Common Core, Common Vision, and Math in the First Two Years

I’ve been thinking about these ideas anyway.  However, a recent comment on a blog post here got me ready to make a post about predicting the future of mathematics in the first two years.  I’d like to be optimistic … past experiences would cause considerable pessimism.   The truth likely lies between.

One of the “45 years of dev math” posts resulted in this comment from Eric:

If Back2Basics is what drifted up to CC Dev Math programs back then, what do you see the impact of CommonCore being on CC Dev Math now?

This post was about the early 1980s, when we had an opportunity to go beyond the grade level approach of the existing dev math courses (one course per grade, replicating content).  Instead of progress, we retrenched … resulting in courses which were subsets of outdated K-12 courses.  Much of the current criticism of dev math is based on these obsolete dev math courses.

We again have an opportunity to advance our curriculum.  This time, the opportunity exists for all mathematics in the first two years.

• The K-12 math world is changing in response to the Common Core State Standards.  Even if politics takes away the assessments for that content, many states and districts have already implemented a curriculum in response to the Common Core.  (see http://www.corestandards.org/Math/)
• The college math world is responding to the Common Vision (see http://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf) which is beginning the process of articulating a set of standards for curriculum and instruction in the first two years.  AMATYC is developing a document providing guidance to faculty & colleges on implementing these standards.  [I’m on the writing team for the AMATYC document.]

The two sets of forces share quite a bit in terms of the nature of the standards.  For example, both K-12 and college standards call for significant increases in numeric methods (statistics and modeling) along with a more advanced framework for what it means to ‘learn mathematics’.

These consistent parallels in the two sets of forces would suggest that the future of college mathematics is bright, that we are on the verge of a new age of outstanding mathematics taught by skilled faculty resulting in the majority of students achieving their dreams.  This is the optimistic prediction mentioned at the start.

On the other hand, we have some prior experiences with basic change.  One example is the ‘lean and lively calculus’ movement (conference and publications in 1986 & 1989).  It is very sad that we had to modify ‘calculus’ with something suggesting ‘good’ (lean & lively) … the very nature of calculus deals with coping with change and determining solutions for problems over time.  As you know, this movement had very little long-term impact on the field (outside of some boutique programs) while the “Thomas Calculus” continues to be taught much like it has been for the past 50 years.

Here are some factors in why we find it so difficult to change college mathematics (the levels beyond developmental mathematics).

1. Professional isolation:  membership in professional organizations is low among faculty teaching in the first two years.  The vast majority of us lead isolated professional lives with limited opportunities to interact with the professional standards.
2. Adjunct faculty as worker bees: especially in community colleges, adjunct faculty teach a large portion of our classes … but are separated from the curriculum change processes.  The existing curriculum tends to be limited by these artificial asymptotes  created by our perceptions and the desire to save money by the institution.
3. Autonomy and pride:  especially full-time faculty tend to place too high an emphasis on autonomy & academic freedom, with the false belief that there is something inherently ‘good’ about opposing all efforts to change the courses the person teaches.  Although most prevalent at universities, this ‘pride’ malady is also a serious infection at community colleges.

I’ve certainly missed some other factors.  These three factors represent strong and difficult to control forces within a complex system of higher education.  Thus, I consider the pessimistic view that ‘nothing will change, really’.

I think there is a force strong enough to overcome these forces restraining progress in our field.  You’d like to know the nature of this strong force?

The attraction of teaching ‘good mathematics’ is fundamental in the make up of mathematicians teaching in college.  If faculty can see a clear path to having more ‘good mathematics’, nothing will stop them from following this path.

If the Common Core, the Common Vision, and the AMATYC new standards can connect with this desire to teach ‘good mathematics’, we will achieve something closer to the optimistic prediction.  The New Life Project has experienced some of this type of inspiration of faculty.  Perhaps AMATYC will create a new project to bring that inspiration to a larger group of faculty teaching in the first two years.

One thing we know for certain about the future:  the future will look very much like the present and the past unless a group of people work together to create something better.  I would like to think that our profession is ready for this challenge.

Are you ready to become engaged with the process of creating a better future for college mathematics?

 
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The Big Missed Opportunity: Forty Five Years of Dev Math, Part III

This is part of a series of posts reflecting on our history in developmental mathematics … especially at community colleges in the USA.  We’ve talked about the ‘origins’, about a ‘golden age’ (or not), and now we move to the first half of the 1980s.

Two major movements were active at about the same time in the early 1980s … one dealt with placement policies, and the other dealt with the content of mathematics courses at this level.  When more than one movement is impacting a profession at the same time, there is always an opportunity for fundamental change.  That is not what happened in this case, and we continue to deal with the ‘incorrect’ responses to that opportunity.

The use of standardized assessments for placement was widespread (though with varied instruments) at the start of this period, as we moved from home-grown placement measures to assessments used at a larger scale (state, region, or nation).  Those tracking data quickly noticed that these measures, often used with mandatory placement, were impacting certain groups at a disproportionate rate.  In some cases, the items on the assessments had been tested for bias; even with tests using only these tested items, the results showed an uncomfortable level of differential impact.

