What’s Wrong with That? Mainstreaming, Co-requisite Remediation

Some of us perceive “co-requisite remediation” as a risk to mathematics education because the model is based on a perceived lack of benefits from stand-alone remedial courses.  I believe that we also have additional reasons to be concerned.

I’ve written previously on academic research on the actual benefits of stand-alone remedial courses, including http://www.devmathrevival.net/?p=2541.  This does not mean that all developmental math courses provide benefits for all students; the data does mean that passing developmental math courses provides benefits in that later performance is greater than would be predicted for the abilities of the student at the onset.

The people and groups advocating co-requisite remediation (aka ‘mainstreaming’) do not use academic research to justify the approach.  Almost all data shared publicly in their efforts is demographic in nature and framed in a way that can only support what they want us to see, just like a graph with a scale chosen so that the results are skewed in the chosen direction.  I want to ignore this dishonesty issue, and move on to matters of substance.

Issue Number 1:  No Problem Being Solved
The advocates start with statements such as the following [TBR is Tennessee Board of Regents]:

Prior to 2014, more than 60 percent of TBR’s students system-wide began college needing remediation in math, reading and/or writing. In response, faculty across the system paid significant attention over the last decade to improving the effectiveness of developmental education. Schools implemented and developed nationally acclaimed models around modularization, computer-aided instruction and personalized learning support rather than traditional developmental instruction.
Despite all of this effort, while more students were completing their developmental work, credit-bearing classes were another matter. Overall, only 12.3 percent of the students who began in developmental instruction completed a credit-bearing mathematics class within an academic year, and 30.9 percent completed a credit-bearing writing class. Something had to change.

[See https://higheredtoday.org/2015/10/21/reimagining-remediation-in-tennessee/]

The implication is that the 12.3% rate is the problem being addressed.  This rate is the result of several factors: number of developmental math courses for each student; quality of those courses; quality of the faculty; institutional support for dev math; appropriateness of the math prerequisite of the college math course; quality of the college math course; advising about college math; quality of the college math faculty; institutional support for the college math course, etc.  The solution blames the ‘problem’ on the first set as a single factor, called ‘developmental math’.  As we know, an ill-defined ‘problem’ will not lead to scientific progress … progress will be luck and local coincidences.

Issue Number 2:  Ignoring Student Differences
By placing the blame on an ill-defined ‘developmental mathematics’, the advocates place all students in the same treatment.  Developmental mathematics courses can range from arithmetic to intermediate algebra; in our grade-level fixation, this corresponds to 4 to 6 different grade levels … can one treatment provide success for all of these students?

I’ve previously published this chart, which provides a more scientific method of matching the new treatment to students.

Matching students to remediation model






Issue Number 3:  Ignoring Course Issues at the College Level
What is an appropriate prerequisite to intro statistics?  How about liberal arts math?  A quantitative reasoning course?  College algebra?  The settings for most data cited by the advocates involve the same prerequisite for all of those — intermediate algebra.   We in AMATYC know that intermediate algebra is not an appropriate prerequisite for non-STEM math courses.

The advocates waste institutional and state resources by providing extra course support for courses which had inappropriate prerequisites … most of the improved throughput could have been achieved by simply correcting the faulty prerequisite on the non-STEM math courses.  However, the advocates don’t mind wasting these resources:  because many students would have passed the college math course WITHOUT support, their “results” are guaranteed to be better.

Issue Number 4:  Ignoring Course Issues at the Developmental Level
The advocates never seem to have raised the basic question:

What pre-college mathematics abilities can be justified as necessary and sufficient for success in various college math courses?

I have written repeatedly about the mis-match between traditional remedial math courses and the needs of college math courses (STEM and non-STEM).  Recall that the advocates treat ‘developmental math’ as a single concept and conclude that it does not help students.  Apparently, the advocates see no benefit in looking at fixing the basic problem … they would rather play the snake-oil-salesman role for co-requisite remediation.  There is no scientific method in their advocacy, so they will end up solving the wrong problem as well as creating some new problems.

If the advocates of co-requisite were really interested in solving the real problems, the advocates would also support basic reform in developmental mathematics such as Mathematical Literacy & Algebraic Literacy and similar efforts.  However, the advocates are generally just as dismissive of these professional efforts as they are the traditional courses.  If the advocates took a little time to investigate, they would discover that the reform courses generally use just-in-time remediation to minimize the number of pre-college math courses for every student.   I’ve never seen or heard an advocate voluntarily mention AMATYC New Life, Carnegie Pathways, or Dana Center New Mathways.

