Yes, Necessary Algebra

The latest MAA Horizons has a great opinion piece by Paul Zorn called “Necessary Algebra” (see http://horizonsaftermath.blogspot.com/ to read it).  In our age of change in the curriculum, we need to keep our eyes on the entire system and the important goals.  To the extent that we want people to be able to reason mathematically and apply their knowledge in powerful ways, algebra is not just necessary … it is essential.

In his article, Paul Zorn gives this informal definition of algebra:

You can manipulate unknowns and knowns to solve equations.

I had another of my discussions with a student about the problems of “PEMDAS”.  This student was having great difficulty keeping straight the algebra we are learning (fairly traditional at this point), partly because the rigid application of PEMDAS got her through the prior math course … and now she did not have a single pre-determined set of steps to get correct answers.  Algebra is all about the legitimate choices we have in working with quantities (with and without unknowns).  Reasoning is dependent upon both knowing that there are choices and understanding some of the implications of those choices.

One of the strong trends in our age is the ‘contextualization’ of learning, and the related method of ‘problem based learning’.  Algebra, and mathematics in general, is both practical now and cognitively useful in the future.  Paul Zorn points out that we typically don’t use much of the specifics from our education in any everyday job — whether we are talking about math, sciences, history, or almost any domain of knowledge.  To limit our education to the immediately practical is to take education out of our classrooms; education is about building capacity, not just about providing methods to solve specific problems that can be understood at the moment.

My own approach to algebra, and mathematics in general, is this:

I always want to include some useless and beautiful mathematics in all of my classes.

Education is the exciting work of strengthening human brains by exploring domains of knowledge.  Algebra has a role to play.  As we reform our curriculum we need to keep algebra as one of the core domains of knowledge.

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