Dev Math: Where Dreams go to Thrive … Part II (Evidence)

Developmental mathematics is where dreams go to thrive; we have evidence that even the traditional courses help students succeed in college.  The narrative suggested by external political forces is often based on a simplistic view of students which is out of touch with reality.  Let’s help by spreading the word on a more complete understanding.

Students who need to take developmental math courses have a wide range of remediation needs.  Peter Bahr’s study on pathways with single or multiple domains of deficiency (https://www.devmathrevival.net/?p=2458) concluded that the basic college outcomes (such as earning a degree) show equivalent outcomes for groups of students (needed remediation versus not).

A totally different analysis by Attewell et al 2006 (see http://knowledgecenter.completionbydesign.org/sites/default/files/16%20Attewell%20JHE%20final%202006.pdf) also reaches a conclusion of equal results between groups in many ways.  Many studies of remediation are simple summaries of enrollment and grades over a short period of time.  The Attewell research was based on a longitudinal study begun on 8th graders in 1988 (thus, the acronym “NELS: 88”) done by the National Center for Educational Statistics.  Over an 12 year period, the study collected high school and college information as well as additional tests and surveys on this sample.

A key methodology in this research is ‘propensity matching’ — using other variables to predict the probability of an event and then using this probability to analyze key data.  For example, high school courses and grades, along with tests, were used to calculate the probability of needing remediation in college … where a sample of students with given probabilities did not take any remediation while another sample did.  An interesting curiosity in the results is the finding that low SES and high SES students have equal enrollment rates in remedial math when ‘propensity matched’.

Thrive: Key Result #1
Students taking remedial courses have a higher rate of earning a 2-year degree than students who do not take remedial courses with similar propensity scores for needing remedial courses.  Instead of comparing students who take remediation with the entire population, this study compared students taking remediation with similar students who did not take remediation.  The results favor remediation (34% versus 31%)

In the bachelor degree setting, the results are the other direction — which the authors analyze in a variety of ways.  One factor is the very different approach to remediation in the two sectors (4-year colleges over-avoid remediation, 2-year colleges slightly over-take remediation).   However, the time-to-degree between the two groups is very similar (4.97 years with remediation, 4.76 years without).

Thrive: Key Result #2
Students taking three or more remedial courses have just slightly reduced results.  This study shows a small decline for students needing multiple remedial courses: 23.5% earn 2-year degree, versus 27.5% of similar students without multiple courses.  The Bahr study, using a local sample, produced equivalent results in this same type of analysis.

It’s worth noting that the results for multiple remedial courses are pretty good even before we use propensity matching:  25.9% complete 2-year degree with multiple remedial courses versus 33.1% without.  This clearly shows that dreams thrive in developmental mathematics, even among students with the largest need.

Thrive: Key Result #3
Students taking 2 or more remedial math courses have results almost equivalent to other students.  The predicted probabilities for students with multiple remedial math courses is 23.8%, compared to similar students without multiple remedial math (26.7%).

Note that this study was based on data from prior to the reform movements in developmental mathematics.  Even then, the results were reasonably good and indicate that the remediation was effective at leveling the playing field.

Thrive: Key Result #4
This is the best of all:  Students who complete all of their math remediation have statistically equivalent degree completion (2-year) compared to similar students (34.0% vs 34.7%)

This result negates the common myth that taking multiple remedial math courses spells doom for students.  The data shows that this is not true, that completing math remediation does what it is meant to do — help students complete their degree.

I encourage you to take a look at this research; it’s likely that you will spot something important to you.  More than that, we should all begin to present a thrive narrative about developmental mathematics — because that is what the data is showing.

 
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Dev Math: Where Dreams go to Thrive

In response to data showing the exponential attrition of long sequences of developmental mathematics courses, some people are using the quote “developmental mathematics is where dreams go to die”.  This phrase has been one of the most influential statements in our field over the past 5 years — not because it is true but because people (especially policy makers) believe that it is true.

This is a normal political strategy: frame an argument in a way that there is only one answer (the one that ‘you’ want).  I’ve seen leaders at my own college use this method, often successfully. … and I imagine that you’ve encountered it as well.  As teachers at heart, this style of communication is not natural for us; we respond by reasoned arguments and academic research with a goal of getting everybody to understand the problem.

The difficulty is that leaders who use the “where dreams go to die” phrase have little interest in understanding the problem.  Their goal is to remove developmental mathematics as a barrier to student success.  The next phrase after “where dreams go to die” is often “co-requisite remediation”, with claims that this solution is a proven success because of all of the data.  Of course, our view of this data is a bit more restrained than the leaders and policy makers; this is not a problem for them, as they have the answer in mind — all we have to do is agree with it.

We must do two basic things so that we can really help our students succeed:

1. Shorten and modernize our mathematics curriculum, both developmental and college level.
2. Consistently use our narrative:  “Developmental mathematics is where dreams go to thrive!”