Issue Number 5:  Jeopardizing the STEM Path
Co-requisite remediation is almost always implemented only for non-STEM paths.  In some cases, a student who does not qualify for the first college-level STEM math course (pre-calculus, for example) is tracked OUT of the STEM programs.  This has led some people to comment that the recent movements are relegating community colleges to the trade-school and vocational roles, since relatively few students arrive ready for STEM math courses.

This relates to issue #2 (equating all students) … students arrive with gaps in abilities for a variety of reasons.  One of my students this semester is an immigrant from Cuba, who placed in to beginning algebra … with a goal of being a medical doctor.  I’ve no doubt that he will achieve his goal, and he is happy with the opportunity he’s had in our developmental math courses.  However, in the world envisioned by the advocates … this student would be told to select a different major.

Issue Number 6:  Ignoring Any Data that Does Not Support the Cause
In the scientific method, we make a hypotheses … we test it, and then we look for the results when others try ideas related to it (same, related or different).  The advocates never cite data that is not flattering to their cause.  I can’t cite much data like that either — because almost all of the data being collected is done at a low-level of sophistication and it therefore not published anywhere else.

Are you aware of any treatment for humans that ALWAYS works for any sample and any population?  That is what the advocates say: Co-requisite remediation is always better.  Do we think that it is reasonable for a model to always work, even when not implemented well?  We should be seeing some failure stories; analyzing failures teaches more than successes.  By only publicizing success stories, the advocates doom their own cause; they are more interested in selling their particular solution than they are in helping create long-term progress for our students.

I’m reminded of an interesting article by John Ioanidis  called “Why Most Published Research Findings Are False  http://robotics.cs.tamu.edu/RSS2015NegativeResults/pmed.0020124.pdf  .  Note that the advocates present data that is not research, so they have even more reason to be ‘false’ positives.


The advocates of co-requisite remediation (mainstreaming) include some within academia.  With the presence of so many issues and defects in their work, I am left with major concerns about the health of higher education:  How can we help our students achieve a quality education and upward mobility when such an ill-founded movement can control so much of our enterprise?

It’s time to push back; a prolonged conversation between doubters and advocates so that we can find real solutions to problems based on a deep analysis of root causes and other contributing factors.  A ‘quick fix’ is seldom either.  We need better solutions, starting with better math courses.

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Active Learning Methods in Developmental Mathematics

We’ve all had this … students who attempt to complete a math course based on memorization; such students often report frustration when asked to apply knowledge in any way that differs from what they ‘learned’.  As mathematicians, we see the process of that frustration as a key part of what mathematics is all about.

As teachers, we sometimes behave in the same memorizing way.  For example, we attend a workshop session on a particular active learning method or methods.  After some planning, we begin to use those methods in our classes and usually feel good about the experience.

Any teaching method will be more effective if the teacher understands the whole story — how the method works and WHY it works, with connections to other knowledge about the learning process.

If you look for data and research on active learning methods, the results look very good.  However, most of that data collection is done by experts using the methods.  An observational study was done using a random sample of college biology teachers, with an eye towards seeing this positive impact of active learning methods.  Some faculty used little ‘active learning’, some used a lot, and some were in-between.  The results?  Well, not so good for ‘active learning’.  See http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3228657/?report=classic for the Andrews article “Active Learning Not Associated with Student Learning in a Random Sample of College Biology Courses”

It turns out that many faculty using active learning methods have memorized the ‘steps’ for the method but did not understand the method well enough to adjust it for their students … and also could not accurately monitor the process.  Putting students in pairs with a problem for ‘think-pair-share’ will not automatically produce better learning.  Understanding is important for us, as well.  The authors of the study listed above believed that was the critical factor for not seeing positive results.

I’ve been saying something for 20 years, and believe it is still true today:

Developmental mathematics … we are a desperate people!

Partially because we’ve been teaching the wrong courses, our work has not been successful over a long period of time and over a large range of locations.  That process results in us looking for something … almost anything … that might help in our classrooms.  In many ways, this is the same attitude that our students bring to our developmental math courses.  We see something — it might help, so we quickly try it out in our classes.  Learning a new teaching method is like any other learning: there is a process, and ‘knowing steps’ does not equal ‘learning’.

Here are some pointers on how to use new teaching methods effectively … ‘active learning’ or otherwise.