Clearly, “something” had to be done.  A professional response might have been to develop an effective short term intervention that would equalize the results.  Another professional response might have been to establish collaborations between community college math faculty and the local K-12 school’s math program.  In general, neither of those responses occurred.  Instead, there was a decline in the rate of mandatory placement:

Students have the right to fail.  If they disagree with the placement measures, they can take the higher course.

I still hear this “right to fail” statement, which I see as a abrogation of our responsibilities:  We let students make a decision known to put them at unnecessary risk (we knew they were likely to fail).  Most colleges did not continue this ‘worst practice’ (as opposed to best practice), with the result that the placement system continued to have a differential impact on known groups of students.  That problem continues to the present day, as a general condition.  [Some colleges, systems, and states use either placement systems that moderates the impact (true multiple measures) OR have implemented new curricula which make the results more tolerable (pathways).]

For some history of placement policies, see https://ccrc.tc.columbia.edu/media/k2/attachments/college-placement-strategies-evolving-considerations-practices.pdf  .

The content movement impacting developmental mathematics in the early 1980s was a ‘trickle-up’ reaction to K-12 math reform in the prior decade or two.  The K-12 math reform is usually called “new math”, which failed because the curriculum was designed by university math education professors with little attention to the teachers who would try to deliver it.  Even though we can see the “DNA” from this New Math within the modern curricular standards of NCTM, AMATYC, and MAA, there was a back-lash in K-12 that drifted up to college … “BACK TO BASICS”.

There were very few college level books that implemented New Math designs; most were (and still are) very similar to the K-12 math predated New Math.  However, here was an opportunity for college math faculty to create developmental mathematics courses with balanced and effective approaches to multiple levels of learning — including reasoning and communication.  Our collective response was to regress even further on the levels we sought to deliver in our curriculum.  We reduced the amount of reading in our books, added examples, grouped the student practice by type, and generally made choices guaranteed to limit the student benefit for their efforts.

The two movements (right to fail, back to basics) involved forces that could have had that synergy necessary for significant long-term change.  We should have had one response to resolve both issues … change our curriculum in a basic way so that entering memory levels of particular skills do not determine success; rather, the entering level of understanding would determine success.

In my view,  the “New Life Project” represents this type of approach with developmental courses that are far less sensitive to remembered skills (Math Literacy, Algebraic Literacy), which means that they are far more accessible to all parts of our student population.  The fact that this solution appeared and gained support 30 years after the first opportunity indicates to me that our profession has been resistant to progress.  It’s not that dev math did not change between 1985 and 2010; it’s that all of the other changes did not address the core problems we face.  We needed other external forces acting upon our work before we were willing to try something different enough to possibly make real progress towards helping all students succeed.

We currently are in the ‘next big opportunity’ to make progress.  Let’s be sure to do things this time that will get us significantly closer to our goals.

 
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A “Golden Age”: Forty Five Years of Dev Math, Part II

In my continuing account of a history of developmental mathematics, we are moving from the early 1970’s to the late 1970’s.  Although ‘dev math’ existed before the 1970s (the ‘origins’), my experience started then … and this period coincides with other shifts (such as the founding of AMATYC).  This post will look at the patterns of the late 1970s and how some of them impact us in 2017.

Faculty in mathematics, and observers, might assume that developmental mathematics has always been trying to justify its existence.  However, for the early part of this story, policy makers tended to ignore both the need for developmental mathematics and out outcomes.  Budgeting in this period would reward enrollment, and developmental math classes were both easy to populate with students and economical for the institution.

These conditions resulted in larger enrollments in our courses, which contributed to one aspect of a ‘golden age’:

Dozens of publishers actively sought authors and new textbooks.  Derivatives of these textbooks still dominate the book ‘market’ today.

One of these textbooks initially begun in this period is “Keedy/Bittinger”, and the “Lial/Miller” texts also began at this time.  Previous textbooks tended to be knock-offs of high school books, and now the focus was placed directly on the needs of our courses and students.  However, the content was still organized by typical topics in chapters like one would see in high school books, and this generally continues until quite recently.  The content was quite traditional and procedural; the innovations focused on the use in a ‘college’ course by adults.  This is when “workbooks” became popular, providing instructors with homework submission before the internet.

The current environment has focused on the price of textbooks.  I think it is interesting that in the 1970s the price of textbooks was just as high (relative to the “CPI”, for example) … and that the buyer got just the book.  Today, with prices a bit above the adjustment for CPI, the buyer often gets online access.  Clearly, perception is the most important issue in an economic decision like ‘buy a textbook’.  [Students also did not have any purchase options in the 1970s.]

As the enterprise of developmental mathematics expanded, some concerns developed around ‘proper placement’.  Since this preceded most of the technology we presume today, “checking prerequisites” was an enormous undertaking for an institution.  Many colleges  had been letting students enroll for courses based on the student’s perception about what was needed.  This period pre-dated the placement tests we are accustomed to, which led to another aspect of a golden age:

Many institutions invested resources in developing their own placement instruments.

