QEP on Developmental Mathematics

I am finishing up my first on-site reaffirmation committee for “SACS” (Southern association of Colleges and Schools).  One of the required components, in fact the emphasis of the on-site visit, is the Quality Enhancement Plan (QEP).  For the college I visited, their QEP was a complete redesign of developmental mathematics.

In the process for selecting their QEP and planning what to do, the faculty and staff at this college researched various alternatives for their work; the conclusion reached by this institution was that they would replace their existing developmental mathematics courses with the New Life model.

The math faculty at this college adjusted some components of the New Life model to fit the local conditions.  However, starting in 2012, MLCS and Transitions will be the only developmental mathematics courses at this college.  The entire campus is incredibly excited about the new system and the benefits for students; everybody from adjunct advisors to the college president was able to articulate the basic ideas of the model.

I mention this because quite a few of the community colleges in the SACS region will be beginning their own process.  When the time comes, I encourage you to be inspired by the college I visited … the New Life model makes an excellent QEP activity.

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Whom Do we Follow?

At the college level, most introductory mathematics has been materials-based … meaning that the curriculum experienced by our students was largely determined by the textbook used.  The vast majority of textbooks considered for a given course would be very similar in ‘objectives’, presentation, and terminology.  Authors would bring minor variations in explanations, and more substantive variations in the range of problems included.

Along comes the ‘redesign-modules-web homework’ push.  The content becomes atomized, with most content described by the algorithms used to generate the problems.  Many of us are delivering courses which emphasize students “doing problems” as a way to get them to “do mathematics”; I would argue that these are not the same, and the differences have weakened our curriculum.

Another push would be the Pathways of the Carnegie Foundation for the Advancement of Teaching (Statway™ and Quantway™), developed in partnership with the Dana Center (Univ Texas- Austin), with assistance from AMATYC.  Rather than driving the curriculum by algorithm, these materials seek to remain true to the mathematical description of the content … the homework system is much more difficult to develop (though they have the best people working on it, and they are succeeding).

So, the question for our profession is this:  Whom do we follow?  Do we follow the atomized content with algorithms defining the outcomes, or do we follow new voices that seek to deliver mathematics needed by our students? 

Perhaps the question is not fair, as some of us are not following anybody … some of us are being told that we WILL walk a certain path, with the atomized content and algorithms; frequently this is due to administrators reaching a critical point in the process, and there is no more patience for a faculty-led process.

As long as we are professionals, we should continue to advocate for our responsibilities relative to our curriculum.  When administrators push, we need to look for all avenues to push back — not to avoid change, not to deny the existence of a problem; no, we need to push back so that the responsibilities remain ours as faculty. 

I hope you, and all of us, will consider our responsibilities … whether we are able to chose whom to follow, or whether somebody attempts to tell us whom to follow.  We have our own professional standards, and our future will depend upon how well we are true to those standards.

 
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Mastery Learning is …

I have heard many faculty speak in favor of mastery learning … and almost as many speak in opposition.

The heart of this set of opposing viewpoints is an incomplete notion of what mastery learning IS.  Many equate mastery learning with basic skills … with repetition … with homework systems.  These are not definitions, nor even descriptions, of ‘mastery learning’.

The origins of ‘mastery learning’ were centered in a philosophical base which claimed that almost all students could learn any particular content to the level of ‘masters’ (usually defined to be a 4.0 or A student) given the correct conditions … with a primary condition to vary being ‘time on task’.  In a classic view of higher education, all students are imbedded within a learning environment so they experience similar conditions; those who perform at a high level are rewarded with 4.0/3.5/A/B grades and encouraged to pursue more learning … those who failed to perform within these constant conditions were told that they needed to make an alternate choice of activity (as in, some other class … some other major … or not in college at all).

Those of us who adopted a mastery learning model turned this conception on its head.  We were not here to sort students; we were here to create the conditions for all students to have the opportunity to become masters of the content.  Our content was not changed, only the conditions for learning.  Our assessments did not reflect lowered expectations, but they did create positive conditions for additional learning.

The current misconception of mastery learning is based on the technology that is often used to deliver ‘content’.  Offering modules, online homework, and requiring ‘80%’ before moving on … these have little to do with mastery learning.  These learning environments focus on basic skills primarily because that is easier for mass-produced homework systems (though it also reflects a bias among many colleagues). 

In essence, mastery learning is only limited by our capacity to design instruction and assessment.  If applications … transfer … problem solving … creativity are important elements in your ideas about mathematics, mastery learning can be designed to support them.

Mastery learning, in 2011, is more about the economics of publishing and grants than it is about the flexibility (and power) of mastery learning.  I have spent many years in a program that had mastery learning as a founding principle, and I understand the complexities of creating a mastery learning model that includes ‘more than basic skills’.  I would suggest that most of these difficulties are present regardless of whether mastery learning is involved. 

Mastery learning does not determine the nature of the mathematics faced by our students.  No, what determines the mathematics that our students experience is our own conceptions of mathematics.  We should, as a community of professionals, have honest discussions about what it means to “learn mathematics”.

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The End of Learning Styles

Although I did not hear this particular report, NPR (National Public Radio) aired a report on the scientific research related to “learning styles”; see http://www.npr.org/blogs/health/2011/08/29/139973743/think-youre-an-auditory-or-visual-learner-scientists-say-its-unlikely 

If this is the end of ‘learning styles’, what does that mean?  Which ‘learning styles’?

I think the end of learning styles can only be a good thing, for teachers and our students.  The basic constructs of ‘learning styles’ involve vague descriptions of sensory processing, skewed to favor one or more categories of input (auditory, visual, kinetic, etc), without regard to the research of cognitive scientists.  Categorizing students within these skewed categories creates dangers, and real damage, to our students.  We all have had students who have been told “I am a very hands-on learner; if I can not touch it and move it, I will never understand it” … and similar statements of limitations for other ‘styles’.

Ed Laughbaum, a long time friend, said in a recent post that ‘basic brain function is the same in all normal brains’; he does not say this lightly, and has good scientific reasons for that statement.  My own humble reading of current research and theories of cognition certainly supports that statement.   Unless the student has a temporary (drug induced, for example) or chronic (birth defect, closed brain injury) biological issue, the learning needs are quite similar across all students with comparable current learning. 

The constructs of learning styles have not worked, and they conflict with science.  Too often, we have accepted “proof by parable” or even “proof by rhyming” … what does “drill & kill” mean?  An “inch wide and a mile deep”?  “She is a visual learner.”  “Our students need manipulatives.”  “Sage on stage … Guide on side.”  I am afraid that our profession, and teaching in general, has been guided more by the appeal of the words in statements rather than by known properties of learning.

It is true that very few of us, and teachers, will be able to study the actual work of cognitive scientists.  We will depend upon others to translate and summarize this work so that we can use it.  If these resources are not available, we must avoid the pop-psychology notions that might seem to have some truth in them.   

If you would like a source, here is the best one-stop summary I have seen: http://act-r.psy.cmu.edu/papers/misapplied.html  , an article called “Applications and Misapplications of Cognitive Psychology to Mathematics Education”.

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