Much of the material on this blog, as well as the wiki (dm-live.wikispaces.com)is meant to help faculty with the first goal.  The new courses, Mathematical Literacy and Algebraic Literacy, allow us to provide great preparation for college level courses within an efficient structure which minimizes exponential attrition.

“Developmental mathematics is where dreams go to thrive”:  We need to articulate this accurate view of our work, which is valid even within the old-fashioned traditional curriculum with too many courses.  I’ve posted about some of the research with a ‘thrive’ conclusion:

• The Case for Remediation  (https://www.devmathrevival.net/?p=2461)
• Research Trends in Developmental Mathematics  (https://www.devmathrevival.net/?p=1176)

Also, a great project at CUNY called “ASAP” gets a glowing external evaluation:  http://www.mdrc.org/project/evaluation-accelerated-study-associate-programs-asap-developmental-education-students#overview  The ASAP model is currently being validated at other institutions.  Please let me know of other research showing that dreams thrive in developmental mathematics.

We should add our own ‘thrive’ stories and data.  For example, at my institution, we had 6 students start in pre-algebra and the proceed up to Calculus I in a four year period … 5 of them passed Calculus I on their first attempt.  If we believe the ‘die’ narrative, you would expect zero or 1 of these to exist; I am sure that most institutions have similar results to mine where the data shows more of a ‘thrive’ result.

Our traditional courses must go; we must do the exciting work of renewing the curriculum based on modern thinking about mathematics combined with more sophisticated approaches to instruction and learning.

However, that work will generally be wasted unless we establish a ‘thrive’ attitude.    The two conditions existing together create a new system that serves students well.  Developmental mathematics is where all dreams go to thrive.

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Algebra in General Education, or “What good is THAT?”

One of the questions I’ve heard for decades is “Is (or should) intermediate algebra be considered developmental?”  Sometimes, people ask this just to know which office or committee is appropriate for some work.  However, the question is fundamental to a few current issues in community colleges.

Surprising to some, one of the current issues is general education.  Most colleges require some mathematics for associate degrees, as part of their general education program.  Here is a definition from AACU (Association of American Colleges and Universities):

General education, invented to help college students gain the knowledge and collaborative capacities they need to navigate a complex world, is today and should remain an essential part of a high-quality college education.  [https://www.aacu.org/publications/general-education-transformed, preface]

What is a common (perhaps the most common) general education mathematics course in the country?  In community colleges, it’s likely to be intermediate algebra.  This is a ‘fail’ in a variety of ways.

1. Algebra is seldom taught as a search for knowledge — the emphasis is almost always on procedures and ‘correct answers’.
2. The content of intermediate algebra seldom maps onto the complex world.  [When was the last time you represented a situation by a rational expression containing polynomials?  Do we need cube roots of variable expressions to ‘navigate’ a complex world?]
3. Intermediate algebra is a re-mix of high school courses, and is not ‘college education’.
4. Intermediate algebra is used as preparation for pre-calculus; using it for general education places conflicting purposes which are almost impossible to reconcile.

We have entire states which have codified the intermediate algebra as general education ‘lie’.  There were good reasons why this was done (sometimes decades ago … sometimes recently).  Is it really our professional judgment as mathematicians that intermediate algebra is a good general education course?  I doubt that very much; the rationale for doing so is almost always rooted in practicality — the system determines that ‘anything higher’ is not realistic.

Of course, that connects to the ‘pathways movement’.  The initial uses of our New Life Project were for the purpose of getting students in to a statistics or quantitative reasoning course, where these courses were alternatives in the general education requirements.  In practice, these pathways were often marketed as “not algebra” which continues to bother me.

Algebra, even symbolic algebra, can be very useful in navigating a complex world.

If we see this statement as having a basic truth, then our general education requirements should reflect that judgment.  Yes, understanding basic statistics will help students navigate a complex world; of course!  However, so does algebra (and trigonometry & geometry).  The word “general” means “not specialized” … how can we justify a math course in one domain as being a ‘good general education course’?

Statistics is necessary, but not sufficient, for general education in college.

All of these ideas then connect to ‘guided pathways’, where the concept is to align the mathematics courses with the student’s program.  This reflects a confusion between general education and program courses; general education is deliberately greater in scope than program courses.  To the extent that we allow or support our colleges using specialized math courses for general education requirements … we contribute to the failure of general education.

In my view, the way to implement general education mathematics in a way that really works is to use a strong quantitative reasoning (QR) design.  My college’s QR course (Math119) is designed this way, with an emphasis on fundamental ideas at a college level:

• Proportional reasoning in a variety of settings (including geometry)
• Rate of change (constant and proportional)
• Statistics
• Algebraic functions and basic modeling

If a college does not have a strong QR course, meeting the general education vision means requiring two or more college mathematics courses (statistics AND college algebra with modeling, for example).  Students in STEM and STEM-related programs will generally have multiple math courses, but … for everybody else … the multiple math courses for general education will not work.  For one thing, people accept that written and/or oral communication needs two courses in general education … sometimes in science as well; for non-mathematicians, they often see one math course as their ‘compromise’.

