Towards Effective Remediation

Do we have a vision of effective remediation … a model which minimizes the pre-college level work for students, in total, while providing an opportunity for all adults to be included in the process of completing credentials leading to better employment and quality of life?  Based on some 39 years in developmental education, what would I suggest?

I have been thinking, as hard as I can, lately on the problems caused by policy makers looking for a simple solution.  Often, the policy makers’ interest in remediation has been prompted by reports issued by groups like Complete College America (CCA); the CCA “Bridge to Nowhere” report is excellent use of rhetorical tools, but is not a good foundation for building policies in support of effective remediation.  The simple solutions involved are usually crafted by groups that do not include people with expertise in developmental education.  Somehow, the viewpoint that we present, as experts, is difficult to understand by non-experts; perhaps some policy makers are worried that experts will only want to preserve the current system, or that we will suggest that even more courses be provided in our field.

Effective remediation involves providing the appropriate learning opportunities for each learner so that the learner reaches college courses with adequate preparation.  Traditionally, we establish remediation in discrete content areas (reading, writing, math), with an independent decision in each area based on a placement test.  Some promising practices have evolved recently with efforts to link developmental content courses, and efforts to include learning skills.   Especially within mathematics, considerable effort has been invested in creating a modularized approach; modularization is a topic of its own.  However, two observations might help us:

1. Each student is considered for 0 to 4 developmental courses in each of the 3 content areas, usually based on one placement test in each area.
2. The content is the developmental courses is often severely constrained by the historical roots of the system; especially in mathematics (though still true in reading and writing), the focus is on mechanics and procedure, with less emphasis on reasoning and analysis.

For us to develop a vision of effective remediation, we need to understand the deeper problems with the existing system such as those suggested by these observations.  In order to provide appropriate learning opportunities (whether courses, workshops, or other experiences), we need a more advanced conceptualization of remediation itself.  We need to more beyond a simple binary choice independently made in discrete content areas based on one test in each.

I suggest that we consider the following framework:

• Students roughly within a standard error of placing in to college work in a content area be provided just-in-time remediation and register for the college course.
• Students over one standard error away are placed into one of two populations based on other measures (such as high school GPA).  Some might be placed into the ‘just-in-time’ remediation group.
• The low-intensity developmental students are placed into a one-semester ‘get ready for college work’ course in one or more content areas.
• The high-intensity developmental students are provided a year of connected course work which blends reading, writing, math, and learning skills designed to address content and thinking needs.

The first two categories involve a significant portion of our developmental students, who have less intense needs; their remediation can be quicker than we often provide now.  For those who ‘almost place’ into college work, the ‘discontinuity’ research on placement tests suggests that we might be able to avoid any developmental enrollments in that content area.   The low-intensity developmental students are those who are not predicted to succeed in college but have limited needs; within mathematics, this group would include those who can review areas of algebra and quantitative reasoning in one course with minimal support outside of the class.

The high-intensity developmental group would include students with broad needs across multiple content areas.  These are the students who now struggle to complete developmental courses.  However, their educational needs are not limited to the content area skills; reasoning skills and study skills are a problem for many students in this group.  I am envisioning a two-semester package of courses (three or four each semester) with intentional overlap of cognitive skills being addressed … the math course, the reading course, and the writing course would all address issues of inference and concise language use.  This high-intensity group would also have a student-success type course to prepare them for the academic demands of the college course that lie outside of a content area.

Here is an image of this model:

A goal of this model is to make a better match between student needs and the remediation that they receive.  Our traditional system is designed for the ‘low-intensity’ type of student, and I believe that these students are well served on average.  The just-in-time remediation group is the source of our current problems from the policy makers; because these people exist in our current developmental program when the evidence raises questions about this practice, policy makers generalize the conclusion to all developmental students. 

The biggest change, and our largest opportunity, comes from the high-intensity group of students.  In our society, these are often called ‘low-skilled’ adults; they might be functionally literate (or perhaps not), and generally have few options in the economy.  Our traditional developmental program tends to be either limited in helpfulness or a problem for these students.  In a mathematics class, the high-intensity students have difficulty with both the mathematical ideas and the language factors in the work.  We tend to expect some magical cognitive growth in these students, as if working on discrete content areas will generate spontaneous global changes in the brain; I have no doubt that this does, in fact, happen to some students … I have seen it.  However, we do not create conditions for the larger cognitive changes.

