Renew the Profession!

I am at the ‘summer institute’ for Statway and Quantway, though the event is now called the ‘national forum’ for the pathways.  Hosted by the Carnegie Foundation, the meeting is being attended by over 100 faculty from across the country … some have been teaching a Statway or Quantway course this past year, some are new faculty from those colleges, and some are faculty from ‘new colleges’ who are looking to join the work.

The most satisfying aspect of the national forum is the dedication of these faculty to renew the profession.  Instead of looking for the answer, these faculty are building their understanding of the learning process for their students; they are listening to experts with theory and knowledge that applies to the issues; and they are collaborating on solutions that will help their students.

This dedication to renew the profession is part of the change process we are all facing in developmental mathematics.  Although some of us are currently dealing with a temporary ‘fix’ such as modules or mastery learning, the profession has a need to understand the learning and student needs so that we can provide courses with a purpose and a value to students. 

The Carnegie work involves phrases such as productive persistence, language & literacy, and advancing teaching.  The specifics of this work are only ‘in the network’ (the networked improvement communities).  Over the next few years, I believe that all of us are going to develop our understanding of the concepts and theories … and the efficacy of specific strategies for specific students in specific sfituations.

I hope that you will join me, and all those already working in these areas.  The time is now to renew the profession of teaching and learning in developmental mathematics.

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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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Research Trends in Developmental Mathematics

If you teach basic statistics in any form, you have probably dealt with the sharp contrast between ‘statistics’ and ‘statistical study’; in other words, there is a large difference between statistical data and the practice of statistics.  Having data does not mean there has been a statistical study.  In a similar way, having data does not mean that there has been research.

Research is an abstraction of this ‘data => statistical study’ to a higher level; research involves a prolonged effort to answer meaningful questions in a field of study, usually involving multiple researchers.  Research, in this meaning, is rare in developmental mathematics — we have lots of data, quite a few studies, but not that much research.  Research strives to provide richer and more subtle answers, and deals with a common core of issues.

One of my friends (thanks, Laura!) recently passed along a link to an article on research in developmental mathematics; this article is by Peter Bahr, whom I had read a few years ago (he’s been busy!).  The current article is called A Case for Deconstructive Research on Community College Students and Their Outcomes, and is available online at http://cepa.stanford.edu/sites/default/files/Bahr%203_26_12.pdf 

This article places research on developmental math within a larger framework of research in community colleges, focusing on student progression.  Which factors in a progression make a difference in the eventual outcome?  One of the conclusions Dr. Bahr reaches is that beginning algebra is a critical course; not passing this course on the first attempt raises the risk that a student will not complete — even if they persist to try the course again.  The article has several other points with practical implications for us, and for policy makers.

Instead of saying that remedial math is part of a ‘bridge to nowhere’ (the mistaken message of Complete College America), research into developmental mathematics takes a more intelligent (and difficult) approach of identifying specific features that have positive or negative impacts on student outcomes.   This research is too specialized for policy makers to understand, even if they understand research as opposed to statistics; part of our responsibility is to articulate what this research means in a manner that policy makers can understand.

I hope that you will use research like the Bahr article to suggest basic changes in your developmental math program.

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Modules in Developemtnal Mathematics — pro and con

I am hearing about colleges either adopting or considering modules in their developmental mathematics program.  Sometimes, this is done as part of an ’emporium model’; however, other designs make use of modules.  Perhaps it would help to have a brief exploration of the pros and cons of modules.

The word ‘modules’ does not have a uniform meaning for us.  In general, a ‘module’ could be another name for a ‘chapter’ — each being a sub-unit within a larger organization of material.  However, most uses of the word ‘module’ refer to one of two approaches to content — uniform sequence of modules or customized sequence.

The difference between the two uses can be subtle, such as a case where the customized exit point is the end of a ‘course’ — some modular programs designate ‘modules 5 to 8’ as a course, and that is where the exit point is.  Customizing is done by either changing the ending module within a course or changing the entry point (starting module) within the course.  Conceptually the contrast for the two designs is important due to the fact that a customized program prevents a summative assessment common for all students.

Over the past several years, I have had discussions with faculty involved in a type of modular program.  Via this obviously non-scientific method, I have developed some pros and cons for modularization.  Most of these apply to either type (uniform or customized).

A modularized approach is usually based on an assumption that the delivery mode is a major source of problems, sometimes stated “we can’t teach this to them the same way they saw it the first time”.   I have not seen any evidence of this being true; it’s not that I want to teach them “the same way” (whatever that means) … it’s that this assumption about the delivery mode often precludes examination of larger issues about the curriculum.  Modularized tends to reinforce notions that ‘mathematics’ is about knowing the procedures to obtain correct answers to problems (often contrived and overly complex).  Our professional standards (such as the AMATYC Beyond Crossroads  … see http://beyondcrossroads.amatyc.org/) begin the discussion about mathematics by describing quantitative literacy.  This aspect — of modularization tending to limit the mathematics considered — is the largest factor in seeing this approach as being weak and temporary.

The other major area of concern, suggested somewhat in the pros and cons, is the professional status of faculty in developmental mathematics.  Administrators and policy makers often do not understand the professional demands of being developmental mathematics faculty; in the modularized approaches, faculty tend to look a lot like tutors.  This similarity then suggests to some that faculty are not necessary, and we can provide a larger pool of tutors.  Our professional standards call for us to see the work in math classrooms as being rigorous in both mathematics and education.  This aspect — the professionalism of faculty — is the most common concern reported by faculty engaged in a modularized program.

Summary:
The attractiveness of modular approaches is easy to understand.  However, the typical implementation of modular approaches will reinforce a traditional content with a weaker assessment system combined with a generally lower faculty professionalism.  When implemented, modular programs will tend to be temporary solutions.  The emerging models — New Life, Carnegie Pathways, Dana Center Mathways — provide a clear alternative to address the problems based on professional standards to create long-term solutions.

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