Why We NEED Stand-Alone Remedial Courses

Extremes are seldom a good thing.  At one extreme, we had 4 or more developmental math courses at many institutions.  In the future, we may end up with zero dev math courses — as people drink the ‘co-requisite cool-aid’.  Moderation is usually a better thing than extremes. We need to consider the diverse reasons why remedial math courses make sense.

Let’s begin with a conjecture … that it is feasible to use co-requisite remediation for students beginning any college math course.  Each of the 3 major types of introductory math courses would have the needed remediation (pre-calculus, statistics, quantitative reasoning), with each of these remediation needs being different from the others.  In some implementations, the co-requisite remediation is built on the entire content of the old dev math course; however, students typically do not need to pass the remedial component — if the college course is passed, the remedial portion is either automatically passed or does not count.

This conjecture follows a common theme in the policy world — ‘stand-alone developmental courses are a barrier to student success’.  We have some evidence that the research data does not support this conclusion — the article recently cited here, written by Peter Bahr, as well as the CUNY “ASAP” program (I’ll post about that research in the near future).  The ‘data’ used for the stand-alone statement is demographic — students who place into a dev math course (especially multiple levels below college) are far less likely to complete a college math course.

Let’s pretend that the research in favor of dev math courses is mistaken, and that the true situation is better estimated by those attacking stand-alone courses.  What are the overall consequences of ‘no more dev math courses’?

In community college programs, students are faced with quantitative issues in a variety of courses outside of mathematics.  Here is a realistic scenario:

• In a biology course, a student needs to understand exponential functions and perhaps basic ideas of logarithms.
• In a nursing course, a student needs to apply dimensional analysis to convert units and determine dosage.
• In an economics class, a student needs to really understand slopes and rate of change (at least in a linear way).
• In a chemistry class, a student needs to apply equation concepts in new ways.

If we no longer have stand-alone developmental math courses, there are basic consequences:

1. ALL courses in client disciplines will also need to do remediation (unless they require a college-level math course).
2. Courses in client disciplines that do require a college math course will need to have that course listed as a prerequisite — even if the math needed is at the developmental level — OR such client discipline courses will also need to do remediation.
3. Courses in client disciplines will always need to do remediation if they require a college math course that does not happen to include all of the background needed.

We might face similar consequences within mathematics, though those seem minor to me.  The consequences are trivial within STEM programs, but that is small consolation to the majority of our students (and colleagues).  The mis-match situation (#3) occurs with stand-alone courses, but will be more widespread without them.

Getting rid of stand-alone dev math courses is extremely short-sighted.  The premise is that all of a student’s needs in developmental mathematics relate to the college math course they will take.  If a student’s program is well served by statistics, does this  mean that all courses in the program are well served by a statistics course?

Even if co-requisite remediation produces sustainable high levels of success, the methodology fails to support our student needs — ‘solving’ one problem while creating several others.  Eliminating stand-alone developmental math courses is not a solution at all … eliminating stand-alone courses puts our students at risk AND harms our colleagues in partner disciplines.  I would also predict that co-requisite remediation will disproportionately ill-serve those who most need our help — students of color and students from lower “SES” (the low-power students).

The root-problem is not stand-alone courses — the root problem is that we have a too-long sequence of antiquated dev math courses.  We have a model for solving this problem in the New Life Project, with two modern courses: Mathematical Literacy, and Algebraic Literacy.  Both courses modernize the curriculum so that it serves mathematics as well as our client disciplines, with a structure that allows most students to have one (at most) pre-college course.

The co-requisite movement states that our responsibility ends with the college math course.  Our relationships with other disciplines is based on a larger responsibility; our work on student success factors within our courses is based on a larger responsibility.  Declaring that “the results are in” and “co-requisite remediation WORKS” … amounts to defining a problem out of existence while ignoring the problem itself.

Nobody needs co-requisite remediation; nobody needs 4 or 5 developmental math courses.  Our students need an efficient modern system for meeting their quantitative needs in college, regardless of their prior level of success.

 
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The Case for Remediation

Today, I am at a state-wide conference on developmental education (“MDEC”), where two presenters have addressed the question “is remediation a failure?”.  As you likely know, much of the recent conversation about developmental mathematics is based on a conclusion that the existing system is a failure.  The ‘failure’ or ‘success’ conclusion depends primarily on who is asking — not on the actual data itself.

