The Capabilities of Developmental Students

What are our students capable of?

I think we end up taking a ‘bipolar’ position on this.  On the one hand, we believe that our students can achieve their goals; we encourage them, nudge them, motivate them, and suggest that they might be capable of higher goals.  Our greatest satisfactions come from watching our students — who needed developmental course work — graduate with a completed degree.  Gowns, in college colors, form a visible symbol of this hope for all of our students.

On the other hand, we seem to design courses which say “I get it … you can’t understand mathematics, really; so I will just expect you to recognize some patterns for which you have a solution in memory.”  We build instruction around the goal of maximizing correct answers for students.  We select textbooks which simplify the presentation and provide clear examples of the procedures, and avoid textbooks which discuss the ideas outside of examples.  We observe that our students do not remember much of what they had last semester, and conclude that this reinforces our design of ‘simplify’.

In fact, our ‘simplify design’ paradigm is part of the problem.  As long as learning focuses on remembering procedures, the powerful brain work that enables long-term changes and transfer of learning do not have a chance to occur (except by accident).  In some ways, most of our students leave our classrooms with the same condition that they arrived … summarized by the one word “unable”.

I can not accept the ‘simplify design’ of curriculum due to its message about the capabilities of our students.  Our students are capable of achieving much, and our society actually depends upon them achieving much.  We can not avoid building this capacity within our ‘developmental’ classrooms.  (It’s ironic that we call our courses ‘developmental’ but tend not to develop capacity.) 

Now, I am not under the influence of some ‘just be happy’ medication.  Obviously, students in developmental mathematics classes have some current limitations.  Our response must be to overcome limitations and build capabilities.  This response is not easy, certainly not just ‘pick the best homework system’.  Just like our students, we will achieve more than we thought possible when we face challenges directly.

And, just like our students, we will find the work is easier … and we understand more … when we work with each other.  You are not alone, and we are capable of designing courses which build capacity within our students.

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STEM or What? What Trajectory?

In community colleges, ‘developmental mathematics’ courses are the highest enrollment math courses.  These courses are based on a ‘calculus’ track, in most cases; I explore this issue in one of the Instant Presentations.  Most of our students are not required to take calculus, or even pre-calculus, for their program.  What is their trajectory?

Many of my students are on a trajectory to meet a general education requirement in mathematics.  In some cases, this is the requirement of my college (a course after beginning algebra); in other cases, it is the requirement of a transfer institution … for those who transfer.  What is the trajectory of general education in mathematics?

The “SIGMAA-QL” (quantitative literacy special interest group of the MAA) conducted a study in 2009 in an attempt to determine any commonality in our general education requirements.  The results are available in the report http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.158.6128&rep=rep1&type=pdf , which I have been studying this week.

This “QL” survey was intended for both 2-year and 4-year institutions, and they tried.  They sent the survey to every MAA-liaison, and this included over 400 at community colleges.  The return?  About 45 out of those CC.  Given the small number, the results could not be summarized.   The response rate was about 25% for 4-year colleges (275 returned, I believe), so the report deals with the 4-year situation.

Within the 4-year environment, the survey sound a surprising amount of ‘diversity’ in the general education requirement across an institution.  However, most of these courses fall into two categories — part of the pre-calculus sequence, or statistics.  What is trajectory we are designing here?  Are we saying that all students should attempt but fail to complete a sequence towards calculus?  Are we saying that ‘getting ready for calculus’ is equivalent to general education? Are we saying that statistics is the only exception for students — no other branch of mathematics has validity for all students?

Given the direct connection between developmental mathematics and these ‘general education’ requirements, we need to do some critical thinking relative to the trajectories we create.  What does it mean to be ‘quantitatively literate’, and how does this differ from ‘quantitative reasoning’?  Dealing with these questions will form a strong foundation for building trajectories which we impose on our students … this imposition needs to be based on a sound argument for their benefit.  (We need an argument stronger than “math is good for you”.)

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Instant Presentations now available!

There is a new page in DevMathRevival.net — called “Instant Presentations”.

The idea here is simple: provide an on-demand presentation that people can share and view.  Similar to a webinar, and more direct.

Initially, the page has 3 presentations — the Mission of Developmental Mathematics; What is Now; the New Life Vision.  Each of these presentations is under 5 minutes, with video and audio.  [The format is “Flash video”, which means that browsers will handle the files for you when you click on them.]

Give it a try!! The direct link is https://www.devmathrevival.net/?page_id=116

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Standards Based Reforms — What Research Says

The United States has seen a number of ‘standards based reforms’ over the past 20 years or so. Many of these deal with school mathematics, though a few of us in the college environment have worked towards a similar process. The most recent effort is the “Common Core Standards” (http://www.corestandards.org/ ), which is the highest profile effort yet.

The Rand Corporation published a report, in 2008, called Standards-Based Reform in the United States: History, Research, and Future Directions (online at http://www.rand.org/content/dam/rand/pubs/reprints/2009/RAND_RP1384.pdf).  I was impressed by some of their observations.

First, “Standards Based Reform” is usually implemented as “Test Based Reform”.  The point here is that content and pedagogy reflects a testing emphasis such that the actual standards are secondary — the tests (such as those used for No Child Left Behind, NCLB) take on the primary importance.  Behind this is a tension you will understand: Standards, by themselves, produce very little change.  “Aligning” testing to the standards is very common, and very understandable, as a method to create change.  Change is not always progress, however.

Second, high-stakes testing with sanctions ‘distorts’ teaching practice; as you’d expect, teachers focus more on preparing for the test when there are sanctions involved.  In general, most of the current testing involves sanctions of some kind such as NCLB or state-level impacts.  Since tests must, by design, address small subsets of the larger domain of knowledge described by the standards, the result tends to produce students who can perform better on the tests connected to the sanctions compared to other measures of their knowledge.  Specifically, they do not do relatively as well on our college placement exams. 

Third, the report goes back to a critical document that describes 4 categories of standards … and also analyzes the track record of some specific efforts.  A shot blog post is not an appropriate venue to report on these comments (I don’t want to inflict a journal-length article on you 🙂 ).

Although community colleges have not faced the standards based reforms and tests with sanctions directly, we deal with the consequences of these efforts.  Some policy makers assume that the “developmental math problem” will go away once the standards are implemented (like the Common Core).  The Rand analysis provides some insight into why the problem is not that simple; we should assume that our problem might change in the next 10 years … not that it will go away.

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