Making Up For Twelve Years

How can we make up for what students did not get from twelve years of math?  Is it possible to have just one or two pre-college math courses, regardless of the entering level of students in a community college?  This is the big issue of our era, and the truth lies in a deeper understanding of the problems we face.  #CoRequisiteMath #NewLifeMath #CollegeMath

The origins of remedial mathematics, which formed developmental mathematics, are in the “college student” concepts of universities.  Being a college student meant that you had a solid high school academic background, and (almost coincidentally) meant that you could register for college algebra.  If a student could not show this high school background, remediation was used to fill it in.

This “college student” approach was originally based on the K-12 curriculum, which has never been very standardized in the USA.  Even with the recent Common Core, great variations exist.  The remediation provided, in mathematics, was usually a package that estimated the most common content as measured by topics and procedures.  We often referred to developmental courses as the “same as high school, only faster and LOUDER”.

In a basic way, remediation was done to estimate the desired college readiness measures (ACT, SAT); those measures, do correlate with placement in to college algebra.  The studies I’ve seen show correlation coefficients between 0.2 and 0.4; significant and meaningful, although these values indicate that only 5% to 15% of the variation is explained.

Meanwhile, we have no validation that the K-12 content as identified by topics and procedures has any causative connection to college mathematics success.  The entire set of them correlates somewhat, but we lack the professional validation of what members of the set (or a different set) are necessary.

Now, all of this means:

K-12 mathematics has a vague connection to readiness for college mathematics.

The conjecture we are exploring, in the current reform efforts, is that only some members of the K-12 math set are needed along with some members of another set (not taught in K-12).  [The reforms are the New Life Project, Dana Center New Mathways, and Carnege Pathways.]

In other words, the issue is not “making up for twelve years”.  The issues involve the particular abilities needed for success in specific college math courses.  Perhaps it really does not matter if a student can not tell me what 8*9 is, or what -4 + (-2) is; perhaps it is more important that students can reason about numbers and quantities at a level necessary for the college course.

In the current reform work, we in the New Life Project have identified some prerequisite learning outcomes needed before our first course (Math Literacy).  Here is what our document states:

Prerequisites to MLCS Course:
Limited quantitative skills are required prior to the MLCS course. Students should be able to do the following prior to this course:

• Understand various meanings for basic operations, including relating each to diverse contextual situations
• Use arithmetic operations to solve stated problems (with and without the aid of technology)
• Order real numbers across types (decimal, fractional, and percent), including correct placement on a number line
• Use number sense and estimation to determine the reasonableness of an answer
• Apply understandings of signed-numbers (integers in particular)

The New Life Project recommends that students be provided any needed instruction for these areas in either a short-term format (‘boot-camp’) or just-in-time (within the course).

These outcomes are vague, because we did not engineer down to the details.  My college is about to begin this process for a new version of our Math Lit course; our initial estimate is that we will need something like 20 hours of class time (perhaps 30) to help students develop the necessary abilities.  We do not have a goal of making up for twelve years … that goal is both unrealistic and not productive.  Instead, we will work on the much smaller set of “what does the student need to succeed in THIS course”.

The same conjecture would extend to other levels.  Whether it is Algebraic Literacy or Intermediate Algebra, what abilities does the student need?  The New Life Project suggests that the Math Literacy course is a good match.  For college algebra needs, the Algebraic Litercay course was designed to provide the abilities needed.

“Covering twelve years” is a bad solution to the wrong problem.  Student readiness for particular math courses is not a matter of ‘twelve years’ … it is a matter of specific abilities, and dealing with those is much more efficient.

Do not confuse these comments with support for “co-requisite remediation”.  Co-requisite remediation takes the extreme step of saying that essentially all students can start a college math course with enough support.  My position is that some portion can do this (more than we might think) … but taking the extreme position of co-requisite remediation is foolish and lacks the professional judgment that we are supposed to apply to our work.

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