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.

 Join Dev Math Revival on Facebook:

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.

 
Join Dev Math Revival on Facebook:

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.

 
Join Dev Math Revival on Facebook:

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.

 Join Dev Math Revival on Facebook: