong answer for students.

I am hopeful that we individually and collectively will respond today with “let us build better courses for ALL students”. No student should be required to take a course known to be defective. In particular, I am hoping that AMATYC will develop a project that links the Math Intensive committee with the New Life Project to work on revitalizing the courses which follow developmental mathematics.

If our profession fails to seize the current opportunity for creating our own modern curriculum, external change agents will control the primary playing field: the initial college level math course(s) such as college algebra, pre-calculus, and similar courses. These courses suffer the same defects as the traditional developmental mathematics curriculum — antiquated topics delivered inefficiently and with harm to the overwhelming majority of college students who will never take a calculus course. [Our calculus courses are just as antiquated and inefficient; external change agents just don’t care about calculus very much. They should!]

We have a problem NOW (2017) because we did not have sufficient motivation to make systemic changes 25 years ago. The profession let a few visionaries create boutique programs which were locally successful but totally isolated from the mainstream of our work. Today’s boutique program is “Pathways”. We need systemic change to create modern mathematics courses for ALL students. Do we really think that non-STEM students deserve a modern course while STEM students slog thru disfunctional artifacts clustered as pre-calculus & calculus courses?

It really is “Time for a Change” … not just in remedial mathematics, but in all college mathematics.

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history of developmental mathematics | Jack Rotman | April 17, 2017 1:47 pm

2 Comments

By Len, August 20, 2017 @ 2:14 pm

If history is any guide the easiest way to change mathematics education is to get it out of the hands of mathematicians. There appears to be no appreciation of the scientific method. If you observe that 50 years of doing the same thing doesn’t work, you should be bright enough to look for changes that do work.
By Jack Rotman, August 21, 2017 @ 7:55 am

Len: Thanks for the comment.
“History” is an interesting word. Many would advocate for getting ‘mathematics educators’ out of the curriculum; in other words, folks whose PhD is in math ed … who frequently have a decent mathematics background but who learn too little about cognitive science. Math Ed folks come to our conferences to suggest we employ the philosophy or method they prefer (constructivism, flipped, whatever). Very little science involved.
Mathematicians, on the other hand, have a great mathematics background and little pretension that they understand how students learn. Some get locked in to a point of view, but most will respond to information on (1) improving curriculum and (2) improving instruction.
I would rather have mathematicians involved, and not math ed professors.

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