Roots and the Mythology of Mathematics

We teach ‘mathematics’.  We believe ‘mathematics’ to be valuable.  What is this ‘mathematics’?

Our students firmly believe that ‘mathematics’ is a difficult mystery hidden from normal people.  Why do they have to ‘learn’ this ‘mathematics’?  When will they use it?  Does anybody really care (outside of a math class)?

Whether we are in a developmental classroom, or pre-calculus, or some other ‘math class’, we do not generally deliver an honest presentation of our subject.  How can I possibly make that statement?  Well, I’ve been thinking for years … and reading other peoples’ informed judgments … and conclude that the core property of mathematics is “the science of quantitative relationships”.  Mathematics is a science, not an abstract play ground; neither is mathematics a complex set of occasionally connected manipulations on various symbols and statements.

Mathematics enjoys a privileged position in American society, a position based more on the mythology of of mathematics than any reality.  Decision makers think ‘more mathematics’ is a good thing, and they can find statistical data that supports that position.  Our skeptics (and there are a few) can present better statistical studies that show that it is actually not the mathematics that makes the difference — there is a common underlying cause.

One of my students said this week (as she asked another question) “How can you stand to teach something that everybody hates so much?”  This was a spontaneous comment, and shows the type of mythology that I speak of.  If ‘mathematics’ was valuable, as we teach it, students would (to varying degrees) understand the benefits and gain motivation for working hard.

Instead, ‘mathematics’ is normally experienced as that complex set of occasionally connected manipulations on various symbols and statements.  We have students ‘simplify variable expressions’, but we have no clue that they realize we are talking about representations of quantities in their lives.  They ‘solve equations’, with no clue of how equations state conditions that people, objects, and properties must meet in specific ways.  We make students ‘graph functions’, without either making sure that they know how functions express the central relationships of quantities important to them or letting them in to the powerful tools of ‘rate of change’.

The roots of mathematics are in the rich intersection of practicality and science.  We have lost our roots, and cover neither side of this intersection.  We survive only because of the mythology surrounding ‘mathematics’; this mythology is not correct, and is offensive to a mathematician (in my view).  We teach mythology instead of mathematics.

Get up!  Look back at our roots as a practical science.  Do all you can to dispell the myths held by people concerning mathematics.  A central part of this work is to build a curricular structure that emphasizes actual mathematics.  You can begin this process by looking at the New Life model for developmental mathematics, as one model based on mathematics not mythology.

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3 Comments

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  By Peter Brown, July 8, 2011 @ 1:06 pm

  Excellent blog. We here have decided to confront this with a pretty serious pilot series using Math In Action as the core- with the wisdom/hope that algebra does help illuminate our world. Be interested in your perspective on this series.

• 

  By Jack Rotman, July 8, 2011 @ 1:37 pm

  Peter:
  Thanks for the comment … do you have a web site that I can look at, for more information on ‘math in action’?
  Jack

• 

  By Brenda Shepard, July 8, 2011 @ 5:42 pm

  Math In Action is a Pearson Series, authored by “The Consortium for Foundation Mathematics”

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