School Mathematics can NOT be Aligned with College Mathematics

How do we help students become ready for college mathematics?  How do avoid students earning credit for learning that should have occurred before college?  Perhaps our conceptualization of these problems is flawed in fundamental ways.

As I write one of my final posts for this blog, I am pondering history and future … and the intersection called the present.  Some of this pondering has been pleasant reflection, while much of the pondering has been either professional regret or stimulating conjecture.  I hope to put some of each ‘pile’ in this post.

[Here, “common core” is a place-holder for school mathematics.]

As usual, a problem and its solutions are based on definitions.

• School mathematics is defined operationally by the curricular materials and accepted pedagogical practices.
• School mathematics is usually characterized by a closed system focused on experiencing a constrained subset of mathematics at constrained levels of learning.
• College mathematics is ill-defined with conflicting goals of historical course content and service to the discipline.
• College mathematics is characterized by a closed system serving history competing with components seeking to build mastery of modern mathematics.

The fact that one system is reasonably well-defined while the other is ill-defined suggests that any goal of alignment is unreasonable.  In other words, the reasonable-sounding effort to create a smooth transition from one level to the next is foolish.

Just as groups sought to deliberately disrupt the work of developmental education, groups using ‘alignment’ are also seeking to disrupt the world of college mathematics.  In their view, college mathematics should be more like school mathematics where the system is well-defined operationally by a limited collection of curricular objects (‘courses’).  The presumption is that the core of the college mathematics system is valid and that we can apply the school mathematics process to standardize the alignment.

All of this ignores two related and critical flaws:

1. School mathematics was (nominally) designed to prepare students for college mathematics.
2. College mathematics (as known today) is a collection of obsolete tools along with a bit of valuable mathematics.

At a CBMS meeting a few years ago, I raised the question “When are we going to question the college mathematics courses consisting of excursions into issues that we don’t care about?”  Some in attendance thanked me for saying that we should change the applications in our courses; sadly, that is not at all what I was saying.  I was suggesting that much of college mathematics presented mathematics that we no longer care about as mathematicians.

Advocating for alignment does not mean such alignment is possible; it’s not.  Advocating for alignment does not mean that people support our curricular goals; they have their own agenda (not ours).

Before we worry overmuch about ‘alignment’, we had better make basic corrections to our own system.  College mathematics could be an exciting world for our students to explore with colorful vistas combining symbolic and computational methods supported by conceptual knowledge.  Do not look to MAA and AMATYC to ‘tell us’ how and when … our organizations are too fearful of offending part of ‘us’.

Build local alliances to support experimentation in modernizing mathematics in college.  Do not let ‘alignment’ lock you in to an obsolete and harmful set of mathematics courses.

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