  1. Experience the method yourself repeatedly:  for example, use the think-pair-share process to learn something new.  Look for the how & why of the method, and develop an intuition for what it looks like when it works.
  2. Read and use multiple sources of information.  You are most likely hearing about a method from somebody who heard about it from somebody who heard about it … each of those stages involves filtering and distortion (just because it’s human communication).  Multiple sources will provide a more accurate picture of the method.
  3. Use the engineering principle: estimate the time it will take, then double the number and use the next larger size.  “10 minutes” becomes “20 hours”.  That’s a little extreme, but valuable as a guideline … nothing breaks a teaching method quicker than rushing it.  This applies to both your planning time, and to the operational time in the classroom for the method.
  4. Don’t be deceived by appearances and initial student reactions, which are often skewed (more positive) by ‘something new’.  Assess the results using multiple measures — direct observation, one-minute paper, survey, quiz, etc.
  5. Assume that your first use is a crude approximation requiring a number of adjustments based on analysis of results.  Proficiency is the result of lots of practice … and learning from that practice.
  6. Allow yourself to reject one method and switch to something else.  We all need to become effective teachers, but we don’t need to become the SAME teacher.  Use methods you can be enthusiastic about, since that helps students almost as much as the details of the method.
  7. Talk about your experiences with colleagues you trust.  You are learning something new, and it’s complicated … verbalizing helps your brain clarify the process and the results.  Ideally, you would form a ‘lesson study’ type group working on the teaching method.

I wrote those pointers with active learning methods in mind, but they apply to any method — including lecture (aka “direct instruction”).  Lecture, sometimes defined as continuous elaboration by the ‘teacher’, is a valuable tool for us; it’s just not adequate in general, and needs to be used intentionally.  My own classes tend to be several lectures of 5 to 10 minutes separated by some active learning method.  You might experience ‘experts’ who claim that we don’t remember what we hear; the irony is that the message the expert is delivering is one which they HEARD.   The critical thing is to have the learner’s brain engaged with the material using multiple teaching methods appropriate to the content; listening is an effective method for some things.

We each need to develop high levels of skills with a variety of teaching methods, because that is what experts do.  Limiting our methods, or using methods poorly, impedes our student’s learning … or even causes damage to their learning.  Just like our students, we need to have a growth mind set.

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Open Educational Resources in Developmental Mathematics

Tired of your students paying over $100 for a textbook?  Frustrated by the cost of getting access to the online homework system that goes with the book?  It’s no news that “OER” is a general movement in colleges & universities.  At some institutions, including mine, there is a direct push for faculty to consider Open Educational Resources (OER) in an effort to save students money.

One concern with OER is that the materials available are almost always (perhaps always) designed for traditional courses, so that OER is a force opposing change in our curriculum.  For example, the “Open Stax” information (https://openstax.org/) information includes this:

“All textbooks meet standard scope and sequence requirements, making them seamlessly adaptable into existing courses.”  [in “About Our Textbooks”]

I’ve not seen any OER materials for Mathematical Literacy, nor for a modern pre-calculus course.  It is easy to understand why OER is traditional in orientation … the resources are judged by how many uses are tracked, and that can be done most easily by fitting materials to old courses.  What might not be as easily seen is the fact that OER is missing an element in the publishing business — the developmental editor, where ‘developmental’ refers to the creation of new textbooks for changing or new markets.  People say that OER is driven by users (faculty); that is not entirely true … I think OER is more driven by carrying on tradition in the name of saving students some money.

Of course, I know that some individual authors deliberately go someplace new.  For example,   see Schremmer’s work at http://www.freemathtexts.org/ where you’ll find nothing traditional.  The problem with this approach is that the materials … as interesting and high quality as they might be … remain on the fringes of the profession.  Perhaps the long-term benefit of these textbooks from the underground is more in the maturation of the profession, more than the particular materials themselves.

Within my college, “OER” even includes generic resources like the Khan Academy and Purple Math.  This inclusion is a bit humorous … math teachers have a strong tradition of connecting their students to such resources, but it has little to do with textbooks.  These free resources also represent a force which encourages us to maintain a traditional curriculum.

If our profession were content with the status quo, then there are few reasons to avoid using OER materials — you might get a traditional ‘book’ complete with online homework system for a lot less than a typical commercial textbook at full-retail price.  Faculty can even modify some of the material to represent their own well-founded (and not well-founded) views … like “never mention PEMDAS, because it’s an awful approach to mathematics”.

Almost everybody teaching developmental mathematics as part of their full-time load has been in contact with representatives of the main commercial publishers.  The publishers are sophisticated, in general, and know that they need to “do something” to keep our business in the face of the OER push, not to mention the presence of Amazon in the used-book market.  I’ve had conversations with field reps & editors from the big 3 (Pearson, McGraw Hill, Cengage); you can get a deal from the companies, though the discount rate appears to be inversely proportional to the company’s current market share.