Colleges might create a one-semester option for the less intense of the high-intensity group — those who can accomplish the goals with a one-semester package.  Smaller colleges might have difficulty with the logistics of this, while larger colleges would probably benefit from having two categories of high-intensity students.  Part of the rationale for the design for high-intensity need students is that preparation for them, is a more complex challenge.  Some will have had special services in the K-12 schools, and some will have significant learning disabilities.  This is the group most at risk; if community colleges are to serve all adults, then our remediation design needs to provide an appropriate pathway through to college work.  The alternative is to have a significant group of adults who will always be economically and socially vulnerable.  This high-intensity group are the ones that we need to educate policy makers about, so that they can understand the needs better — both the student needs, and our needs if we are to truly help them.

If you would like to do some reading on research related to this model, much of what I am thinking of resides in reports from the Community College Research Center (CCRC) at Columbia (http://ccrc.tc.columbia.edu/). Two specific articles: placement tests in general (http://ccrc.tc.columbia.edu/Publication.asp?uid=1033) and skipping developmental based on discontinuity analysis (http://ccrc.tc.columbia.edu/Publication.asp?uid=1035).    An article of interest by Tom Bailey and others on state policy appears at http://articles.courant.com/2012-05-18/news/hc-op-bailey-college-remedial-education-bill-too-r-20120518_1_remedial-classes-community-college-research-center-remedial-education.

Join Dev Math Revival on Facebook:

What the Experts Say … about Remediation

In our profession (developmental mathematics), the most common phrase this year seems to be “remediation is a failure”; states consider banning all developmental courses, and organizations call remediation a ‘bridge to nowhere’.  What is the validity of these statements?  What is the true status of developmental education in 2012? 

To start with, take a look at a recent article by Hunter Boylan and Alexandros Goudas called “Knee-Jerk Reforms on Remediation”   see      http://www.insidehighered.com/views/2012/06/19/essay-flawed-interpretations-research-remedial-education#ixzz1yG6A5hL2.  Boylan and Goudas review the largest studies that are cited for the ‘failure’ statement, and easily point out the limitations of the research involved.  Some studies employ a discontinuity analysis around the cut score for placement into developmental courses as an estimate of the effects of remediation.  Other studies employ large data sets over a period of time to produce a demographic summary of who is referred to developmental math, who completes developmental, and who completes a college course.  Like other demographic work, these studies can not prove causality.  Neither type of study is a scientific basis for measuring the effect of developmental courses; both are valid estimates to determine the presence of a problem.

Now, I need to address two things … first, why the ‘failure’ message is the default position for so many people inside and outside of the profession; second, what is the true condition of developmental mathematics. 

The failure message is most heard from two sources:  the non-profits advocating for change and a completion agenda, and the foundations funding much of our experimentation.  Neither of these sources is unbiased.  However, sheer repetition from apparently independent sources creates the impression that the failure message is valid.  I think the use of certain metaphors (like ‘bridge to nowhere’) creates an impression of certainty of conclusions, and suggests a cultural acceptance of ‘failure’.  One problem we face is that we have used similar tactics ourselves, as in ‘drill and kill’ and ‘guide on the side’; proof by metaphor …or proof by rhyming … is not scientifically valid.

The true condition of developmental mathematics is much more subtle, which brings with it opportunities and challenges.  A simple ‘failure’ message is easier to interpret and act upon (basically, throw it out!).  The fact is that developmental mathematics delivers some benefits to many students.  The problem is not a total failure of the concept but a lack of an appropriate model to implement the mission and goals.  Developmental mathematics has its roots in remedial mathematics, which was a deliberate repetition of school mathematics; this, in turn, was based on a selective admissions college or university approach.  The vast majority of developmental mathematics is currently carried out in the community college setting, with a diverse population of students; many of these students have an occupational goal … although they may eventually consider a university, their current education is employment based.  Of course, many other students have a university goal.

We have not had a model appropriate for our population of students.  We need to create a deliberate sequence of mathematical experiences to prepare students as quickly as possible for places they will have quantitative needs, whether STEM-bound or not.  Even for STEM students, our existing curriculum is not a deliberate model; the current model presumes that exposure to a topic at a simple level will enable more advanced thinking in a complex setting.  We need a model that emphasizes basic mathematical ideas from the beginning (the ‘good stuff’, as I call it), and let go of making sure that students can produce volumes of correct answers to symbolic questions with fractions and percents … or equations with fractions or radicals.  Mathematical reasoning is far more important than a bag of 100 symbolic tricks and procedures.

The true condition of our profession is that we have become confused by the combination of our own frustrations and these external failure messages.  Ours is a noble calling … if done correctly, developmental mathematics can be part of the process that enables people to be upwardly mobile; instead of the younger generation having a lower standard of living, we can part of the process that creates a better life for the next generation.  Developmental mathematics can also be part of the process of major adjustment for adults who find that their occupation is no longer available.

