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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Michigan Student Success Summit

The Michigan Center for Student Success hosted a summit this week, and I gave a short presentation on the New Life model.

Here is the link to that presentation (PDF): http://jackrotman.devmathrevival.net/Prominent%20efforts%20to%20redesign%20developmental%20mathematics%20Stu%20Success%20Summit%20Sept2011%20JackRotman.pdf

 
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Excuse Aunt Sally … part II

Sometimes, an experience in class illustrates a concern.

In today’s beginning algebra class, we were doing order of operations with signed numbers … the first problem for students to do had a quotient and then a product.  MANY students in class were convinced that they needed to multiply first; their rationale was “PEMDAS” — where multiply clearly comes before divide. The problem looked like -16 ÷ (-4) ·2; not very complex … and more than half the class insisted on multiplying -4 and 2 before dividing.

Now, it is true that the type of problem involved is not that important; it’s not needed to model any situation, does not find any reasonable answer, and does not support future learning (outside of order of operations).  The correct answer for this particular problem is not very valuable.

However, our students should be developing a coherent system of knowledge.  In an earlier post, I suggested that “Dear Aunt Sally be Excused” from all math classes; my rationale was that PEMDAS directly causes confusion in algebraic reasoning.  This post is further suggesting that PEMDAS is not very functional even within the original domain of use (order of operations, no variables).

I am becoming more convinced that “PEMDAS” should be avoided in all mathematics classes … whether it is school mathematics or college mathematics.  PEMDAS is short-sighted and misleading; PEMDAS does not support an organized system of understanding.  PEMDAS harms students in the long term, and somewhat in the short-term.

 
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