Equity and Stand-Alone Remedial Math Courses

One of the key errors that co-requisite (mainstreaming) advocates make is the treatment of ‘developmental mathematics courses’ as a single concept.  We would not expect college students who place into arithmetic to have comparable outcomes to those who place into intermediate algebra.  However, most ‘research’ cited with damning results uses that approach.  We need to have a more sophisticated understanding of our work, especially with respect to equity (ethnicity in particular).

A local study by Elizabeth Mary Flow-Delwiche (2012) looked at a variety of issues in a particular community college over a 10 year period; the article is “Community College Developmental Mathematics: Is More Better?“, which you can see at http://mipar.umbc.edu/files/2015/01/Flow-Delwiche-Mathematics-2012.pdf   I want to look at two issues in particular.

The first issue is the basic distribution of original placement by ethnicity.  In this study, ‘minority’ means ‘black or hispanic’; although these ethnicity identities are not equivalent, the grouping makes enough sense to look at the results.  The study covers a 10 year period, using cohorts from an 8 year period; partway through the 8 year period, the cutoffs were raised for mathematics.

Here is the ‘original’ distribution of placement by ethnicity using the data in the study:

After the cutoff change, here is the distribution of placement:

Clearly, the higher cutoffs did exactly what one would expect … lower initial placements in mathematics.  However, within this data is a very disturbing fact:

The modal placement for minorities is ‘3 levels below college’ (usually pre-algebra)

This ‘initial placement’ data appears to be difficult to obtain; I can’t share the data from my own college, because we do not have ‘3 levels below’ in our math courses.  However, the fact that minorities … black students in particular … place most commonly in the lowest dev math course is consistent with the summaries I have seen.

We know that a longer sequence of math courses always carries a higher risk, due to exponential attrition; see my post on that https://www.devmathrevival.net/?p=1685    Overall, the pass rates for minorities is less than the ‘average’ … which means that the exponential attrition risk is likely higher for minorities.

The response to this research is not ‘get rid of developmental mathematics’; the research, in fact, shows a consistent pattern of benefits for stand-alone remedial math courses.  This current study shows equivalent pass rates in college math courses, regardless of how low the original placement was (1-, 2-, or 3-levels below); in fact, the huge Achieve the Dream (ATD) data set shows the same thing.  See page 46 of the current research study.

The advocates of co-requisite (mainstreaming) focus on the fact that 20% or more of the students ‘referred’ to developmental mathematics never take any math AND the fact that only 10% to 15% of those who do ever pass a college math course.  The advocates suggest that a developmental math placement is a dis-motivator for students, and claim that placing them into college math will be a motivator.  Of all the research I’ve read, nothing backs this up — there are plenty of attitudinal measures, but not about placement; I suspect that if such studies existed, the advocates would be including this in their propaganda.

However, there is plenty of research to suggest that initial college courses … in any subject … create a higher risk for students; it’s not just mathematics.  So, the issue is not “all dev math is evil”; the issue is “can we shorten the path while still providing sufficient benefits for the students”.    This goes back to the good reasons to have stand-alone remedial math courses (see https://www.devmathrevival.net/?p=2461 ); although we often focus on just ‘getting ready for college math’, developmental mathematics plays a bigger role in preparing students.  The current reform efforts (such as the New Life Project with Math Literacy and Algebraic Literacy) provide guidance and models for a shorter dev math sequence.

Even if a course does not directly work on student skills and capabilities, modern developmental mathematics courses prepare students for a broad set of college courses (just like ‘reading’ and ‘writing’).  It’s not just math and science classes that need the preparation; the vast majority of academic disciplines are quantitatively focused in their modern work, though many introductory courses are still taught qualitatively … because the ‘students are not ready’.  Our colleagues in other disciplines should be up in arms over co-requisite remediation — because it is a direct threat to the success of their students.

Developmental mathematics is where dreams go to thrive; our job is to modernize our curriculum using a shorter sequence to give a powerful boost for all students … especially students of color.

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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 https://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.

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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Data on Co-requisite Statistics (‘mainstreaming’)

Should students who appear to need beginning algebra be placed directly in a college statistics course?  For some people, this is no longer a question — they have concluded that the answer is an unqualified ‘yes’.  A recent research study appears to provide evidence; however, the study measured properties outside of what they intended and does not answer a basic question.

So, the study is “Should Students Assessed as Needing Remedial Mathematics Take College-Level Quantitative Courses Instead? A Randomized Controlled Trial” by Logue et al.  You can read they report at http://epa.sagepub.com/content/early/2016/05/24/0162373716649056.full.pdf

The design is reasonably good.  About 2000 students who had been placed into beginning algebra at a CUNY community college were invited to participate in the experiment.  Of those who agreed (about 900), participants were randomly assigned in to one of 3 treatments:

1. Elementary Algebra regular    39% passed
2. Elementary Algebra with weekly workshops   45% passed
3. College Statistics with weekly workshops    56% passed

At these colleges, the typical pass rate for elementary algebra was 37% while statistics had a normal pass rate of 69%.

The first question about this study should be … Why is the normal pass rate in elementary algebra so appallingly low?  I suspect that the CUNY community colleges are not isolated in having such a low pass rate, but that does not change the fact that the rate is unacceptable.

