The Magic Solution to Learning in Developmental Mathematics

Contextualize … discovery learning … group work … experiments … homework systems … calculators … modules … learning communities … clickers … tutoring … and smiles.

What was that a list of?  To some extent, that was a list of ‘magic solutions’ offered by somebody to improve (often ‘dramatically improve’, according to that person) the learning in our developmental mathematics classrooms.  Every single advocate of these solutions has some ‘data’ (often labeled ‘research’) to support their answer to our problems; if they don’t have this data themselves, then they are a convert or follower — often a person at a foundation or policy group.

These are not solutions, let alone magic solutions.  Solutions deal with problems; solutions make sense.  Solutions fit within the surrounding systems to enable both long-term maintenance and ‘scalability’. 

Here is the magic solution to learning in developmental mathematics:

Offer sound mathematics with academic value, supported by skilled professional educators who can help every student learn by employing a diverse set of tools, focusing on cognitive growth in students.

We currently do not have sound mathematics in the majority of our courses; there are emerging models that provide some specific alternatives (New Life, Carnegie Pathways, Dana Center Mathways).   Many of our colleagues (perhaps the vast majority in some places) have limited skills further hampered by a limited conceptualization of their profession; organizations such as AMATYC and its state affiliates provide professional development to supplement the internal opportunities.  As a profession, we have not articulated a standard set of tools necessary for faculty to meet the needs of our students.  And, far too often, we look at surface outcomes of success (completion, passing) instead of looking at measures of meaningful growth in our students.

As you can see, there is nothing simple or quick about this magic solution.  I still call it ‘magic’, because this solution creates a qualitative shift in our profession — instead of ‘avoidance’, we have a positive target; instead of a discouraged and sometimes desperate people, we can be inspired and proud (both as mathematicians and as educators).  I admit that this magic solution is not quick, nor is it easy; however, it is a real solution, not a temporary distraction like the items listed at the start of this post.  [Those items are possible tools to use, not solutions.]

Many of us are currently involved with projects that are not really a solution, whether this consists of modules or mastery learning or a temporary redesign such as emporium.  Do not worry about this work; it is part of the process … not the end.  Whether it takes 2 years or 5 years, the incomplete solution will be identified as such, and the next stage will be started.  THAT (the next stage) is what you should be concerned about. 

Behind this basic change is a more developed and refined use of research.  Much of the ‘data’ used in our profession (internally or externally) is just a little better than the charts in USA Today — they are not statistically sound, and do not fit into a body of research for our profession.  Most of this data is better left ‘ignored’.  Our work should be informed by theory and research that develops over time; fads are a distraction from basic change.

I hope that you can focus on the larger picture, on what is a ‘magic solution’; perhaps you can look at the emerging models for inspiration or encouragement.  Our success in this endeavor called developmental mathematics depends more on our internal visions of solutions than on a temporary distraction or ‘data’.

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2 Comments

• 

  By schremmer, July 15, 2012 @ 6:00 pm

  Re. “sound mathematics”

  The problem is that, even from the viewpoint of just specifying the contents, “sound” is far from being meaningful. For one, you may have thought of the contents in the “formalist” or even “constructivist” manner while I may think of them in a platonic manner.

  For instance, how are we to “specify” what a real number is? For that matter how are we to “specify” a rational number? Etc

  But even if we agree on what constitutes “sound” mathematics from the viewpoint of the nature of the “topics”, and of the way these are related, we may not agree on what is a “sound” way to go from this to that, to prove this on the basis of that:
  Formal proof as in high school geometry? Obviously “gapless proofs” are sound. But they are also essentially unreadable. The Bourbaki style? “Convincing arguments” as per Stephen Toulmin? Appeal to the “real-world” as in Model Theory? Etc

  Regards
  –schremmer

• 

  By Jack Rotman, July 16, 2012 @ 11:38 am

  Clearly, ‘sound mathematics’ was meant to describe a judgment by individuals and the profession; I would not expect us, or any group of people, to agree (de facto) what this means. Within the profession of developmental mathematics, this should be the foundation of our conversations — not any of the distracting ‘solution’. Worthless mathematics is still worthless when twice as many students complete the courses.
  I would add that ‘sound mathematics’ can not be considered as a universal constant — the local conditions, and the population being served, must be considered.

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