Ignore Common Core?

Can college math faculty ignore the Common Core?  Specifically, can those of us working in developmental mathematics ignore the Common Core?

If you need to read more about the Common Core Math Standards, take a look here http://www.corestandards.org/the-standards/mathematics. The Standards are listed for each grade K to 8, and then high school by area of mathematics.

As you might know, a primary motivation for the Common Core was that of alignment … getting K-12 outcomes to align with expectations, especially for college readiness.  This alignment is connected to the standardized tests used for ‘No Child Left Behind’ (NCLB) as well as some teacher evaluations.  [A current theme in teacher evaluations is the use of ‘value added models’ (VAM), which is a statistical methodology to estimate the impact of individual teachers; I may address VAM in a future post.]

A logical approach might be to think that … if a student places in to developmental mathematics … there is no reason that we need to be especially aware of the Common Core.  If this placement is accurate, we might conclude that the Common Core ‘did not work’ for whatever reason, so our work is independent.

Look at the situation in a different ‘frame’:  Because the Common Core is closely tied to standardized testing and NCLB, the mathematics assessed is often discrete skills with a focus on procedures and simple applications.  This emphasis in K-12 will, therefore, tend to produce students in college — whether ‘developmental’ or not — who have a less complex package of mathematical proficiency.   

I have been suspecting something like this happening in the last few years (even before Common Core, though the Common Core will expand the impact) … students obtain about the same average scores on placement test even though their functioning, mathematically, is more limited.  Solving a linear inequality might go okay for them, and then difficulty emerges when there is a discussion about how to represent the solutions in a different way.  Finding slope from two ordered pairs might be okay, and then confusion appears when slope needs to be interpreted in words or a context.

Recently, I did a post on “Lockhart’s Lament”; in that essay, an observation is that a sure way to ruin a subject is to require all students to ‘take it’.  With the Common Core, we have a movement to make all students take the same subject for almost all of their K-12 experience.  Since this ‘subject’ is almost always tied to standardized tests and sometimes to teacher evaluations, the forces operate on the subject to reduce all topics to operational steps.  (I’m reminded of the “paint by numbers” analogy in Lockhart’s Lament.)

Policy makers are often looking for simple solutions, which makes the Common Core look very attractive as well as standardized tests.  If only we could present ‘understanding and reasoning’ as simple solutions for the mathematical needs of K-12 students.  Are not those the central enablers of success for students  in our college courses?

We ignore the Common Core at our own peril.  Some college faculty actively support the use of the Common Core mathematics standards, and there is a real danger that this wish will be granted.  There is no single mathematical standard in the Common Core that I object to; the tragedy is that the summation (or integration in the mathematical sense, if you will) of the Common Core is a worsening of the mathematics problem in colleges … starting with developmental, but including all college mathematics in the first two years.
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Do we need developmental education?

You may have seen the news story about Connecticut considering a law that would eliminate all developmental education in the state … except for imbedded remediation and an ‘intensive college readiness program’. General story: http://communitycollegespotlight.org/content/connecticut-may-end-remedial-requirement_8674/ and more details http://www.insidehighered.com/news/2012/04/04/connecticut-legislature-mulls-elimination-remedial-courses

I see two basic issues raised by this.  An obvious issue is a statement about the perceived value of developmental education.  In the case of mathematics, some developmental programs have 4 courses before the first college-level math class; a logical analysis of this system can easily show that there is a basic design flaw … a two-year ‘getting ready for college’ track is enough credits for a major, but these are courses that do not have value in themselves.  A rejection of this design is basic in our development of the New Life model, where we reduce that pre-college work to 1 or 2 courses, depending on the student’s program.  Does a rejection of the 2-year developmental math program imply that it can be replaced by a ‘just in time’ remediation model, combined with a boot-camp experience?

The other basic issue raised is the change process.  We appear to be in a period when politicians are policy makers in broad areas of education.  It’s not like the state said ‘We are spending way too much money … and not getting enough benefit; we are appointing a task force of experts who are charged with creating a model that meets the needs of our communities in a process that is much more efficient’.  Whatever the process was, the lawmakers believe that they have a solution that can be legislated.  Have we done such a poor job of articulating the power of a good developmental program that lawmakers believe that this is a solution? 

I have no doubt that some students — even many students — would be well served by the ‘imbedded + boot camp’ model; historically, we have underestimated the capabilities of students to cope with challenges … if they have a little more support.  However, I believe that this model will leave many students defeated; these will be the types of students for whom community colleges were created — the ‘first generation college’, the un-empowered and vulnerable, and those for whom the K-12 system did not ‘work’ … as well as the returning adult. 

We need to do a better job of articulating the power of what we do everyday.  Our courses are not just about some collection of basic skills, that our goals include developing learning and thinking in our students; we need to tell people in authority that we have expertise and methods that produce results.

We also need to be willing to ‘take the criticism’ … that our developmental programs have become entrenched and stagnant systems that do not serve enough students nor well enough for all students, that we can develop models that better serve our students with dramatically reduced credits and costs.  If we continue to insist on the same-old programs, or even if we fail to recognize this problem, then we deserve to have others (like politicians) determine a better system.  I believe that we are wise enough to do the right thing.

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Developmental: Skills or Capabilities?

At a recent conference (MDEC, the Michigan affiliate of NADE), we were having a conversation with Hunter Boylan about developmental education. One of the participants commented that a major concern was that students sometimes leave developmental courses as developmental students.

