Mythical Course Holds Key for Reforming Mathematics

The concern is not that “those who ignore history are bound to repeat it”.  No, the concern is that those who ignore history create conditions that hurt students.  In the case of mathematics, the mythical course called intermediate algebra holds the key for reforming mathematics … and policy makers often fall in to self-defeating behavior because they ignore history.

Here is the core question:

Is it possible for a course to be ‘college level mathematics’ if it does not have an intermediate algebra prerequisite?

In an opinion (Sacramento Bee), Katie Hern writes of the challenges facing the dozens of California community colleges who have implemented an alternative statistics pathway (http://www.sacbee.com/2012/11/10/4974786/new-approach-to-remedial-math.html).  These colleges are either in the Statway network, or they are doing a stat path as part of the California Acceleration Project (http://cap.3csn.org/).  Policy makers in the state, along with math faculty unaware of history, may block this work.

Many problems exist within the current mathematics curriculum, and intermediate algebra is a core contributor to these problems.  With just a bit of cynicism, here are statements that define intermediate algebra in the 21st century landscape in this country:

1. Intermediate algebra is the course that protects faculty teaching ‘college math’ courses from students who might need extra help.
2. Intermediate algebra is a distorted version of a high school algebra II course from 1965.
3. Intermediate algebra is the perfect course to show students that mathematics can be totally without redeeming value.
4. Intermediate algebra is the last math course to employ technology in intelligent ways.
5. Intermediate algebra is the final course that you can assign to a high school math teacher with the directions “just do what you do in the day … the students are not likely to succeed anyway”.
6. Intermediate algebra is the course used to kill any dreams of being in a STEM field.

I do not know of any high school which offers a math course as mind-numbing as our intermediate algebra courses.  We have this belief that our intermediate algebra course is roughly equivalent to a second year algebra course in high school; even before Common Core … even before the NCTM standards … this was not true.  Back when community colleges were being born and growing rapidly in developmental math work (roughly 1965 to 1975), the curricular materials for our intermediate algebra courses were based on the general framework of an algebra II course that existed for a short time.  The high school curriculum changed — and we did not.

We might believe that our intermediate algebra course is still a good thing; after all, matching (or not matching) a high school course does not have anything to do with the merits of a course in college.  What good does an intermediate algebra course do our students?  Most readers will think something like “get students ready for college algebra or pre-calculus”; this would mean that the learning in intermediate algebra prepares students for the learning in those courses.  We confuse ‘covering the right topics’ with ‘preparing students’; college algebra and pre-calculus are more than finite sets of procedures to symbolically derive answers.  A college mathematics course is all about understanding mathematics as a science so that students both see the intellectual beauty and can apply their mathematics.  Does factoring the sum of cubes, or rationalizing a denominator, have anything to do with preparing students for that?

As a profession, we need to recognize the false nature of our beliefs about intermediate algebra.  Until we do, our students will continue to face artificially long sequences of math courses without any basic value.  If we can embrace a shared vision of college mathematics … ‘understanding mathematics as a science, can see the intellectual beauty and can apply it’ … we will open the doors to a better future.  Imagine a math curriculum where we emphasize good mathematics, the joy of learning mathematics, and developing reasoning abilities; perhaps we can build a curriculum which inspires students to consider STEM fields.

The mythical course (intermediate algebra) has been used as an artificial and false measure of ‘college mathematics’.  Our shared professional judgment, involving compromise as all shared work does, forms a reliable means to measure ‘college mathematics’.

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2 Comments

• 

  By schremmer, November 26, 2012 @ 9:18 pm

  I agree with Rotman. In fact, every semester, I get one or two students in my section of developmental algebra (out of 20 starting the course) to skip intermediate algebra and take Precalculus 1 in my section where I use Lagrange’s approach to the investigation of functions.

  The point of using it is that, conceptually, it makes sense to the students and, given the payoff, the students spontaneously learn what algebra they need—which is not all that much, the biggest lack being that they do not know how to divide polynomials.

  Regards
  –schremmer

• 

  By schremmer, November 26, 2012 @ 9:22 pm

  I should also say that those few students who skip intermediate algebra almost invariably get one of the 4 or 5 A in Precalculus 1 and all then continue to Precalculus 2 and Calculus 1. Most of them, though, had not even considered the possibility back in developmental algebra.

  Regards
  –schremmer

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