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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Implementing Better Math Courses, Part II: Helping All Students

The traditional developmental math curriculum generally fails the mission to help students succeed in college mathematics; this failure is due to both exponential attrition (too many courses) and to an obsolete curriculum.  In this post, I will describe a specific implementation plan that addresses these problems for ALL students.  #NewLifeMath

I call this implementation “medium” because it goes beyond the low results of pathways models.  The next level of implementation involves eliminating all courses prior to the beginning algebra level … and replacing beginning algebra with Math Literacy for College Students.

Here is an image of this implementation:

This implementation means that the majority of students can have a maximum of one pre-college math course (developmental level), since most students do not need to take a pre-calculus course.  The Math Lit course was designed to serve the needs of all students — STEM and not-STEM; even though many of the initial uses of Math Lit were in pathways implementations, the course is much more powerful than that limited usage.

Doing this medium implementation results in significant benefits to students.  In order to make this work, the institution needs to address interface issues — both prior to Math Lit and after Math Lit.

Math Lit has a limited set of prerequisite knowledge that enables more students to succeed, compared to a beginning algebra course.  However, this set is not trivial.  Institutions doing a medium implementation will need to address remediation ‘prior’ to Math Lit for 20% to 40% of the population in the course.  One methodology to meet this need is to offer boot-camps prior to the semester, or during the first week.  The other method (which my institution is starting this fall) is to embed the remediation within the Math Lit course; in our case, we are creating a second version of Math Lit for 6 credits (with remediation) to run parallel to our 4-credit Math Lit course.

After Math Lit in this model, there is an interface with intermediate algebra.  At some institutions, this will work just fine … because the intermediate algebra course includes sufficient review of basic algebra.  In other institutions, some adjustments in intermediate algebra are needed.  My own institution is playing this safe for now … after Math Lit, students can take a ‘fast track’ algebra course that covers both beginning and intermediate algebra.  I don’t expect our structure to be long-standing, for a variety of reasons (most importantly, that we are likely to reach for the next level of implementation where intermediate algebra is replaced by algebraic literacy).

I suspect a common response to this implementation model is something like “this will not provide enough algebra skills for STEM”.  I would point out two factors that might help deal with this apparent problem:

1. Taking beginning algebra prior to intermediate algebra is currently associated with lower pass rates (controlling for ACT Math score).  [See https://www.devmathrevival.net/?p=2412]
2. The basic issue for STEM students is not skills — it is reasoning.  [See AMATYC Beyond Crossroads http://beyondcrossroads.matyc.org/   and the MAA CRAFTY work http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/crafty ]

This medium implementation model is conceptually similar to the Dana Center New Mathways Project, where they follow up their adaptation of Math Lit (“FMR”) with their STEM path courses.  Like them, we have confidence based on professional work over a period of decades that this implementation model will succeed.

In a pathways model, only those students who are going to take statistics or quantitative reasoning get the benefits of a modern math course.  In the medium implementation, this set of benefits is provided to ALL students.  In addition, the medium implementation eliminates the penalties of having more than 2 developmental math courses in the curriculum, by dropping all courses prior to Math Lit.  The result is that the majority of students will have 1 (or zero) developmental math course, with improved preparation as well.

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Why Does Co-Requisite Remediation “Work”?

Our academic leaders and policy makers continue to get strongly worded messages about the great results using co-requisite remediation.  Led by Complete College America (CCA), the originators of such messages suggest that this method avoids the failures of developmental mathematics.   [For example, see http://completecollege.org/spanningthedivide/#remediation-as-a-corequisite-not-a-prerequisite] Those of us in the field need to understand why intelligent people with the best of intentions continue to suggest this uni-directional ‘fix’ for a complex problem.  #CCA #CorequisiteRemediation

I want to focus on the educational component of the situation — not the political or fiscal.  In particular, I want to explore why the co-requisite remediation results have been so encouraging to these influencers.

One of the steps in my process was a nice conversation with Myra Snell.  I’ve known Myra for a while now, and she was involved with the New Life Project as well as the Carnegie Foundation’s Statway work.   What I got from this conversation is that Myra believes that there is a structural cause for the increased ‘throughput’ in the co-requisite models.  “Throughput” refers to the rate at which students complete their college math requirement.  Considerable data exists on the throughput using a traditional developmental math model (pre-algebra, beginning algebra, then intermediate algebra); these rates usually are from 7% to 15% for the larger studies.  In each of the co-requisite systems, the throughput is usually about 60%.  Since the curriculum varies across these implementations, Myra’s conclusion is that the cause is structural … the structures of co-requisite remediation.

The conclusion is logical, although it is difficult to determine if it is reasonable.  Scientific research in education is very rare, and the data used for the remediation results is very simplistic.  However, there can be no question that the target of increased throughput is an appropriate and good target.  In order for me to conclude that the structure is the cause for the increased results, I need to see patterns in the data suggesting that ‘how well’ a method is done relates to the level of results … well done methods should connect to the best results, less well done methods connect with lower results.  A condition of “all results are equal” does not seem reasonable to me.

Given that different approaches to co-requisite remediation, done to varying degrees of quality, produce similar results indicates some different conclusions to me.

