What Does the Future Look Like? College Mathematics that Works!

We live in a transition time, for college mathematics.  Developmental Mathematics is shifting away from the traditional curriculum, with an over-use of “prerequisite remediation” in the short term.  At the same time, both of the primary professional organizations for our work (MAA and AMATYC) have been calling for basic shifts in both what we teach and how we teach within the ‘standard’ college level mathematics courses.  What does our eventual ‘target’ look like?  Can we anticipate where we will end up?

In a basic way, the answer to the last question is ‘yes’, due to the fact that all of the forces shaping the future are known at the present time.  We don’t know precisely which forces will have a larger influence, and that is fundamental since the forces are not operating in the same direction.  Imagine yourself in an n-dimensional force field where you can see the vectors around you.  Although the wind varies over time, some types of vectors dominate your environment.

These vectors around us originate from power sources.  Professional standards (MAA, AMATYC, etc) send out vectors in the direction of higher levels of reasoning, modern content, more diverse content, and more sophisticated instructional methodologies.  The K-12 educational system, the Common Core in particular, send out vectors in very similar directions.  Policy influencers, higher education provosts and chancellors, and state legislators send out vectors representing forces in different directions from those in the prior lists.

In the short term, this latter set of forces will dominate … because some of the individuals involved have sufficient decision making power that they can impose a set of practices on portions of our work.  However, these practices will not survive long term except to the extent that they support the prevailing set of forces around us.  As the people in authority change faces, the practices will tend to revert … either to the pre-existing conditions (bad) or to a condition making progress in the direction of the prevailing forces.

Here is a description, a picture, of where we will be in 10 to 15 years.

  • Remediation will be smaller than in the past, but still normally discrete (not combined with college courses as in co-requisite models).  Arithmetic will be ‘taught’ but never as a separate course and never will be a barrier to a college education.  Content will focus on the primary domains of basic mathematical reasoning — algebra, geometry, trigonometry, statistics, and modeling.  No more than two remedial courses will ever be required of students, regardless of their ‘starting condition’.
  • “College Algebra” will not be used as a course title.  Similar courses for non-STEM majors will have titles such as “Functions and Modeling in a Modern World.  The content of this course, never used as a prerequisite to standard calculus, will be from the same domains as remedial mathematics — algebra, geometry, trigonometry, statistics, and modeling.
  • “Pre-calculus” courses will be replaced by a one-semester “Intro to Math Analysis” course which focuses on the primary issue for success in calculus: reasoning with flexibility supported by procedural understanding.  This course will have a very strategic focus in terms of objects and skills involved, with a shorter topic list than prior courses … taught in a way which results in a true readiness for calculus.
  • “Calculus” courses will be re-structured to focus on a combination of symbolic and numeric work.  The first semester of the two-semester sequence will include derivatives and integration for basic forms, as well as an introduction to scientific modeling using matrices such as those encountered in the client disciplines; this eliminates the need for our client disciplines to teach basic quantitative methods, and provides modern content to serve those disciplines.  The second (and final) semester calculus course focuses on multi-variable processes combined with a more complete approach to scientific modeling — appropriate for students who may eventually conduct their own research in a client discipline
  • “Liberal Arts Math” and “Quantitative Reasoning”  will have merged in to a new QR course at most institutions.  At some institutions, these courses are replaced by the “Functions and Modeling” course (which is fundamentally a QR course).  Where QR exists as a separate course, the ‘practical’ content will be de-emphasized relative to today’s courses, with an increase in symbolic mathematics. The primary distinction between QR and Functions and Modeling is that QR does not include as much trigonometry.
  • “Intro Statistics” will exist with similar content to the best of today’s courses.  The primary change will be a relative decrease in the number of students taking a Stat course to meet a degree requirement, as program planners realize that their mathematical needs are more diverse than statistics … and that requiring statistics should not be based on just a desire to avoid college algebra (which does not exist in this ‘now’).
  • Students will become inspired to consider a major in mathematical sciences by the diverse quality content along with the effective methods used within the courses.  Instead of a focus on weeding out students not ‘worthy’ of majoring in mathematics, we will focus on including all students on the mathematical road to maximize the distance covered.

I see an exiting future, once we get past the relatively short-term impacts of changes imposed from outside.  In the long-term, nothing can stop us from achieving a desired goal … except for our own doubts and lack of clarity.

My hope is that you see something in this image of the future to get excited about, something that plays the role of a beautiful sunrise in the forest.  If you can SEE where you want to go, you can get there … and it is a lot easier to survive temporary struggles along the way.

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