The second question about the study should be … Would we expect a strong connection between completing remediation (or not) with performance in elementary statistics?   The authors of this study make the following statement:

it has been proposed that students can pass college-level statistics more easily than remedial algebra because the former is less abstract and ses everyday examples

In other words, statistics is not abstract … not mathematics at the college level.  The fact that statistics focuses on ‘real world’ data is not the problem; the fact that the study of statistics does not involve properties and relationships within a mathematical system IS a problem.  I’ve written on that previously (see “Plus Four: The Role of Statistics in Mathematics Education at https://www.devmathrevival.net/?p=976)

The study uses ‘mainstreaming’ in their descriptions of the statistics sections in their experiment; I find that an interesting and perhaps better phrase than ‘co-requisite’.  It’s unlikely that the policy makers will move to a different phrase.

The authors of this study conclude that many students who place into elementary algebra could take college-level math (represented by statistics in their study) with additional support.  The problem is that they never dealt with the connection question:  How much algebra does a student need to know in order to succeed in basic statistics?  The analysis I am aware of is “not much”; in the Statway (™) program, most of the remediation is in the domains of numeracy and proportional reasoning … very limited algebra.

This is the basic problem posed in all of the ‘research’ on co-requisite remediation:  students are placed into low-algebra courses (statistics, liberal arts math), and … when they generally succeed .. the proclamation is the ‘co-requisite remediation works!’.  That’s not what is happening at all.  Mostly what the research is ‘proving’ is that those particular college ‘math’ courses had an inappropriate prerequisite of algebra (beginning or intermediate).

Part of our responsibility is to explain to non-math experts what the relationships are between various math courses, using language and concepts that they can understand while preserving fidelity with our own work.  We need to make sure that policy makers understand that it is not an issue of us ‘not wanting to change’ … the issue is that we have a different understanding of the problem and potential solutions.  In many colleges, the math department is already ahead of where the policy makers want us to ‘go’.

I encourage you to read this study thoroughly;  Because it using a ‘control’ and ‘random assignment’ design, this study is likely to become a star for policy makers.  We need to understand the study and provide a better interpretation.

 
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Where Dreams go to Thrive … Part III (More Evidence)

The leading cause of bad policy decisions is the phrase “Research clearly shows … ” which suggests that all of us should accept one interpretation of some unnamed set of ‘research’ (most of which is not research at all).  Understanding the needs of students not prepared for college mathematics is a long-term process, involving prolonged conversations among professionals as we attempt to understand what the data and the research say about our work and our students.

My goal is to present another scientific research article on the impacts of developmental education — remedial mathematics in particular.  This article is by Bettinger & Long called “Addressing The Needs Of Under-Prepared Students In Higher Education: Does College Remediation Work?” which you can download at http://www.nber.org/papers/w11325.pdf

This research is based on a large sample of students in Ohio.  The strategy is to adjust for selection bias that is so strong in all studies on remediation — Students referred to remediation tend to have both lower specific skills (math) and more academic challenges.  The authors define a series of variables for this purpose, and eventually calculate a ‘local area treatment effect’ (LATE) which is partially based on the fact that cutoffs for remediation vary significantly among the 45 institutions of higher education in the data.  The analysis of “LATE” involved a restriction on the sample — towards the middle, where the cutoffs have more impact; this analysis excludes the weakest (roughly 10%) of the overall sample.

Key Finding #1: Equal Outcomes for those in Remediation
For outcomes such as dropping out and degree completion (bachelor’s) students who had remediation achieved similar outcomes to those who did not, once the selection bias was accounted for.

Key Finding #2: For those most impacted by remediation cutoffs, outcomes are improved
The “LATE” analysis showed that remedial students had a lower rate of dropping out and a higher rate of degree completion compared to similar students without remediation.  The authors attribute this as an accurate (perhaps even conservative) estimate of the benefits of remediation.

Here is a nice quote from their summary:

We estimate that students in remediation have better educational outcomes in comparison to students with similar backgrounds and preparation who were not required to take the courses.  [pg 19]

The research also explored the impact of remediation on student interest (as measured by type of major); you might find that discussion interesting, though it is not directly related to the question of ‘thrive’ in remedial math.  I say that because the initial major data was taken from the survey attached to the ACT exam — usually completed long before a student examines their actual choices at the college they enroll at.  The authors do find an interaction between remediation and changing type of majors (specifically, changing out of math-related majors).

This study, as the others I’ve listed lately, provide a different picture of developmental mathematics than we hear in the loud conversations by policy makers (Complete College America, for example) and proponents of ‘co-requisite remediation’.  Those external forces almost always refer to ‘research’ that is simple (few variables) and aggregated; they have not dealt with the selection bias problem at all.  If you read the pronouncements carefully, you’ll notice that the biggest evidence of our failure in remedial mathematics is the large group of students who never attempt their remedial math course(s); this ‘damning conclusion’ is presented without any evidence that the nature of the remedial math courses had any causative connection to that lack of attempt.

As professionals, it is our job to both learn about the valid research on our work (the good and not-so-good) and to inform others about what this research says.

Evidence exists which truly does indicate that remedial mathematics is where dreams go to thrive.

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