CBE … Competency Based Education in Collegiate Mathematics

Recently, I wrote about “Benny” in a post related to Individual Personalized Instruction (IPI).  We don’t hear about IPI like we once did, though we do hear about the online homework systems that implement an individual study plan or ‘pie’.  Instead of IPI, we are hearing about “CBE” — Competency Based Education (or Learning); take a look at this note on the US Department of Education site http://www.ed.gov/oii-news/competency-based-learning-or-personalized-learning

That particular piece is directed towards a K-12 audience; we are hearing very similar things for the college situations.  The Department (Education) sent accreditors a Dear Colleague Letter (GEN-14-23) this past December, as academia responds to the call to move away from “seat time” as the standard for documenting progress towards degrees and certification.  A former Provost at my college predicted that colleges will no longer issue grades by 2016, because we would be using CBE and portfolios (said this about 10 years ago); clearly, that has not happened … but we should not assume that the status quo is ‘safe’.

In my experience, most faculty have a strong opinion on the use of CBE … some favoring it, probably more opposing it.  As implemented at most institutions in mathematics, I think CBE is a disservice to faculty and students.  However, this is more about the learning objectives and assessments used, rather than CBE itself.

We need to understand that the world outside academia has real suspicions about the learning in our classes.  The doubts are based on the sometimes vague outcomes declared for our courses, and the perceptions are especially skewed about mathematics.  We tend to base grades on a combination of effort (attendance, completing homework, etc) along with tests written by classroom teachers (often perceived to be picky or focused on one type of problem).

One of the projects I did this past year was a study of pre-calculus courses at different institutions in my state, which lacks a controlling or governing body for colleges.  To understand the variation in courses, I wanted to look at the learning outcomes.  This effort did not last long … because most of the institutions treated learning outcomes as corporate ‘secret recipes’.  Other states do have transparency on learning outcomes — when all institutions are required to use the same ones.

This relates to the political and policy interest in CBE:

CBE will improve education by making outcomes explicit, and ensuring that assessment is aligned with those outcomes.

Sometimes, I think those outside of academia believe that we (inside) prefer to have ill-defined outcomes so that we can hide what we are doing.  We are facing pressure to change this, from a variety of sources.  Mathematics in the first two years can improve our reputation … while helping our students … if we respond in a positive manner to these pressures.

So, here is the basic problem:

Most mathematics courses are defined by the topics included, and learning outcomes focus on manipulating the objects within those topics.  The use of CBE tends to result in finely-grained assessments of those procedures.
Understanding, reasoning, and application of ideas are usually not included in the CBE implementation.

Compare these two learning outcomes (whether used in CBE or not):

• Given an appropriate function with polynomial terms, the student will derive a formula for the inverse function.
• Given an appropriate function with polynomial terms,  the student will explain how to find the inverse function, will find the inverse function, and will then verify that the inverse function meets the definition.

Showing competence on the first outcome deals with a low level learning process; the second rises to higher levels … and reflects the type of emphasis I am hearing from faculty across the country.

I do not see “CBE” as a problem.  The problem is our learning outcomes for mathematics courses, which are focused on behaviors of limited value in mathematics.  A related problem is that mathematics faculty need more professional development on assessment ideas, so that we can improve the quality of our assessments.  Without changing our learning outcomes, the use of a methodology like CBE will wrap a system around some bad stuff — which can make the result look better, without improving the value to students.

We need to answer the question “What does learning mathematics mean in THIS course?”  for every course we teach.  Assessments (whether CBE or not) follow from the learning outcomes we write as an answer to that question.

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Equity and Participation; our Response

This was one of those news reports that really got my attention as an educator.  There are many, of course, which should get my attention as a person and citizen; this report talked right to the ‘teacher’ in my brain.

The role of AP courses has been debated; in the mathematics community, we have some concern about how much benefit actually accrues to the majority of students in AP calculus.  However, as long as AP courses are offered … our goal needs to be equity: no group of students should be participating or not-participating at significantly different rates.

My college serves a blended district — a small-to-medium city (Lansing) and a surrounding area made up of suburbs and rural communities.  AP courses are offered in both the city and suburbs.  Here is a quick breakdown for two of the local districts for student population and AP population.

The school data came from a tool at marketplace.org; see http://www.marketplace.org/topics/education/learning-curve/spending-100-million-break-down-ap-class-barriers.  The city population data came from the 2010 Census.

One way to look at this data:  The Lansing high schools are about 73% ‘minority’; the AP classes in Lansing are about 60% minority.  Another view: the AP participation rate for white students is 50% higher than their proportion of the population would indicate, while the black student participation is 25% lower.

We might conclude that this discrepancy is a Lansing school problem; that is not the case.  The same pattern is present in Holt … just not quite as extreme, due to the smaller minority student population.

In case you are wondering, the national figures are:

We’ve known that minority students are over-represented in developmental math courses in college.  This recent data suggests that the equity problem extends through the whole range of abilities.  I respect the difficult work that our K-12 colleagues are doing, often without support or respect; this equity problem is not about the teachers … it’s about society and us.

We can, and must, do better.  How will we respond?  I think we recognize signs of a problem; what actions can be taken?

