Placement Tests To Go?

Placement Tests are an important part of the process at the vast majority of community colleges, especially relative to mathematics.  Over on the
MATHEDCC discussion list, Fred asked an honest question about finding an online placement test that was not a commercial test.  Most of the public responses to his query have been critiques of placement tests in general (some would say toilet-emptying, self-affirming statements).  Under the surface, is it possible that we do not need placement tests?

Some readers will have an extreme reaction to a question raising the possibility that placement tests are not good.  Let me clearly state my opinion after working with them for 39 years:  Most placement tests are reasonably good assessments of the content that they were designed to measure.  Given the limitations that users place on them (users being most of us), the tests achieve the best measurements possible.  Of course, these statements don’t tell you if I think placement tests are ‘good’ or not … and that is my point.  Our use of placement tests might be good or not; the tests themselves are just what they are designed to be.

The use of placement tests involves several issues.  The largest issue right now is whether placement test results are the only factor in initial math placements.  The best research I have seen suggests that we should supplement test results with other information, especially high school performance (overall) for recent ‘graduates’ (whether they graduated or not).  Some states have a common data system for K-16 which makes this relatively easy; others (like my state) have significant barriers.

Another issue deals with the content definitions for placement tests.  Some of us see the companies involved as ‘evil’, with a higher priority on money or prestige than on helping students.  I suspect that this point of view is held by people who have not been involved with the companies work.  Although it is true that some of the field representatives of the companies are not helpful academically … the people with actual control at the companies are focused on academic success.  Personally, I fault ‘us’ more than the companies.  We have been telling the companies that the content for the tests needs to identify skills that the student does or does not have; skills are forgotten, and are vulnerable to trivial details.  If we would focus more on comprehension, application, and reasoning … the placement tests would have more meaning for us and our students.

A related issue is the use of placement tests in a deficiency model, such as some modular programs.  We sometimes expect a placement test to indicate whether a student ‘knows percents’ (alternatively, ‘does not need the module on percents’).  We should not use placement test for diagnostic purposes.  We might use well-designed diagnostic tests for this purpose, though I actually have more concerns about diagnostic tests than placement tests.  Diagnostic tests involve the effective ‘waiving’ of instruction; as a profession, I do not think we can support a 20-item diagnostic test as being equivalent to the instructional value of 3 weeks of class.  I digress!

Another issue with our use of placement tests is ironic:  We do not apply number sense to the results of a test.  For measurements of objects, we know that there is no signficant difference between 3.1 meters and 3.2 meters — if the measurements are made with a meter measure.  However, for placement tests having essentially 1 digit of precision, we often make a distinction between a 64 and a 61.  Take a look at the standard errors for your placement tests, and remain humble.  If tests are the only measure used, a ‘line’ needs to be drawn somewhere; this line might separate the 64 from the 61, but that does not mean that they are really different. Too often, we look at placement tests as if they were precision calipers when they are really meter measures.

The title of this post has two meanings (at least).  The obvious would be ‘will placement tests go away?’; I do not think so, and I would not advocate that.  Another meaning is ‘placement tests as ‘take-out’ process’ (like drive-in restaurants) … “would you like fries with that algebra test?”.  In other words, ‘give the student what they want’; over on the MATHEDCC discussion, this was the point for some people — just let students decide on their best math course.  Self-selection has been the subject of research, which I think has generally found less effective than placement based on tests for the entire population of students.

We do not need to get rid of placement tests.  We need to support changes in the content of those tests, and we need to show a better understanding of the measurements resulting from placement tests.  The ‘placement test problem’ is more about us as math faculty than it is about the tests.

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Editing Math: Writing as a Guide to Better Mathematics Learning

I was talking to a colleague who teaches writing about the placement test, wondering if the test they happen to use gives them results that seem valid for getting students in to the best course.  As we were talking, I wondered … could we learn from the writing placement tests and writing courses about how to help our students?

The writing placement test we were talking about is one of the very common instruments used to place students at community colleges.  The test contains a series of writing samples (one at a time); students need to identify sentences with errors, and then also answer a question or two about the writing.  When I asked my colleague about how well this worked, he said that it primarily just tested editing skills as opposed to writing skills.

Would math learning be improved if we held ‘editing’ in higher esteem?  Would students become more able to think in mathematical terms if they routinely examined their mathematical writing?  Should our math placement tests involve the process of students editing mathematical work to identify either strategic or tactical errors?

Like many of us, I routinely tell my students to check their work for errors.  Competing with this ‘proofreading’ direction is the type of ‘check’ suggested in most textbooks (put it back in).  The concept of editing applies to mathematical work, which we practice when we develop handouts and other materials for our students.

In developmental mathematics, a portion of our population are not yet ‘college level’ in their writing; students are challenged to write clear sentences and paragraphs … and challenged to write clear mathematical steps and solutions.  Writing is the most direct measure of the knowledge held by the student, which is a tool for the student to look for gaps and confusions.   Perhaps editing this work is a step along the path towards more developed metacognitive skills.

I would like to try this concept in my classes: Editing mathematics as a learning tool.

Separate from the classroom use, I wonder — should math placement tests involve different processes other than “get the answer”?  Would we get better measures of readiness if students needed to examine a few steps of mathematical work to identify errors? 

 
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Ignore Common Core?

Can college math faculty ignore the Common Core?  Specifically, can those of us working in developmental mathematics ignore the Common Core?

If you need to read more about the Common Core Math Standards, take a look here http://www.corestandards.org/the-standards/mathematics. The Standards are listed for each grade K to 8, and then high school by area of mathematics.

