Implementing Better Math Courses, Part I: A Starting Point

I want to share some specific options for implementing courses from the New Life Project, both to encourage more people to consider using those courses and to also increase our collective understanding of changes in the field.  In this Part I, I’ll talk about the easiest implementation; later parts will describe increasingly complete replacements of the traditional curriculum.  #NewLifeMath #MathLiteracy

The easiest curriculum reform to implement is often the side-by-side approach, also called ‘pathways’.  In this structure, the existing courses are left intact but some students are referred out of beginning algebra … based on a target of either statistics or quantitative reasoning.

This pathways model looks something like this:

Overall, about half of the known implementations of New Life courses is done within this ‘low’ implementation (side-by-side, or pathways).

The advantages of the low (pathways) implementation are:

• Easier to get ‘buy-in’ from other math faculty
• Allows for learning process (for teaching differently, with different content)

Some of the disadvantages are:

1. Depends upon effective advising for ‘recruiting’ students
2. Complicated structure and communication
3. Perhaps too easy to get buy-in from other math faculty
4. Provides benefits to some students, while the remainder experience an unimproved curriculum

In general, this pathways model (also called ‘low implementation’) is done by colleges.  When states implement the courses, they usually do so at the next level — replacing beginning algebra with “MLCS”.  In my view, the pathways (side-by-side) structure is not sufficiently stable to survive long-term.  As in my institution, however, this pathways model allows a math department to begin the process of curriculum reform without major disruptions.

The disadvantages listed for this model may actually be an advantage for some institutions.  In coping with the advising and communication challenges, the college may see improvements in those general processes.  I’ve heard of those types of outcomes happening at some institutions, though the positive outcomes depend upon good planning and lots of hard work; in my institution, for example, those disadvantages did not result in significant improvements in general systems.

Within the mathematics community, this pathways model is what ‘got traction’ a few years ago.  The side-by-side nature is not a long-term solution, and tends to reinforce that antiquated curriculum in college algebra or pre-calculus.  A more mature response to our curriculum would achieve some level of replacement; those replacement models will be explored when I talk about “medium” (MLCS instead of beginning algebra) and “high” (MLCS and Algebraic Literacy instead of traditional developmental algebra courses).

Overall, this pathways (side-by-side) low implementation model is an excellent choice for how to start the long-term process of improving our curriculum.  The key is to judge what your department and institution are ready for … pushing for a replacement of the old courses can be counter-productive, if the readiness is not there.  Once a department is working in the pathways model, we can more easily build the readiness for the replacement stages.

Nationally, the Carnegie Foundation’s Pathways (Quantway, Statway) are pretty much limited to the ‘low’ implementation; the purpose of those pathways is to accelerate math for students who are not in the ‘STEM’ path.  On the other hand, the Dana Center’s New Mathways Project is flexible enough to allow for both pathways (side-by-side) and replacement models.  Like the New Life project, the Dana Center work includes the MLCS course (called “Foundations of Mathematical Reasoning”, or FMR).  Differences emerge when we get to the replacement models.

If you are considering implementing a new course like MLCS or FMR, I hope the points above are helpful.  Feel free to leave a comment or send me an email for clarification or further information!

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2 Comments

• 

  By schremmer, March 21, 2016 @ 12:11 pm

  Seems to me that these “Pathways” are defined in terms of “topics”. This game has been played for about half a century to no avail.

  “positive outcomes depend” on the subject matter making sense. See, for instance, Hung-Hsi Wu in the response to the Elizabeth Green’s New York Times article which appeared in the Notices of the AMS and in which he writes If Americans do “stink” at math, clearly it is because they find the math in school to be unlearnable. […] For the past four decades or so the mathematics contained in standard textbooks has played havoc with the teaching and learning of school mathematics.

  While I have long advocated shortening said “pathways”, I have long argued that the way to do this is to shift the attention from the “topics” to developing a body of knowledge that encompasses them as pointed out by Hestenes. And, while I am it, the main difficulty in doing so has been pointed out by Atherton. See items 3 and 4 at

• 

  By schremmer, March 21, 2016 @ 12:22 pm

  Still having a hard time with links. Here are two more tries:

  http://freemathtexts.org/THETICAL/Psychology-Educology.php

  Atherton and Hestenes

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