Co-Requisite Remediation in Tennessee

Has Complete College America (CCA) collaborated with the Tennessee Board of Regents (TBR) to create a great solution … or, have they inflicted an invalid model on the students of the state?  I suggest that “data” will not answer this question. #CCA #CorequisiteRemdiation

To summarize some key features of the Tennessee plan in mathematics, implemented state-wide this fall (2015):

  • All students are placed in to college-credit mathematics
  • If the ACT Math score is below 19, that college level math course will be statistics or quantitative reasoning
  • If the ACT Math score is below 19, the student is required to enroll in a co-requisite ‘support’ course
  • This co-requisite support course involves all developmental math learning outcomes

These elements are taken from a TBR memo (

From what I can see, actual practice is pretty close to this plan … learning support classes are paired with a QR course and an intro statistics course (but not college algebra or pre-calculus).  The learning support courses list topics from arithmetic, algebra, geometry and statistics.  I noticed that the QR courses tend to be more of a liberal arts math course — set theory, finance, voting, etc (the course is called ‘contemporary mathematics’).  In the 4-year college setting, this type of liberal arts math course is usually offered without any math prerequisite.

The initial data from the Tennessee pilot look very good; in fact, my provost is smitten with the Tennessee program, and wants us to consider doing the same thing.  I think the plan will “work” fairly well in Tennessee because of the non-symbolic nature of their QR course (intro statistics is notoriously non-symbolic, in the algebraic sense) … and the fact that they block students from STEM.  [They also had an inappropriate prerequisite on the non-STEM courses; see below.]

In Michigan, we have tried to establish 3 paths in math … college algebra/pre-calculus, statistics, and QR.  For statistics and QR, we have established a ‘beginning algebra level’ prerequisite (algebra or math literacy).  This level maps roughly to an ACT math score of 17, and we require more algebra in my QR course than in the Tennessee course. When the Tennessee plan ‘works well’, part of that is due to the fact that students never needed any remediation for stat or QR if their ACT math was 16 to 18.

In other words, the good results from the co-requisite pilot is due, in significant part, to the math prerequisite for college level courses.  ACT math = 19 (the Tennessee cutoff)  is a bit low for college algebra, but it is too high for statistics and QR (even if the QR is more algebraic, like mine).  Tennessee could have achieved the benefits for about 30 to 40% of their students by changing the prerequisite on two courses to be more realistic; they had established a ‘intermediate algebra’ prerequisite for all college math when that is not appropriate.  Changing the prerequisite would have helped many of the students without requiring them to take another class.

The problem we face is not that there are ‘bad ideas’ being used; the problem is that policy makers are evaluating ideas at a global level only, when the meaning of any statistical study is derived from analysis done at a fine-grain level.  Aggregated data is either useless or dangerous, and ‘aggregated’ is all policy makers consider.

CCA says “the results are in”.  Nope, not at all … we have some preliminary data about some efforts, which are not necessarily showing what the aggregated data suggests.

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Algebraic Literacy … a Key Session at AMATYC 2015

I invite you to attend a key session at the AMATYC conference next month:  Algebraic Literacy, A Bridge to Somewhere  (Saturday, November 21, 11:55am, in Bayside C).

This will be a positive, outcomes-oriented session.

  • Review of data on developmental mathematics, and intermediate algebra in particular (including ‘Bridge to Nowhere’)
  • Legacy of Intermediate Algebra (with archaeological value, not mathematical)
  • Engineering a Course to meet the needs of students
  • Learning Outcomes in Algebraic Literacy
  • Sample Algebraic Literacy lessons (Creative Commons license)

I will have several handouts for those attending (references, outcomes of Algebraic Literacy, sample lessons).

The work in this session will reflect the coming changes in mathematics in the first two years … modern content designed to meet student needs.  The conference features a symposium by the Dana Center including “Reasoning with Functions”, which is part of this same movement to make basic improvements in our work.