As you might know, a primary motivation for the Common Core was that of alignment … getting K-12 outcomes to align with expectations, especially for college readiness.  This alignment is connected to the standardized tests used for ‘No Child Left Behind’ (NCLB) as well as some teacher evaluations.  [A current theme in teacher evaluations is the use of ‘value added models’ (VAM), which is a statistical methodology to estimate the impact of individual teachers; I may address VAM in a future post.]

A logical approach might be to think that … if a student places in to developmental mathematics … there is no reason that we need to be especially aware of the Common Core.  If this placement is accurate, we might conclude that the Common Core ‘did not work’ for whatever reason, so our work is independent.

Look at the situation in a different ‘frame’:  Because the Common Core is closely tied to standardized testing and NCLB, the mathematics assessed is often discrete skills with a focus on procedures and simple applications.  This emphasis in K-12 will, therefore, tend to produce students in college — whether ‘developmental’ or not — who have a less complex package of mathematical proficiency.   

I have been suspecting something like this happening in the last few years (even before Common Core, though the Common Core will expand the impact) … students obtain about the same average scores on placement test even though their functioning, mathematically, is more limited.  Solving a linear inequality might go okay for them, and then difficulty emerges when there is a discussion about how to represent the solutions in a different way.  Finding slope from two ordered pairs might be okay, and then confusion appears when slope needs to be interpreted in words or a context.

Recently, I did a post on “Lockhart’s Lament”; in that essay, an observation is that a sure way to ruin a subject is to require all students to ‘take it’.  With the Common Core, we have a movement to make all students take the same subject for almost all of their K-12 experience.  Since this ‘subject’ is almost always tied to standardized tests and sometimes to teacher evaluations, the forces operate on the subject to reduce all topics to operational steps.  (I’m reminded of the “paint by numbers” analogy in Lockhart’s Lament.)

Policy makers are often looking for simple solutions, which makes the Common Core look very attractive as well as standardized tests.  If only we could present ‘understanding and reasoning’ as simple solutions for the mathematical needs of K-12 students.  Are not those the central enablers of success for students  in our college courses?

We ignore the Common Core at our own peril.  Some college faculty actively support the use of the Common Core mathematics standards, and there is a real danger that this wish will be granted.  There is no single mathematical standard in the Common Core that I object to; the tragedy is that the summation (or integration in the mathematical sense, if you will) of the Common Core is a worsening of the mathematics problem in colleges … starting with developmental, but including all college mathematics in the first two years.
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Reducing Costs of Developmental Math

The ‘cost’ of developmental mathematics is one of the major issues being faced by states and institutions.  Although this is commonly stated as a financial cost, an equally important cost is present — the cost to our students (time, credits).  There is also a risk involved, given that most studies of developmental education seem to report that students placed into developmental courses have a lower chance of completing programs.

Is there a solution?  Is there a simple solution?

In a recent post (https://www.devmathrevival.net/?p=756) I talked about what a reasonable prerequisite to beginning algebra could be.  That post hinted at some solutions which could be implemented to reduce costs.

Here is a simpler solution that can be done right away, and may not have the kinds of problems you might predict:  Place students into beginning algebra, even if their placement test suggests something before that.

I admit that this is a strange suggestion.  However, think about how ‘strange’ our current system can be … at many institutions, students who start in pre-algebra have about a 20% ‘chance’ of completing their college level math requirement.  Are we helping that 20% so much that this process is worth the risk to the other 80%?

Before you jump up and down, screaming “THIS IS NOT GOING TO WORK” … look at some potential numbers.  If we assume that 70% of the students placed into pre-algebra pass that course, and that 50% of those who proceed to beginning algebra pass that second course, we have a net 35% who complete beginning algebra in the second semester.  This 35% assumes that ALL students will pass pre-algebra continue to beginning algebra; this is not reasonable.  Based on estimates from my data work at my college, from 70% to 80% actually go on to the second course.  Applying the highest rate (80%) to the 35% value gives us a realistic net of 28% … about 28% of students who start in pre-algebra complete the beginning algebra course the second semester.

What would we expect to happen to students who go directly to the beginning algebra course?  Would they be half as likely to pass that course, compared to having taken pre-algebra?  This “half” seems like a reasonable estimate (and may be too low).  Half of 50% … is 25%.  Since 25% is generally not statistically different from 28%, there is a good chance that placing all students in to beginning algebra would not create any additional risk to the student — and would save a semester of credits.

There is actually evidence that suggests this 25% ‘direct’ rate is too low.  A study (http://ccrc.tc.columbia.edu/Publication.asp?UID=1030) shows the predicted pass rates for students above and below the cutoff on a placement test (Accuplacer in this case); the predicted values for rates of C or better are above 30% for all placement test scores.  If this is accurate, then it would actually help students to never place them in to pre-algebra.

Based on years of talking with students struggling in beginning algebra, there is another reason why ‘skipping’ pre-algebra might help quite a few students: of the students who pass pre-algebra, quite a few of them were not challenged by the material … in fact, many do not study … and still pass.  This “no study, and pass” experience is exactly the opposite of what most students need; students need to know that working hard and continuing are critical for academic success.  As long as a pre-algebra course is primarily procedural, with a focus on correct answers, it will not contribute to habits that help students in later courses.

Think of that … a simple solution that saves a lot (money & credits for students, costs and resources for colleges), with either no risk or even some significant benefits.  Let’s agree to not place any student into pre-algebra (or whatever your course is called); if their placement test suggests that they don’t have enough ‘basic skills’, we would be better off placing them into beginning algebra anyway, perhaps with a sheet of references for refreshing those skills.

 
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