We’ve got to stop using high school courses taught in college as a general education option.  We’ve got to advocate for the value of algebra within general education.

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Progression in Math — A Different Perspective

Much is made these days of the “7 percent problem” (sometimes 8%) — the percent of those placing in to the lowest math course who ever pass a college math course.  This progression ‘problem’ has fueled the pushes for big changes … including co-requisite remediation and/or the elimination of developmental mathematics.  The ‘problem’ is not as simple as these policy advocates suggest, and our job is to present a more complete picture of the real problem.

A policy brief was published in 2013 by folks at USC Rossier (Fong et al); it’s available at http://www.uscrossier.org/pullias/wp-content/uploads/2013/10/Different_View_Progression_Brief.pdf.  Their key finding is represented in this chart:

The analysis here looks at actual student progression in a sequence, as opposed to overall counts of enrollment and passes.  This particular data is from California (more on that later), the Los Angeles City Colleges specifically.  Here is their methodology, using the arithmetic population as an example:

1. Count those who place at a level: 15,106 place into Arithmetic
2. In that group, count those who enroll in Arithmetic:  9255 enroll in Arithmetic (61%)
3. Of those enrolled, count those who pass Arithmetic: 5961 pass Arithmetic (64%)
4. Of those who pass Arithmetic, count those who enroll in Pre-Algebra: 4310 enroll in Pre-Algebra (72%)
5. Of those who pass Arithmetic and enroll in Pre-Algebra, count those who pass Pre-Algebra: 3410 (79%)
6. Compare this to those who place into Pre-Algebra: 68% of those placing in Pre-Algebra pass that course
7. Of those who pass Arithmetic and then pass Pre-Algebra, count those who enroll in Elementary Algebra: 2833 enroll in Elementary Algebra (83%)
8. Of those who pass Arithmetic, then pass Pre-Algebra, and enroll in Elementary Algebra, count those who pass Elementary Algebra: 2127 pass Elementary Algebra (75%)
9. Compare this to those who place into Elementary Algebra: 70% of those placing into Elementary Algebra pass that course
10. Of those who pass Arithmetic, then Pre-Algebra, and then Elementary Algebra, count those who enroll in Intermediate Algebra: 1393 enroll in Intermediate Algebra (65%)
11. Of those who pass Arithmetic, then Pre-Algebra, and then Elementary Algebra, then enroll in Intermediate Algebra, count those who pass Intermediate Algebra: 1004 pass Intermediate Algebra (72%)
12. Compare this to those who place directly into Intermediate Algebra: 73% of those placing into Intermediate Algebra pass that course

One point of this perspective is the comparisons … in each case, the progression is approximately equal, and sometimes favors those who came from the prior math course.  This is not the popular story line!

I would point out two things in addition to this data.  First, my own work on my institution’s data is not quite as positive as this; those ‘conditional probabilities’ show a disadvantage for the progression (especially at the pre-algebra to elementary algebra transition).  Second, the retention rates (from one course to the next) are in the magnitude that I expect; in my presentations on ‘exponential attrition’ I often estimate this retention rate as being approximately equal to the course pass rate … and that is what their study found.

One of the points that the authors make is that the traditional progression data tends to assume that all students need to complete intermediate algebra (and then take a college math course).  Even prior to our pathways work, this assumption was not warranted — in community colleges, students have many programs to choose from, and some of them either require no mathematics or basic stuff (pre-algebra or elementary algebra).

The traditional analysis, then, is flawed in a basic, fatal way — it does not reflect real student choices and requirements.  For the same data that produced the chart above, this is the traditional analysis (from their policy brief):

This is what we might call a ‘non-trivial difference in analysis’!  One methodology makes developmental mathematics look like a cemetery where student dreams go to die; the other makes it look like students will succeed as long as they don’t give up.   One says “Stop hurting students!!” while the other says “How can we make this even better?”

So, I’ve got to talk about the “California” comment earlier.  The policy brief reports that the math requirement changed for associate degrees, in California, during the period of their study: it started as elementary algebra, and was changed to intermediate algebra.  I don’t know if this is accurate — it fits some things I find online but conflicts with a few.  I do know that this requirement is not that appropriate (nor was elementary algebra) — these are variations of high school courses, and should not be used as a general education requirement in college.  We can do better than this.

This alternate view of progression does nothing to minimize the penalties of a long sequence.  A three-course-sequence has a penalty of about 60% — we lose 60% of the students at the retention points between courses.  That is an unacceptable penalty; the New Life project provides a solution with Mathematical Literacy replacing both pre-algebra and elementary algebra (with no arithmetic either) and Algebraic Literacy replacing intermediate algebra (and also allowing about half of ‘elementary algebra students’ to start a course higher).

Let’s work on that question: “How can we make this even better?”

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