 
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Language as an Impediment to Improving Mathematics Education

A recent article in the Chronicle of Higher Education was:

Remedial Educators Contest Reformers’ ‘Rhetoric of Failure’ ( http://chronicle.com/article/Remedial-Educators-Contest/145351/)

This is a good article, worth the time to read and think about.  I was drawn to the phrase “Rhetoric of Failure”, a phrase that Uri Treisman used in a presentation at the NADE conference.  However, I’ve been bothered by another aspect.

Think about the word ‘reformers’ in the title … the word is being used to describe the groups (mostly external) who are trying to impose a different design for getting students in to credit-bearing courses (Florida, Connecticut, etc) with the most common strategy being the avoidance of developmental education.

One can not reform a system by avoiding it.

Reformers are those who seek significant changes in an existing system.  I am a reformer; perhaps you are.  We seem to have little power to resist the revolutionaries who want to avoid the system.  Part of this lack of power is likely due to the fact that few people outside of our profession know of the reform work we’ve been doing.  Sure, many have heard of the Carnegie projects (Statway™ and Quantway™); as a high-profile endeavor, that work has been widely publicized outside of mathematics education.  However, few (very few) outside of our profession have heard of our effective work at truly reforming developmental mathematics — the New Life project.

Do the destroyers know that we have a better model that will accelerate students to credit-bearing courses based on a professional re-design of the curriculum combined with a modernization of teaching?  How many people know that there are far more New Life implementations than any grant funded work, past or present?

Calling a group ‘reformers’ is assigning them an intent to improve a system; when revolutionaries make drastic changes, a better word would be ‘destroyers’.  Now, sometimes we need revolutions … sometimes we need destruction.  As I understand the views in the social sciences about change, revolutions and destruction are usually ineffective at producing long-term change.  I know of no reason why mathematics education would be any different.

As long as the ‘reform’ word is used for revolutionary changes, improving mathematics education will be very limited; we are, in fact, likely to regress (which is the most common result of a revolution).  We need to articulate our visions for reform with clear statements of our rationale; we need to challenge statements that attribute ‘reform’ to a revolutionary process.  We need to be comfortable telling external groups that imposing change (a bullying behavior) is not going to fix a problem; revolutions seldom work.

Calling something a ‘reform’ does not make it a good thing.

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Are You There, Mr. Gates? Flip that MOOC right over, guy!

Some of us have been thinking about the influence that foundations (and rich people) are having on education.  What was once an influence of the national science foundation is now the influence of the gates foundation, with a smaller group of people making decisions based on priorities that are not open to public review or political approval.

A recent article described how Mr. Gates suggested to community college trustees that a ‘flipped MOOC’ might be a good solution — especially for developmental mathematics.  [See http://chronicle.com/article/MOOCs-Could-Help-2-Year/142123/].   I suspect that the article is misquoting the ‘doctor-not’ (Mr. Gates); an intelligent person would not use an oxymoron like ‘flipped MOOC’.  (Flipped means ‘lectures’ happen outside of class time; MOOC’s do not have class time.)

However, that minor detail (that is is not possible) will not make any difference.  Because it was Mr. Gates saying it, many of our leaders (college trustees) will be confident that it is true.  I expect to hear from my College’s trustees within a few weeks, as they wonder whether we would like to try a flipped MOOC model at our college to solve our dev math problem.

Coincidentally, I saw a very good presentation on an inverted design for instruction — a better name than ‘flipped’.  This presentation was at my state conference (MichMATYC) — a talk given by Robert Talbert (Grand Valley State University); a reference is http://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1183&context=colleagues .  I was impressed by the amount of analysis done by Dr. Talbert to create the inverted calculus classroom; the process is much more complicated than ‘lecture outside of class time’.

To some extent, the ‘flipped MOOC’ phrase illustrates the linguistic process for the evolution of word usage: the initial use of a phrase is specific, becomes accepted, and then is applied in usage to unrelated objects in order to imply something positive (or at least ‘current’).  As educators, we have been damaged by this “phrase drift” many times over the years (mastery learning, back to basics, applications, calculator friendly, collaborative, student centered, and others).  The difference in this period is that our future is being heavily influenced by people who have less understanding of curriculum and instruction … rather than more.

There was a time when ‘trends’ in education were declared by top-level academicians and national policy heads.  These people (generally office holders of some kind) were deeply networked in the collegiate life.  No more; we are spending most of our time either agreeing with or arguing with people ‘on the outside’ — foundations in the completion agenda, philanthropists, and legislators.  It’s not that we should ignore the concerns of outside stakeholders.  The problem is that the outsiders have taken control from us; we react to them.

So, I ask:  Mr. Gates, are you there?   When do we get to have a productive conversation about the problems we are trying to solve?  We could look for problems where we agree on solutions … problems where we agree on the problem but not on solutions … and problems where we see the problem differently.  I know this, Mr. Gates — the process being used so far has put a lot of money is promising practices and technology without much sustained benefit; your return-on-investment is not so good.

When do we have a productive conversation?  Until we have real conversations with the people and groups trying to solve the problems (with the best of intentions) … until we work together, and not in reaction … until we accept both the worthy and not-so-good about the old system … only then do we have any hope of building something that will both solve problems and be capable of surviving in our world.

If you want to ‘solve the developmental mathematics problem’, Mr. Gates, I suggest you start by collecting a team of the 10 best thinkers and practitioners in the field who work with you over a 10-year period.  We want to solve problems; we strive to have students succeed and complete.  Can you recognize the need to have us as partners?

Are you there, Mr. Gates?

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