For those not able to attend the conference, the materials will be posted online later.  I hope that you will be able to participate in these changes, ideally by attending the session at the conference.

[Algebraic Literacy is the 2nd course in the New Life Project curricular model, intended to replace intermediate algebra.]

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College Algebra is Not Pre-Calculus, and Neither is Pre-calc

“Everybody knows what college algebra is!”  This was said by a math chair from a university in my state, as we worked though our state’s new transfer requirement for mathematics.  Of course, he was wrong … though he has a lot of company.  Today’s main question is this:  Is college algebra a subset of pre-calculus?

The original college algebra course developed in the 19th century at the universities of the day (Harvard, Yale, Bowdain, etc), with a focus on meeting a math requirement for their degree.  Of course, those times were very different … the Yale Catalog listed every student, and every student had the same default schedule.  College algebra was everybody’s math course as a freshman; those ‘desiring’ calculus took it as a Junior.  See

That tradition carries forward to the present day, in the work of the MAA.  The MAA College Algebra guidelines remain a narrative for a general education class, not a pre-calculus course.  See

The use of the name ‘college algebra’ for a calculus prerequisite appears to be a regional variation.  In states use ‘college algebra’ as a prerequisite for pre-calculus; other states use college algebra as the first semester of pre-calculus … or as their one-semester pre-calculus (as in “college algebra and trig”).

Our situation has become illogical and disfunctional.

When publishers market their textbooks, sometimes the key difference between college algebra and pre-calculus is this: pre-calc emphasizes a unit circle for trig functions, while college algebra uses right triangles.  Other than that, the pre-calculus book has more complicated problems, but no substantive differences.  Both courses trace their ancestry back to the 19th century mathematics course later known as ‘college algebra’.  [Search for Jeff Suzuki’s talk on college algebra.]

Neither course is really pre-calculus.

Of course, I don’t mean “students can not take these prior to calculus”; they do, though the benefits are small and accidental.  A pre-calculus course would be designed to prepare students for the work of a calculus course.  We make the fatal mistake of equating the ability to solve complicated symbolic problems with the capacity to reason with those objects.

A good preparation for calculus begins much earlier for many students.  “Developmental” mathematics is being re-formed to focus on understanding and reasoning, with a de-emphasis on artificially complex symbolic work.  A mathematical literacy course is a better preparation for calculus than the traditional algebra course.

More importantly, Algebraic Literacy is where we can begin the serious work of preparation for calculus.  Intermediate algebra is a documented failure as preparation for college mathematics; algebraic literacy is designed deliberately for these purposes.  The Algebraic Literacy course has learning outcomes backward-designed to meet the needs of calculus preparation … to be followed by a well-designed course at the next level which completes that preparation.

Here are some conditions necessary for good calculus preparation, based on the available information:

  • diversity of content (algebra, geometry, trig as minimum)
  • non-trivial reasoning about mathematical objects
  • concrete (context) and abstract situations
  • properties of functions, and relationships between types
  • reasoning and visualization involving related quantities (2, 3, or 4 at a time)
  • procedural expertise and flexibility

I do not intend for this list to be exhaustive.  The intent is to focus on key outcomes so we can determine when we have a real pre-calculus experience that will work for our students.  It is my belief that the great majority (>99%) of our current courses used as a calculus prerequisite are not reasonable preparations for the demands of such a course.

Some of our colleagues are beginning the work of correcting the curriculum; we need to support that work when possible.  If you’d like to explore what the new curriculum would look like, the Algebraic Literacy course provides a good starting point;  I’ll be doing a session at the AMATYC conference (Nov 21, 11:55am) in New Orleans.

We can solve this problem, together.

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A Simpler Vision: The New Life Curricular Model

I wanted to post a document I used for some college administrators, which helped them understand a different view of the mathematics curriculum.  This document is a simpler version of the one we have been using for math faculty.

Here is the simpler version:


New Math Pathways General Vision simplified 8 14 15













The full version looks like this:

New Math Pathways General Vision July2015







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