With these discount deals, you can get a commercial textbook (as an e-book) with the online homework system for $50 to $80 per student.  The question might be:

Is the small savings ($10 to $40 less for OER with homework, compared to commercial book) a significant factor for students?

I think that the difference in cost between OER and commercial materials is relatively small now, and will tend to stay small.

So, I return to a prior statement, paraphrased:

OER materials tend to perpetuate the traditional math curriculum in colleges.

If you find OER materials that you are happy with, you might be able to save your current students some money (depending on how well your department can negotiate with publishers).  However, using OER will generally take you out of the process of basic improvements to your curriculum.  In my view, we should avoid using OER in both developmental mathematics and college mathematics so that we can maintain our focus on improving the curriculum first.

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Regional Accreditation and the Problems in Developmental Mathematics

This post is directed at my colleagues in community colleges and similar institutions … and the bodies that conduct our accreditation processes.  My conjecture is that the accreditation process contributes to the problems we have in developmental mathematics, and that this situation deserves corrective action on the part of the regional accreditation bodies.

The regional accreditation bodies use criteria for faculty credentials; in the case of the HLC, the specific wording is:

Faculty teaching general education courses, or other non-occupational courses, hold a master’s degree or higher in the discipline or subfield. If a faculty member holds a master’s degree or higher in a discipline or subfield other than that in which he or she is teaching, that faculty member should have completed a minimum of 18 graduate credit hours in the discipline or subfield in which they teach.
(see http://download.hlcommission.org/FacultyGuidelines_2016_OPB.pdf)

In all cases that I am aware of, remedial courses are not included in the ‘other non-occupational courses’ category.  The result is the common practice:

Anybody holding a bachelor’s degree, in any field, is qualified to teach developmental mathematics.

Within this common practice, a significant portion of faculty teaching developmental mathematics were original credentialed for high school teaching … usually in mathematics, but not always.  Teaching high school mathematics is a worthy profession, often undertaken by dedicated individuals who are either not-appreciated or blatantly disrespected.  However, the context for teaching developmental mathematics is fundamentally different from teaching high school mathematics.

Among those fundamental differences is the fact that developmental mathematics at an institution is directly connected to college-level math courses.  The developmental algebra courses are expected to prepare students for specific college-algebra or pre-calculus courses, with an expectation of content mastery and retention … those elements have a much lower priority in the high school setting.

Another critical difference between the high school and developmental math contexts is that the developmental math faculty need to interact positively with faculty teaching the college level courses.  Since so many of the developmental mathematics faculty have less qualifications, this presents a cultural and social problem:

How can faculty of college-level mathematics have professional respect for faculty of developmental math courses with ‘lower’ qualifications?

A typical developmental math course has a focus on procedural skills and passing, while the college-level math courses tend to emphasize application and theory … sometimes with a much lower emphasis on passing.  In many colleges, this difference in emphasis leads to either a de facto or official separation of developmental math from college math.

The biggest single problem we have in developmental mathematics is the emphasis on a long sequence of courses — 3 or 4 courses below college level.  The inertia for this structure is based, in large part, on the parallel to grade levels in K-12 work … arithmetic (K-6), pre-algebra (7-8), beginning algebra (9) and intermediate algebra (10 or 11).  I have found that many faculty in developmental mathematics have a difficult time letting go of this grade-level focus (courses in K-12).

The fact that the accreditation process ‘ignores’ developmental math teaching qualifications is the problem I think needs to be addressed.  Should faculty teaching developmental mathematics have the same credential requirement as college-level math faculty?  There are strong arguments for this approach.  Should faculty teaching developmental mathematics have credential requirements beyond that of K-12 math teachers?  In my view, definitely yes.

At this point in time, it is not realistic to hold developmental math faculty to the same credential requirement as college level math — we just don’t have enough people qualified at that level.  However, I think we can develop some reasonable standard which approaches that goal.  Perhaps  ‘masters in math education, or a minimum of 9 graduate credits in mathematics’ could be used as an alternative (in addition to the ‘regular’ credential for general education).  The professional organizations, primarily AMATYC, could develop such a criteria in collaboration with the accrediting bodies.

My purpose is more about pointing out the problem and need to develop a solution, rather than advocate a particular criteria.  Achieving a solution could be measured practically:

Can all mathematics faculty in a community college, regardless of normal teaching assignments, understand and contribute to all curricular discussions involving any math course at the institution?

Until we see this result, students will continue to experience a developmental math program that tends to be too long and overly connected to the K-12 ‘grade level’ structure.


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