The true condition of developmental mathematics is an opportunity for the transformative change to sound mathematics to help our students succeed in college and in society (quantitatively).  We face great opportunities; we are not a failure.  We need to look past the external messages to examine our profession with honesty and vision.  Together, we can meet this opportunity with pride and enthusiasm.

 
Join Dev Math Revival on Facebook:

Math Applications … Magic of “Is”

What price are we willing to pay for ‘correct answers’?  What gains (benefits) should students expect for dealing with applications in a math class?

In our beginning algebra class this week, we spent much of our time on applications.  Many of these were the typical puzzle problems involving tickets and cars, integers and angles.  As is normal for this course, students really wanted some magic — a rule that would help them get the correct answer for all of the problems.  Some of the students remembered some magic from a prior math class; one piece of magic was the word ‘is’ … the other piece of magic was a triangle (for mixtures).

We often provide rules (whether perfect or not) that are meant to help students get more correct answers for applications (broadly stated as word problems involving a context).  We tell students that “of” means multiply, and that “is” means equal; the prototype for both rules is the “a is n% of b” template (a worthless model, as normally taught).  Students who have experienced this ‘correct answer’ driven course encounter many problems when faced with a narrative about an application, where ‘of’ is the normal preposition and ‘is’ is the normal verb connecting phrases.  We train our students to surface-process language for the sake of correct answers, and wonder why students continue to have problems with applications.

One of the most challenging problems we did this week was this simply-stated problem:

A store claims that they markup books by 30%, and the selling price for one book is $79.95. Find the cost of the book to the store (before the markup was added).

Every student in this particular class was a graduate of our pre-algebra course, where this same problem was done as part of a longer chapter on percents and applications.  Every student in this class wanted to either multiply by 30% or divide by 30%; a few students thought that there was a second step where they needed to add or subtract this result.

Quite a few of the students could do this problem:

A store sells a book that has a cost of $61.50, and they have a markup on books of 30%. Find the selling price.

Their success on this arithmetic problem was not based on understanding the words any better (the words are the same).  Their success was based on the ‘magic’ rules we had given them that happen to work: multiply by the percent, add or subtract if needed.

The whole point of experiencing applications such as these is to build up the student’s mathematical reasoning.  There might be magic in the world, but magic is not reasoning.  Correct answers based on locally-working magic is worse than wrong answers based on weak reasoning.   If our courses include applications, keep the magic of “is” out of the course … and all other magic. 

 
Join Dev Math Revival on Facebook:

Reform Models in Developmental Mathematics

For many years, our developmental mathematics programs were based on a remedial image — filling in the ‘swiss cheese’ of student’s knowledge of school mathematics, with the school mathematics based on an archaic content (circa 1965).  Now, for the first time, we have an opportunity to explore a model of developmental mathematics that is based on mathematical needs of students — designed especially for community colleges.

During the June 6 (2012) webinar, Uri Treisman presented some general concepts to guide our work in reforming our curriculum; my component of the webinar dealt with applying these concepts in our departments.  In this post, I want to share two possible structures for reform of developmental mathematics as presented that day.  [The recording of the webinar will be available later this summer.]

One approach to reform is to target reform for particular groups of students.  You might identify students who need an intro statistics course, or those who need a quantitative reasoning course, and design a prerequisite course just for these students.  In this approach, the existing developmental mathematics curriculum is left undisturbed … at least for now.  The resulting curricular model looks something like this:

This ‘targetted’ approach is reflected in the Statway and Quantway work, for example.  However, this is not the only … nor necessarily best … approach.  Since our content is heavily influenced by archaic high school content, the mathematical needs of students — especially in reasoning and transfer of learning — would be better served by a total reform.

A reform for all students (total reform) has a goal of replacing existing courses.  In this model, the beginning algebra course is replaced by mathematical literacy course (which is also part of the target reform model); the intermediate algebra course is replaced by a reform algebra course … which some students would not have to take to meet their math needs. 

This reform for all students model creates this visual:

The reform algebra course (“B” in this visual) might be the one described as “Transitions” in the New Life model; see http://dm-live.wikispaces.com/TransitionsCourse.  Some colleges might consider a combined beginning & intermediate algebra course for course B; this is not a reform course (as the content is the traditional … and archaic … material).  Another option in this total reform model is to create a faster path in pre-calculus — blend ‘course B’ (reform algebra) and pre-calculus in to a 2 semester sequence for those students. 

Reform in developmental mathematics is needed.  However, reform in developmental mathematics is not sufficient; we also need to reform the introductory college mathematics courses to reflect current needs and professional knowledge.  Our students deserve the best mathematics we can provide, both in developmental and college-level courses.

 
Join Dev Math Revival on Facebook: