Math is Different

A student applies for a community college, having set a personal goal of earning an associate degree in a field with good employment prospects.  The college informs her that she needs to take a placement test to confirm that she has her basic skills in science and history; clearly, a student needs to have those basic skills before taking college courses that involve science or culture.

The student, Lindsay, takes the tests; she learns that she has to take two remedial science classes and one remedial history class before she can start her program; these courses correspond to 8th and 10th grade science and to 9th grade history.  With relief, she learns that she does not need to take a course like her 12th grade mathematics.

What’s that you say?  This is ridiculous and untrue?  Yes, clearly I’m making this up.  However, it is possible that our approach to mathematics in college is just as ridiculous.

We say, and do many others, that “Math is Different”.  Of course.  Does the set of differences justify the punitive approach we use for mathematics?  We place students in boxes, each with a label for the degree of deficiency.  These boxes have no known connection to college courses, justified by a belief that ‘high school’ must be mastered before ‘college’.  The most common math courses taken by college students were never designed to provide benefits in college; they are copies (sometimes poor copies) of outdated school mathematics imposed on students.

Do we have students who truly need remediation in mathematics?  Absolutely; the rate is probably large — over 20% of incoming students probably need some remedial math course before they have a reasonable chance of success in college courses in science or mathematics.  Some students come to a community college with extensive needs in mathematics, and need help with number sense, proportional reasoning, algebraic reasoning, basic ideas of geometry, and more.  Many come to us with weak skills in algebraic reasoning and basic geometry — combined with needs for other areas of mathematics.

Placing students into a sequence of courses covering years of school mathematics makes no sense in college.  Research suggesting that many students are equally successful placed directly into college courses reflects a design problem, as much as ‘remedial is not working’.    As an analogy — I had a flash drive stop working this week.  Now, a flash drive needs a port and an operating system; there is a sequence of things here.  Our approach to remediation is like installing a new cover on the flash drive so it looks more like the computer, instead of making sure that the system works together.

Redesign of developmental and introductory college math courses is not enough.  Instructional delivery systems will not solve our problems.

We need to look at root causes and basic relationships so we can identify student capabilities that will make a difference.  In developmental mathematics, the New Life Project has done this type of analysis; take a look at http://dm-live.wikispaces.com/ for information.  Not as much has been done for basic college mathematics (college algebra, pre-calculus, etc); the MAA CRAFTY materials provide a start — see http://www.maa.org/sites/default/files/pdf/CUPM/crafty/CRAFTY-Coll-Alg-Guidelines.pdf  for information.

Math is different; students are different.  Take a look at the differential pass rates among groups of students.  The types of students most of us really want to help — those lacking prior success (predominantly poor and minority students) have significantly lower course pass rates in our current courses.  Sometimes, the differential is so severe that completion of the sequence is a trivial number of such groups.  The conditional probability of “need 3 developmental math courses AND is black/African American” is somewhere around 5%, compared to about 18% for all students.  A cynic might say that the primary purpose of developmental mathematics is to make sure that the high paying jobs stay in the hands of the ‘haves’.  I do not believe that we want to block the upward mobility of students in our communities.

We need new math courses, courses designed to provide benefits; courses designed to provide equity to our students.

All other improvements in mathematics at colleges will be temporary relief at best.  The system is not designed to succeed, and that is the problem needing our attention.

 
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2 Comments

• 

  By schremmer, February 21, 2014 @ 10:43 am

  Re. “We need to look at root causes” and “We need new math courses”, see for another “Existence Theorem”, and for instance,
  Regards
  –schremmer

• 

  By schremmer, February 21, 2014 @ 2:05 pm

  Re. “We need to look at root causes” and “We need new math courses”, see for another “Existence Theorem”, and for instance,
  How Content Matters
  Regards
  –schremmer

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