• Introductory statistics might have a very small set of prerequisite skills, perhaps so small a set as to result in ‘no remediation’ being almost equal to co-requisite remediation.
• Some liberal arts math courses might have properties similar to intro statistics with respect to prerequisite skills.
• Some co-requisite remediation models involve increased time-on-task in class for the content of the college course; that increased class time might be the salient variable.
• The prerequisites for college math are likely to have been inappropriate, especially for statistics and liberal arts math/quantitative reasoning.
• Assessments used for placement are more likely to give false ‘remediation’ signals than they are false ‘college level’ signals.

Three of these points relate to prerequisite issues for the college math courses used in co-requisite remediation.  Briefly stated, I think the co-requisite results are strong indictments of how we have set prerequisites … far too often, a higher-than-necessary prerequisite has been used for inappropriate purposes (such as course transfer or state policy).  In the New Life model, we list one course prior to statistics or quantitative reasoning.  I think it is reasonable to achieve similar results with the MLCS model; if 60% of incoming students place directly in the college course … and 40% into MLCS, the predicted throughput is between 55% and 60%.  [This assumes a 70% pass rate in both courses, which is reasonable in my view.]  That throughput with a prerequisite course compares favorably to the co-requisite results.

The other point in my list (time-on-task) is a structural issue that would make sense:  If we add class time where help is available for the college math course, more students would be able to complete the course.  The states using co-requisite remediation have provided funds to support this extra class time; will they be willing to continue this investment in the long term?  That issue is not a matter of science, but of politics (both state and institution); my view of the history of our work is that extra class time is usually an unstable condition.

Overall, I think the ‘success’ seen with corequisite remediation is due to the very small sets of prerequisite skills present for the courses involved along with the benefits of additional time-on-task.   I  do not think we will see quite the same levels of results for the methods over time; a slide into the 50% to 55% throughput rate seems likely, as the systems become the new normal.

It is my view that we can achieve a stable system with comparable results (throughput) by using Math Literacy as the prerequisite course … without having to fail 40% of the students as is seen in the corequisite systems.

 
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Implementing Better Math Courses, Part I: A Starting Point

I want to share some specific options for implementing courses from the New Life Project, both to encourage more people to consider using those courses and to also increase our collective understanding of changes in the field.  In this Part I, I’ll talk about the easiest implementation; later parts will describe increasingly complete replacements of the traditional curriculum.  #NewLifeMath #MathLiteracy

The easiest curriculum reform to implement is often the side-by-side approach, also called ‘pathways’.  In this structure, the existing courses are left intact but some students are referred out of beginning algebra … based on a target of either statistics or quantitative reasoning.

This pathways model looks something like this:

Overall, about half of the known implementations of New Life courses is done within this ‘low’ implementation (side-by-side, or pathways).

The advantages of the low (pathways) implementation are:

• Easier to get ‘buy-in’ from other math faculty
• Allows for learning process (for teaching differently, with different content)

Some of the disadvantages are:

1. Depends upon effective advising for ‘recruiting’ students
2. Complicated structure and communication
3. Perhaps too easy to get buy-in from other math faculty
4. Provides benefits to some students, while the remainder experience an unimproved curriculum

In general, this pathways model (also called ‘low implementation’) is done by colleges.  When states implement the courses, they usually do so at the next level — replacing beginning algebra with “MLCS”.  In my view, the pathways (side-by-side) structure is not sufficiently stable to survive long-term.  As in my institution, however, this pathways model allows a math department to begin the process of curriculum reform without major disruptions.

The disadvantages listed for this model may actually be an advantage for some institutions.  In coping with the advising and communication challenges, the college may see improvements in those general processes.  I’ve heard of those types of outcomes happening at some institutions, though the positive outcomes depend upon good planning and lots of hard work; in my institution, for example, those disadvantages did not result in significant improvements in general systems.

Within the mathematics community, this pathways model is what ‘got traction’ a few years ago.  The side-by-side nature is not a long-term solution, and tends to reinforce that antiquated curriculum in college algebra or pre-calculus.  A more mature response to our curriculum would achieve some level of replacement; those replacement models will be explored when I talk about “medium” (MLCS instead of beginning algebra) and “high” (MLCS and Algebraic Literacy instead of traditional developmental algebra courses).

Overall, this pathways (side-by-side) low implementation model is an excellent choice for how to start the long-term process of improving our curriculum.  The key is to judge what your department and institution are ready for … pushing for a replacement of the old courses can be counter-productive, if the readiness is not there.  Once a department is working in the pathways model, we can more easily build the readiness for the replacement stages.

Nationally, the Carnegie Foundation’s Pathways (Quantway, Statway) are pretty much limited to the ‘low’ implementation; the purpose of those pathways is to accelerate math for students who are not in the ‘STEM’ path.  On the other hand, the Dana Center’s New Mathways Project is flexible enough to allow for both pathways (side-by-side) and replacement models.  Like the New Life project, the Dana Center work includes the MLCS course (called “Foundations of Mathematical Reasoning”, or FMR).  Differences emerge when we get to the replacement models.

If you are considering implementing a new course like MLCS or FMR, I hope the points above are helpful.  Feel free to leave a comment or send me an email for clarification or further information!

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