Curriculum and Pedogogical Reform In College Mathematics: Regression

What SHOULD we teach?  How SHOULD we teach?

Those questions underlie discussions of professional standards.  In fact, AMATYC had a new project in the early 1990s with the acronym “CPR” — Curriculum and Pedagogical Reform for the first two years (sometimes listed as “CPR-MATYC” to emphasize the AMATYC connection).  The leaders of this work were knowledgeable professionals at the forefront of college mathematics who wanted to provide a set of standards that would help lead the practice of teaching college mathematics across the country.  The leaders knew that some elements of such standards would conflict with common practice, and that curricular inertia would cause others to have a negative initial reaction.  However, the leaders also sought to create the best possible reference for the profession.  Although they could not know this, such standards also provide a roadmap to counter external threats developing a decade or so later.

The result of CPR was the original AMATYC Standards, given the title “Crossroads”.  That document does, in fact, contain a fair amount of direction on “should” in terms of content and pedagogy.

Updates to the standards, however, have avoided direct statements on should.  The 2nd standards (Beyond Crossroads) focused on a process cycle instead of updating the content and teaching standards in the original.   The latest standards (#3, “IMPACT”) goes further away from ‘should’ statements to become primarily a collection of trends and practices.

For those curious about such matters, I am thinking about this now because I am sorting through old (and really old) files as part of retirement.  Reading it again, I remember excitement of the original CPR work (I did some reviewing and position paper writing) compared to the discouragement of working on the most recent standards.  I’ve been fortunate to have had a role in all 3 AMATYC “standards”, though I find myself discouraged by the trends in the actual products.  Apparently, we collectively think it is fine to teach awful mathematics in despicable ways as long as you incorporate an occasional ‘cool’ trick in class.

Is this the best we can do?

Math Education in the Face of Climate Change

Our profession is denying climate change.  We continue to create greenhouse gasses with little regard for the planet nor for the vulnerable organisms who become collateral damage for our ignorance.  Our organizations celebrate the isolated experiment in ‘smaller carbon footprint’ while the vast majority of our companies are focused more on tradition than on science.  We are the enemy.

This metaphor is meant to convey the tragic condition of mathematics education in the year 2019.  Some of us have had major changes imposed on us relative to developmental mathematics, which generally leave all other college mathematics unscathed.  Even in some of those places, we still offer just as many traditional developmental math courses.  In almost all cases, the important processes in our industry remain as they were 40 and 50 years ago.

One of the attack lines against developmental mathematics has been “remedial math is where dreams go to die”, and it is true that our traditional developmental math courses did not serve our students well.   The response data to this criticism is trimodal — some of us replaced the traditional courses with fewer and more modern courses, some of us eliminated dev math with ‘corequisite’ strategies, and the rest of us continue business as usual.

If you really want to see dream death in mathematics, study our ‘pre-calculus’ content and courses.  Students enter into the prep for calculus with dreams of being a scientist or engineer or computer scientist; they almost always experience a brain-deadening mix of algebraic procedures and memorization which seems to have the goal of eliminating the ‘unfit’ before calculus I.

In mainstream college mathematics, we hold to tradition … all of this ‘stuff’ is needed for calculus; the rationale:  we have always taught this ‘stuff’ in pre-calculus.  We sometimes can justify the greenhouse gasses of pre-calculus by citing a contrived calculus problem which happens to require this contrived pre-calculus topic.  Our current books — including “OER” materials — for pre-calculus are still descendants of a gen-ed college algebra course never intended to be in a calculus path (see College Algebra … an Archeological Study).

Evidence of this bizarre mix of dream killing curriculum is our habit of having “college algebra for pre-calculus” as the prerequisite for pre-calculus.  College algebra has nothing to do with pre-calculus, just as pre-calculus has nothing to do with calculus (see College Algebra is Not Pre-Calculus, and Neither is Pre-calc and College Algebra is Still Not Pre-Calculus 🙁 ).

Pre-calculus is where STEM dreams go to die.

The most egregious contribution to ‘climate change’ in mathematics?  The fact that numerical methods and modeling are not integrated into the curriculum (at all levels).  All of our client disciplines are heavily dependent on a collection of matrix and modeling methods and technology.  Nobody ever needed all of the manual calculus methods we taught, but many of them were critical before computational mathematics.  With computational mathematics, fewer manual methods are needed — more conceptual rigor is required, along with content to support appropriate numerical methods.

This image comes from a page on this Envisioning Our Future, and is an attempt to envision a solution to our climate change problem.  Eliminating wasted energy and keeping dreams alive are essential criteria for judging the validity of such solutions, and I have no doubt that my ‘vision’ will not be our shared solution.  We need to work together to create viable solutions locally, share these solutions regionally, and eventually develop a national pattern of ‘good college mathematics’ courses.

