Algebra in General Education, or “What good is THAT?”

One of the questions I’ve heard for decades is “Is (or should) intermediate algebra be considered developmental?” Sometimes, people ask this just to know which office or committee is appropriate for some work. However, the question is fundamental to a few current issues in community colleges.

Surprising to some, one of the current issues is general education. Most colleges require some mathematics for associate degrees, as part of their general education program. Here is a definition from AACU (Association of American Colleges and Universities):

General education, invented to help college students gain the knowledge and collaborative capacities they need to navigate a complex world, is today and should remain an essential part of a high-quality college education. [https://www.aacu.org/publications/general-education-transformed, preface]

What is a common (perhaps the most common) general education mathematics course in the country? In community colleges, it’s likely to be intermediate algebra. This is a ‘fail’ in a variety of ways.

Algebra is seldom taught as a search for knowledge — the emphasis is almost always on procedures and ‘correct answers’.
The content of intermediate algebra seldom maps onto the complex world. [When was the last time you represented a situation by a rational expression containing polynomials? Do we need cube roots of variable expressions to ‘navigate’ a complex world?]
Intermediate algebra is a re-mix of high school courses, and is not ‘college education’.
Intermediate algebra is used as preparation for pre-calculus; using it for general education places conflicting purposes which are almost impossible to reconcile.

We have entire states which have codified the intermediate algebra as general education ‘lie’. There were good reasons why this was done (sometimes decades ago … sometimes recently). Is it really our professional judgment as mathematicians that intermediate algebra is a good general education course? I doubt that very much; the rationale for doing so is almost always rooted in practicality — the system determines that ‘anything higher’ is not realistic.

Of course, that connects to the ‘pathways movement’. The initial uses of our New Life Project were for the purpose of getting students in to a statistics or quantitative reasoning course, where these courses were alternatives in the general education requirements. In practice, these pathways were often marketed as “not algebra” which continues to bother me.

Algebra, even symbolic algebra, can be very useful in navigating a complex world.

If we see this statement as having a basic truth, then our general education requirements should reflect that judgment. Yes, understanding basic statistics will help students navigate a complex world; of course! However, so does algebra (and trigonometry & geometry). The word “general” means “not specialized” … how can we justify a math course in one domain as being a ‘good general education course’?

Statistics is necessary, but not sufficient, for general education in college.

All of these ideas then connect to ‘guided pathways’, where the concept is to align the mathematics courses with the student’s program. This reflects a confusion between general education and program courses; general education is deliberately greater in scope than program courses. To the extent that we allow or support our colleges using specialized math courses for general education requirements … we contribute to the failure of general education.

In my view, the way to implement general education mathematics in a way that really works is to use a strong quantitative reasoning (QR) design. My college’s QR course (Math119) is designed this way, with an emphasis on fundamental ideas at a college level:

Proportional reasoning in a variety of settings (including geometry)
Rate of change (constant and proportional)
Statistics
Algebraic functions and basic modeling

If a college does not have a strong QR course, meeting the general education vision means requiring two or more college mathematics courses (statistics AND college algebra with modeling, for example). Students in STEM and STEM-related programs will generally have multiple math courses, but … for everybody else … the multiple math courses for general education will not work. For one thing, people accept that written and/or oral communication needs two courses in general education … sometimes in science as well; for non-mathematicians, they often see one math course as their ‘compromise’.

We’ve got to stop using high school courses taught in college as a general education option. We’ve got to advocate for the value of algebra within general education.

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college completion, politics of developmental mathematics | Jack Rotman | May 11, 2016 8:32 am

4 Comments

By Vernon, May 11, 2016 @ 9:04 am

Well stated Jack, thanks. In many ways, it feels like we are regressing to older less student focused mathematics. Hopefully, the pathways construct will move developmental mathematics to a true AMATYC Standards Mathematics.
By schremmer, May 11, 2016 @ 9:15 am

Re;

blockquote>[A]n emphasis on fundamental ideas at a college level:

Proportional reasoning in a variety of settings (including geometry)

Rate of change (constant and proportional)

Statistics

Algebraic functions and basic modeling

Self-evident?

The story line is elementary my dear Watson.

This is about as convincing as any one of a couple of dozen lists anyone could make up?

Above all, our students need to learn “to read pencil hand”, to learn that to argue is not a dirty word, that assertions must be supported, er …
By Jack Rotman, May 11, 2016 @ 10:50 am

You are assuming that my goal was to sway people’s opinion with that list. I wasn’t. It’s just a description of our course.

I have no idea what you mean by ‘read pencil hand’.
As for argument and supported assertions, those actually come up within the course (though as a minor component); those process issues have value for us as mathematicians or scientists but not so much for our client disciplines.
By schremmer, May 13, 2016 @ 11:10 pm

1. “Read pencil in hand”. Whenever a mathematician reads a paper, s/he recreates in his/her own terms what s/he reads which, admittedly, does not necessarily require a pencil but, certainly some writing utensil. Back in my days, every mathematician I knew used the phrase. But the “writing” is still very much necessary for the “reading”.

2.The list was just that, a list and that was whet I was objecting to. Anyone can write a list, particularly administrators. Even I can write a list. Why these particular list items though? Why not others? Why four, why not three or seven? What I would have liked to see is WHY you chose these items for your course.

3. The problem I have with the current “conception of learning” in the kind of courses you have been writing about is precisely that thinking is deemed to be only of secondary importance for the great unwashed masses—whose importance is only to give us an excuse to get out of the house in the morning for a small fee and for the publisher to steal a fortune.

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