What did they mean by ‘developmental students’?  I think the basic concern is that students were leaving our courses without the capabilities (not abilities) to handle college academic work.  One of my colleagues who is a ‘reading’ faculty commented that it seems like the developmental course was a collection of discrete skills which did not add up to any additional capabilities.

There is a somewhat different point of view for professionals engaged with NADE or the National Center for Developmental Education (which is directed by Hunter Boylan).  Their framework specifically includes ‘personal growth’, referring to a collection of cognitive and affective factors … which I categorize as ‘capabilities’.    [The “NADE-type” definition of developmental implies that it is not a nicer name for remedial; most of us in the mathematics community equate the two phrases.   As implemented, most developmental math programs are ‘remedial’; I wish they were not.]

In reading, for example, parsing a phrase … vocabulary … decoding … these are groups of skills; however, without additional capabilities, students remain developmental in their functioning — resulting in a higher risk of failure in college courses.  That is, basic literacy skills are not sufficient in a good developmental reading program.

How does a typical developmental math program compare?  Sadly, I think we are the epitome of skill courses that do not impact the capabilities of our students.  A beginning algebra course usually has 8 to 10 chapters of material, with a preponderance of … parsing phrases … vocabulary … procedures; our ‘applications’ are mostly stylized puzzle problems which avoid the need to think deeply about relationships.  In fact, we sometimes take pride in providing rules or tools to cope with word problems so students do not have to analyze them. 

A basic reason behind the New Life project is this:  serving up skills with symbols does not change the capabilities of our students.  Dealing with basic concepts, connections, transfer, analysis … this process changes the capabilities of our students.  It is our belief that good preparation for college work is based on an emphasis on deeper academic work in ‘developmental’ courses.

As you look at the learning outcomes for New Life (or the New Mathways), keep in mind that the model is making a serious attempt to build student capabilities.  Since there is not a linear sequence of basic skills, you will have to work harder to understand what the curriculum is trying to accomplish for our students.

Any course — ‘developmental’ or not — that only seeks to add skills to a student, without a larger focus on capabilities, is a missed opportunity.  When that course is used in a gate-keeper fashion (like mathematics is), we need to move towards a design that truly helps our students.

 
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Reducing Costs of Developmental Math

The ‘cost’ of developmental mathematics is one of the major issues being faced by states and institutions.  Although this is commonly stated as a financial cost, an equally important cost is present — the cost to our students (time, credits).  There is also a risk involved, given that most studies of developmental education seem to report that students placed into developmental courses have a lower chance of completing programs.

Is there a solution?  Is there a simple solution?

In a recent post (https://www.devmathrevival.net/?p=756) I talked about what a reasonable prerequisite to beginning algebra could be.  That post hinted at some solutions which could be implemented to reduce costs.

Here is a simpler solution that can be done right away, and may not have the kinds of problems you might predict:  Place students into beginning algebra, even if their placement test suggests something before that.

I admit that this is a strange suggestion.  However, think about how ‘strange’ our current system can be … at many institutions, students who start in pre-algebra have about a 20% ‘chance’ of completing their college level math requirement.  Are we helping that 20% so much that this process is worth the risk to the other 80%?

Before you jump up and down, screaming “THIS IS NOT GOING TO WORK” … look at some potential numbers.  If we assume that 70% of the students placed into pre-algebra pass that course, and that 50% of those who proceed to beginning algebra pass that second course, we have a net 35% who complete beginning algebra in the second semester.  This 35% assumes that ALL students will pass pre-algebra continue to beginning algebra; this is not reasonable.  Based on estimates from my data work at my college, from 70% to 80% actually go on to the second course.  Applying the highest rate (80%) to the 35% value gives us a realistic net of 28% … about 28% of students who start in pre-algebra complete the beginning algebra course the second semester.

What would we expect to happen to students who go directly to the beginning algebra course?  Would they be half as likely to pass that course, compared to having taken pre-algebra?  This “half” seems like a reasonable estimate (and may be too low).  Half of 50% … is 25%.  Since 25% is generally not statistically different from 28%, there is a good chance that placing all students in to beginning algebra would not create any additional risk to the student — and would save a semester of credits.

There is actually evidence that suggests this 25% ‘direct’ rate is too low.  A study (http://ccrc.tc.columbia.edu/Publication.asp?UID=1030) shows the predicted pass rates for students above and below the cutoff on a placement test (Accuplacer in this case); the predicted values for rates of C or better are above 30% for all placement test scores.  If this is accurate, then it would actually help students to never place them in to pre-algebra.

Based on years of talking with students struggling in beginning algebra, there is another reason why ‘skipping’ pre-algebra might help quite a few students: of the students who pass pre-algebra, quite a few of them were not challenged by the material … in fact, many do not study … and still pass.  This “no study, and pass” experience is exactly the opposite of what most students need; students need to know that working hard and continuing are critical for academic success.  As long as a pre-algebra course is primarily procedural, with a focus on correct answers, it will not contribute to habits that help students in later courses.

Think of that … a simple solution that saves a lot (money & credits for students, costs and resources for colleges), with either no risk or even some significant benefits.  Let’s agree to not place any student into pre-algebra (or whatever your course is called); if their placement test suggests that they don’t have enough ‘basic skills’, we would be better off placing them into beginning algebra anyway, perhaps with a sheet of references for refreshing those skills.

 
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