In many institutions, this meant that math departments did some analysis of what students needed to know before a given class.  Likely, a majority of these efforts produced assessments very similar to the items on Accuplacer and Compass, with a focus on one type of error … not letting a student register for a class when the test indicated a high chance of not passing.  Some of these institutions were in New Jersey, where (a few years later) the items from these original institutional placement tests were incorporated into the New Jersey Basic Skills tests, which is where many of the Accuplacer original items came from.

The emphasis on avoiding a single type of error has been at the center of mathematics placement until the present, though forces are pushing us to move beyond this concern.  We have been so focused on avoiding “over placement” that we have a strong tendency to under place students — putting them in courses for which there is little need.  That pattern has left us open to external criticism, and lies at the core of the “Complete College America” attack on remedial mathematics.

Placing students has been more about “avoiding failure” in a higher course than with the question of the “best placement” for students.

The current efforts in true ‘multiple measures’ placement are aimed at answering the better question.

I think it is important to recognize that some of the institutional efforts at placement in this era were more sophisticated in their goals and more creative in the resulting assessments.  Many of this novel approaches were shared at the first few AMATYC conferences I attended a decade later.  However, almost all of these indications of diversity were overwhelmed later during the ‘systemic years’ (another period in our history, in the 1990s).  We have generally lost the institutional placement instruments, with a few surviving as supplemental devices used by individual faculty or specific courses

Obviously, this period I am calling “a golden age” was not such a good thing.  The trends begun here caused us to under-place millions of students, and also to use textbooks which presented high-school mathematics at a low level of learning.  However, this period saw growth and large investments by both institutions and publishers.

As we move from a 1970s ‘golden age’ into the 1980s, we will be describing the impact of “back to basics” in an era prior to any content standards in the profession.

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The Origins: Forty Five Years of Dev Math, Part I

I’m getting somewhat close to the end of my career, and I expect that AMATYC 2017 is the last AMATYC conference that  I will attend.  Most likely, it is natural for people to contemplate the arc of history at this point (whether this arc bends towards justice is another question).  I will be writing a series of posts on the history of (my) developmental mathematics, which might be presented at a session in San Diego.

For me, the origins lie in a coincidence:  having ‘trained’ as a high school math teacher, I was unable to find a teaching job that did not involve moving.  I applied for a part-time job at the local community college, and in a fit of inexplicable errors, was hired.  The job involved supporting the operations of the college’s “Math Lab”, where several remedial math courses were offered in a self-paced, mastery format.   The time was the early 1970s.

In general, those remedial courses were intentional copies of K-12 courses from a short period prior to this time.  We had middle-school math (basic math), beginning algebra, geometry, and intermediate algebra; soon after I started, we began offering a metric system course, a desk-top computer course, and a sequence of two statistics courses (which had a beginning algebra prerequisite … quite ahead of its time).  The faculty in charge of the courses for students were, in general, current or former high school math teachers; familiarity with K-12 math was a high priority in hiring, and support for student success was not even considered.

The core of the ‘developmental math’ curriculum was the 3 course sequence aligning with grades 8, 9, and 11 .. basic math, beginning algebra and intermediate algebra.  At this time, the mode for a student’s high school math was ‘algebra I’, with a fourth of recent HS graduates never having had any algebra course.  Those on a ‘college-prep’ track certainly had more, but the community college policies were not targeted towards the college-prep students.

This was the time period when a pattern was started that still holds in many parts of the country:

Since most of the students graduating from high school had not taken ‘algebra II’, intermediate algebra is ‘college credit’ and often meets an associate degree requirement for general education.

The rationale for this policy lost its validity within about decade, as the majority of students began to graduate with algebra II credit on their transcript.  Colleges have been slow to update their general education policies to reflect fundamental shifts in HS course taking behavior.

In terms of “hot topics” in developmental mathematics education, it was all about two systemic features:

• Curricular materials that required little reading and provided ‘clear’ examples with lots of practice.
• Alternative delivery methods, including self-paced and programmed learning.

The first element reflected the high-school context for  the period prior to this … school textbooks were intended to be ‘teacher-proof’ (anybody could teach math), and the content was all about procedures to calculate answers in arithmetic and algebra.  That context has changed in a basic way, as the result of the teaching standards over the past 30 years (NCTM, AMATYC, etc).  Like the general education policy, math faculty have not altered the core focus of the curriculum; most current materials still focus on clear examples and lots of practice (though there is often more reading involved).

Our focus in alternative delivery methods, though cast in naive terms, was actually critical to trends that continue through today.  Most of us find it funny that ‘programmed learning’ was a “Thing”; the central idea was to have an assessment ‘every page’ and the student was ‘branched’ to a different next page, depending upon their answer.  In more recent times, this idea has been done in a more mature fashion with adaptive computer tutor designs.

The essential transaction that was being developed in these early days was “student — does math — correct OR recycles to re-learn it, repeat”.  Faculty had a role, but this role was not seen as the most essential role for student learning.  In contrast, much of our current professional development puts great emphasis on faculty interacting with students.  Although there is an obvious and valid basis for this emphasis, I wonder if perhaps we would be better off focusing more on the student interaction with mathematics.

A subsequent post will look at the period of a few years following this ‘origins’ time of the early 1970s.

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