The “failure” conclusion is presented by a set of change agents (CCA, CCRC, JFF); if you don’t know those acronyms, it’s worth your time to learn them (Complete College America; Community College Research Center; Jobs For the Future).  These conclusions are almost always based on a specific standard:

Of the students placed into developmental mathematics, how many of them take and pass a college-level math course.

In other words, the ‘failure’ conclusion is based on reducing the process of developmental mathematics down to a narrow and binary variable.  One of today’s presenters pointed out that the ‘failure’ conclusion for developmental math is actually a initial-college-course issue — most initial college courses have high failure rates and reduced retention to the next level.

The ‘success’ conclusion is reached by some researchers who employ a more sophisticated analysis.  A particular example of this is Peter Bahr, who has published several studies.  One of these is “Revisiting the Efficacy of Postsecondary Remediation”, which you can see at http://muse.jhu.edu/journals/review_of_higher_education/v033/33.2.bahr.html#b17.

My findings indicate that, with just two systematic exceptions, skill-deficient students who attain college-level English and math skill experience the various academic outcomes at rates that are very similar to those of college-prepared students who attain college-level competency in English and math. Thus, the results of this study demonstrate that postsecondary remediation is highly efficacious with respect to ameliorating both moderate and severe skill deficiencies, and both single and dual skill deficiencies, for those skill-deficient students who proceed successfully through the remedial sequence.  [discussion section of article]

In other words, students who arrive at college needing developmental mathematics achieve similar academic outcomes in completion, compared to those who arrived college-ready.  There is, of course, the problem of getting students through a sequence of developmental courses … and the problems of antiquated content.  Fixing those problems would further improve the results of remediation.

One of the issues we discuss in statistics is “know the author” … who wrote the study, and what was their motivation?  The authors who conclude ‘failure’ (CCA, CCRC, JFF) are either direct change agents or designed to support change; in addition, these authors have seldom included any depth in their analysis of developmental mathematics.  Compare this to the Bahr article cited; Bahr is an academic (sociologist) looking for patterns in data relative to larger issues of theory (equity, access, etc); Bahr did extensive analysis of the curriculum in ‘developmental math’ within the study, prior to producing any conclusions.

Who are you going to believe?

Some of us live in places where our answer does not matter … for now, because other people in power roles have decided who they are going to believe.  We have to trust that the current storms of change will eventually subside and a more reasoned approach can be applied.

In mathematics, we have our own reasons for modernizing the curriculum; sometimes, we can make progress on this goal at the same time as the ‘directed reforms’.  Some of us may have to delay that work, until the current storm fades.

Our work is important; remediation has value.  Look for opportunities to make changes based on professional standards and decisions.

I’ll look for other research with sound designs to share.  If you are aware of any, let me know!

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Co-Requisite Remediation and CCA (Saving Mathematics, Part V)

Complete College America (CCA) released a new report on co-requisite remediation this week.  Actually, that statement is not true … the CCA released a web site which shows some data on co-requisite remediation, with some user interaction.  What’s missing?  Anything that would help a practitioner judge whether they should consider co-requisite remediation!  #CCA #Corequisite #SaveMath

Many of us are dealing with policy makers in our states or institutions who see co-requisite remediation as the solution to the “developmental math problem”.  There are, in fact, serious problems in developmental mathematics; there are also serious problems with how ‘college math’ has been defined, and how policy makers are defining a problem away instead of solving it.

Within developmental mathematics, we have been working hard teaching the wrong stuff to our students, frequently using less-than-ideal methods to help them learn.  Our curriculum has too many courses, and the combination is lethal … not many students reach their dream.  When students proceed from developmental math to college algebra or pre-calculus, they often find that the gap in expectations between the two levels is very difficult to deal with.

Co-requisite remediation steps in to this complex problem domain, and declares that all will be fine if we just put students into college math with some support.  The most common (and sometimes the ONLY) co-requisite remediation done is in Intro Statistics and Quantitative Reasoning [QR] (or Liberal Arts Math).  The history, frequently, is that students had to pass intermediate algebra prior to these courses … even though that background has nothing to do with the learning; the requirement was to establish “college level”.

So, the CCA and allies declare that students can take Stat or QR instead of developmental math.  Of course this is ‘successful’; the old prerequisite was unreasonable, and the co-requisite method puts students directly in to courses they are relatively ready for, and also provides extra support (in some cases).  Many colleges, including mine, had already lowered the prerequisite for Stat and QR years ago; our results from both Stat and QR are better than what the CCA states for their co-requisite model.

