Modern Dev Math

Let’s pretend that we don’t have external groups and policy makers directing or demanding that we make fundamental changes in developmental mathematics.  Instead, let us examine the level of ‘fit’ between the traditional developmental mathematics curriculum and the majority of students arriving at our colleges this fall.

I want to start with a little bit of data.  This chart shows the typical high school math taking patterns for two cohorts of students.  [See  http://www.bls.gov/opub/ted/2012/ted_20121016.htm ]

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There has been a fundamental shift in the mathematics that our students have been exposed to, and we have reason to expect that the trends will continue.  We know that this increased level of math courses in high school does not translate directly into increased mathematical competence.  I am more interested in structural factors.

Intermediate algebra has been the capstone of developmental mathematics for fifty years.  At that time, the majority of students did not take algebra 2 in high school … so it was logical to have intermediate algebra be ‘sort of developmental’ and ‘sort of college level’.   By about 2000, this had shifted so that the majority of students had taken algebra 2 or beyond.

The first lesson is:

Intermediate algebra is remedial for the majority of our students, and should be considered developmental math in college.

This seems to be one lesson that policy makers and influencers have ignored.  We still have entire states that define intermediate algebra as ‘college math’, and a number that count intermediate algebra for general education requirements.

At the lower levels of developmental mathematics, the median of our curriculum includes a pre-algebra course … and may also include arithmetic.  Fifty years ago, some of this made sense.  When the students highest math was algebra 1 in most cases, providing remediation one level below that was appropriate.  By fifteen years ago, the majority of students had taken algebra 2 or beyond.  The second lesson is:

Providing and requiring remediation two or more levels below the highest math class taken is inappropriate given the median student experience.

At some point, this mismatch is going to be noticed by regulators and/or policy influencers.  We offer courses in arithmetic and pre-algebra without being able to demonstrate significant benefits to students, when the majority of students completed significantly higher math courses in high school.

In addition to the changes in course taking, there have also been fundamental shifts in the nature of the mathematics being learned in high school.  Our typical developmental math classes still resemble an average high school (or middle school) math class from 1970, in terms of content.  This period emphasized procedural skills and limited ‘applications’ (focusing on stylized problems requiring the use of the procedural skills).  Since then, we have had the NCTM standards and the Common Core State Standards.

Whatever we may think of those standards, the K-12 math experience has changed.  The emphasis on standardized tests creates a minor force that might shift the K-12 curriculum towards procedures … except that the standardized tests general place a higher premium on mathematical reasoning.  Our college math courses are making a similar shift towards reasoning.  Another historical lesson is:

Developmental mathematics is out-of-date with high schools, and also emphasizes the wrong things in preparing students for college mathematics.

We will never abandon procedures in our math courses.  It is clear, however, that procedural skill is insufficient.  Our traditional developmental mathematics curriculum focuses on correcting skill gaps in procedures aligned with grade levels from fifty years ago.  We appear to start with an unquestioned premise that remediation needs to walk through each grade’s math content from 5 decades ago … grade 8 before grade 9, etc.  This is a K-12 paradigm with no basis in current collegiate needs.

The 3- or 4-course sequence of remedial mathematics is, and always will be, dysfunctional as a model for college developmental education.

There is no need to spend a semester on grade 8 mathematics, nor a need to spend a semester on grade 9 mathematics.  When students lack the mathematical abilities needed for college mathematics, the needs are almost always a combination of reasoning and procedural skills.  If we can not envision a one-semester solution for this problem, connected to general education mathematics, we have not used the creativity and imagination that mathematicians are known for.  Take a look at the Mathematical Literacy course MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2 .  If students are preparing for pre-calculus or college algebra, take a look at the Algebraic Literacy course  Algebraic Literacy Goals and Outcomes Oct2013 cross referenced

Pretending that the policy influencers and external forces are absent is not possible.  However, it is possible for us to advocate for a better mathematical solution that addresses the needs of our students in an efficient model reflecting the mathematics required.

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