Are you so attached to tradition that you are willing to contribute to this ‘climate change’ in higher education?  Or, do you want STEM dreams to live and thrive?  Perhaps you are willing to consider fundamental change to our curriculum just based on the criteria “teach good mathematics”. We might have pride in our individual teaching practices, but none of us can have pride in delivering bad or awful mathematics to tomorrow’s scientists.

Our traditional courses create dangerous levels of greenhouse gasses (bad mathematics) and contribute directly to climate change (the death of dreams).  We need to reduce our carbon footprint (more ‘good mathematics’) and actively improve the climate (student dreams).

What are you doing to ‘fight climate change’ in college mathematics?

Where is the Position Paper on Co-Reqs? Math in the First Year?

Two major movements are “sweeping” across the college landscape — co-requisites in mathematics (and English), and “college math course in the first year”.  Those who have “drunk the cool aid” see both changes as progress, while an academic response continues to be more of minor interest and waiting for real data on the impact of the changes on real students.  In this context, a lack of clear communication is equivalent to a yielding of the discussion.  In my view, AMATYC has done exactly that.

I want to make sure that you know of my long and generally positive relationship with AMATYC.  I first attended a conference of the “American Mathematical Association of Two-Year Colleges” in 1987. I had been teaching for about 14 years at that point, and was being impacted by a loss of enthusiasm for the work.  That conference was a major turning point for my professional life, as well as the start of many relationships that continued for decades.

AMATYC produces position and policy statements on a variety of topics, and these generally lag behind the need — understandable, given the processes that allow for broad input from members  This lag time is normally a few years … when ‘handheld calculators’ were first an issue, the AMATYC statement on them was developed about 3 or 4 years later.  When issues came up about credentialing, the statement on qualifications came out about 4 years later.

We are now in the 5th year of the co-requisite infusion.  (Infusion suggests an external agent seeking to modify the internal functioning of a body.).  I don’t believe anybody in AMATYC is even considering a position statement on co-requisite mathematics.  Instead, the conferences are increasingly populated by sessions sharing experiences with implementations.  In the absence of official statements, the presence of multiple sessions on a practice amounts to an implicit approval of that practice.

Do we, as professionals or members of AMATYC, support co-requisite remediation without qualification?

Like good political strategy, the news cycle is being dominated by one ‘side’.  Our silence … individually and as AMATYC … relinquish the power to those seeking to disrupt our work.  [And, yes, the groups have stated that they are working to disrupt our work.  I won’t name them, as I do not want to provide any more PR for them.  It’s time for our side of the story.]

I’ve posted before on the practice of co-requisite remediation; Why Does Co-Requisite Remediation “Work”? and TBR and the Co-Requisite Fraud as well as The Selfishness of the Corequisite Model.  Of course, we should consider new models.  Of course, our use of fundamentally new structures impacting students must be based on scientific evidence and research — not ‘data’ grown specifically to support a particular practice.

The other ‘movement’ (Math in the First Year) is based on some of the worst uses of statistics I have ever seen in academia.  Of course, I’ve posted on that: Policy based on Correlation: Institutionalizing Inequity.  The flaws in this movement are so obvious that I would expect any basic statistics student to spot them within a few minutes.

Do you see the flaw of ‘first year’ in this image?

Does AMATYC have a position statement on ‘math in the first year’?  Nope.  There is a policy on placement, but not on a practice which places students in situations where they can suffer academic harm.  “Math in the first year” basically says that if you get a random student to pass a math course early like the best students do, that all students accrue the benefits of the best students (academic grit, financial stability, etc).

I always strive to be honest, and that involves me divulging that my relationship with AMATYC has faded away.  Perhaps the current leadership is actively working with the committees to develop policy statements.  However, I do know that the latest ‘standards’ (IMPACT) have very little to guide our decisions on such basic issues; the web site for IMPACT has a link, but no content.  What does all of this silence say about us?

Will we continue to be silent?

Faculty Standards … AMATYC IMPACT

Are you looking for guidance on the core issues in college mathematics?

• Curriculum and content
• Course design and instruction
• Learning environment
• Assessment

Here is a document developed by the AMATYC IMPACT project: AMATYC IMPACT Faculty Standards 2018

This document reflects the best professional judgment of our time, using sources such as prior AMATYC standards, MAA documents, and the “Common Vision” (https://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf).  The primary author was Jack Rotman, with content extracted and updated from those other sources; outstanding editing was provided by Mark Monroe (Iowa Valley community college), Pat Hirschy (Asnuntuck Community College, retired), and Anthony Piccolino (Palm Beach State).

I hope that you find this resource helpful as you strive to make your curriculum and instruction modern while serving the needs of your students.

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