The co-requisite ‘movement’ is an illusion.  The work succeeds (almost totally) because students are placed in to math courses that have minimal needs for algebra.  I get better results by just changing the prerequisite to Stat and QR.

We also face a risk to mathematics in this illusion:  students with dreams that involve STEM are frequently told that this dream is being shelved in favor of co-requisite remediation, that they will take either Stat or QR.  The path to calculus is either not available or involves work that is not articulated well to students.  Policy makers are treating math as a barrier to cope with, a problem to solve with the least remediation.  The need for mid- and high-skill STEM workers is well documented, but the co-requisite ‘solution’ often blocks the largest pool of students from those fields … the minorities, the poor, the students served by under-performing schools.

Society needs our work to succeed for all students.  We can not accept a solution which reduces upward mobility; a solution which does not provide ‘2nd chances’ is a risk to both mathematics and to a democratic society.

Don’t get me wrong — Stat and QR have a major role to play in our curriculum, and these courses might be the most common math courses students should take in college.  My main message is that we need to question the illusion called ‘co-requisite remediation’, AND we need to articulate a vision of our curriculum which enables ALL students to consider STEM and STEM-like careers.   [The New Life Project provides a vision of such a curriculum.]

If you really want to read the CCA “Report”, go to http://completecollege.org/spanningthedivide/#the-bridge-builders

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Intermediate Algebra Must Die!!

“Intermediate Algebra Must Die!” … I said this at two recent meetings (first at a conference, then at my college).  The need for this demise is ‘over-determined’, to use a social science phrase:  several factors, each of which would be sufficient, are present to create a conclusion with multiple rationales from different perspectives.  #IntermediateAlgebra #AlgebraicLiteracy  #NewLifeProject

The first rationale for the necessary demise of Intermediate Algebra comes from data concerning preparation for ‘college math’ (most often college algebra or pre-calculus).  The CCRC and ACT both have discontinuity regression research showing that intermediate algebra does not prepare students.  [See the first part of my presentation on Algebraic Literacy at https://www.devmathrevival.net/?p=2331.]  The most optimistic results show a 2% to 5% gain in pass rates after an intermediate algebra course compared to students with similar backgrounds; of the 4 data sets, 1 had this very small positive result … 2 have ‘null’ (no gain), and 1 has ‘negative’ (students do worse after intermediate algebra, compared to similar students who did not).

The second rationale for the necessary demise of Intermediate Algebra comes from the policies about degree requirements at our institutions.  At hundreds of institutions, students can meet a general education requirement for a degree by using the remedial math course called ‘Intermediate Algebra’.  This policy makes two horrible statements at once:  first, that we don’t think it is important for students to learn additional mathematics; second, that we don’t think students have sufficient abilities to learn additional mathematics.  We are not just accommodating negative perceptions about learning mathematics, we are reinforcing them.

The third rationale for the necessary demise of Intermediate Algebra comes from its origins:  Intermediate Algebra was copied from the high school curriculum during a period when procedure and repetition were emphasized (in reaction to the original ‘new math’) in a design based on low standards for teacher credentials (the thought was ‘make it teacher-proof’).  This origin of the course is clearly related to the data referenced above; however, this rationale is based on the contradictory nature of the course compared to any set of modern curricular standards (as in Common Core, or even the original NCTM standards).  Intermediate Algebra is a professional embarrassment.

The last rationale for the necessary demise of Intermediate Algebra comes from the politicization of developmental mathematics:  as long as we are teaching ‘high school courses’, policy makers are going to attack our curriculum in colleges.  These stakeholders do not see why they should pay a second time for the same treatment, and many do not see any appropriate benefit from the course.  This rationale, like the third, suggests that all traditional developmental mathematics be removed ASAP and replaced (to the extent needed) by modern courses designed for college use (such as the New Life Project courses, Mathematical Literacy and Algebraic Literacy).  A course being “pre-college” does not mean “high school”.

We need to ‘own our problem’; for too long, we have continued our weak copies of weak high school courses to stand in the way of actually preparing students.  We have taken the easy road, sometimes creating a significant revenue source for our colleges, when we should have focused on our students’ needs in college.  We have reinforced the “I can’t do math” belief, and sold our profession short.  We have placed our entire curriculum at risk by requiring many students to take high school courses in college.

Intermediate algebra must die!

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