Conversation II: Herb & Jack on the Why — Practicality of Theory

In response to a post about STEM students and the traditional developmental mathematics curriculum, Herb Gross began with this quote (from a prior talk he gave):

The music is not in the guitar.

I think Herb is saying that mathematics is not in the visible tools used, whether these tools are procedures written down or technology used to answer questions.  This is a great point, and it suggests that we question any suggestion that we limit the content of mathematics courses to just those things seen as ‘practical’.  Seeing mathematics as being bound by the practical (for STEM or non-STEM) is a self-defeating behavior; a health profession is based on continuing growth, and growth depends upon research both applied and theoretical (the two work together in surprising ways).  Our students are future policy makers — do we want them to only value mathematics that is practical NOW?  (Think University of Wisconsin budget cuts.)

The music, and the mathematics, is based on connections among concepts.  This speaks to the growth of mathematical reasoning and critical thinking.  Herb adds this comment:

So I am not overly impressed with the pass rate improving as much as I am in seeing what the effect is further down the road.  In fact one of the reasons I don’t like non-algebra/calculus based courses is that even the students who are most successful in these courses tend to know how to crunch numbers into the calculator but have little feel as to what to do when the distribution is anything other than normal.

I think Herb is speaking to a basic goal of education — the improvements retained over a longer period of time, meaning improved capabilities.  The comment Herb makes is important, and I think it applies to most algebra based courses; I also wonder about calculus based courses.  Look at this re-phrasing of a critical part of Herb’s comment:

Students tend to know how to manipulate symbols or numbers often with the use of tools but have little understanding as to what to do with mathematical concepts applied to a new situation. (JR)

Creating scalable change within an individual involves some of the same work as creating scalable change in a profession.  A more complete view of learning is required, with less focus on ‘passing’; passing is a great thing, but it can not be the core measure of our success.  We seek to create mathematical abilities, including the willingness to apply existing knowledge to new situations where this knowledge is not sufficient.

Students in STEM programs need a broad foundation in mathematics, combining procedural and conceptual fluency.  To some of us, we follow that statement with “Non-STEM students to not”; this is where we can make large mistakes.  The mathematical needs of citizens and the mathematical needs of our partner disciplines are not different in a basic way — they need procedural and conceptual fluency as well.  The difference, overall, is a matter of degree and extent.  STEM students need MORE, not so much ‘different’.

Our work in the AMATYC New Life project supports this single-source approach to mathematics — the Mathematical Literacy course serves the needs of all students.  The initial uses of the course have often been for non-STEM students; however, the outcomes of the course were designed back from the needs of all students.  I agree with the design of the New Mathways Project (Dana Center), which has a similar course serving all students.

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