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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placement, politics of developmental mathematics | Jack Rotman | March 24, 2012 4:04 pm

4 Comments

By Laura, March 24, 2012 @ 5:55 pm

I agree that some students are placed into prealgebra who could be successful in elementary algebra, but, as you say, not all students. This suggests to me a problem with placement, not with the prealgebra class.

The students that really need prealgebra are often also poor readers, have limited number sense, and score low on other measures of college readiness. Their study skills are limited, and many have some degree of learning disability. Except for rare cases, there are reasons that they are in prealgebra as adults. When their socioeconomic situation or personal lives are unstable, that makes it worse.

I don’t think it is a good idea to put these students into an EA class that they are not equipped to pass, not only because it is bad for them but because it makes it very difficult to do group work and maintain a positive class climate in the EA class.

But, you’re right, current placement is efficient but that’s about all it has going for it.
By Jack Rotman, March 26, 2012 @ 12:55 pm

Good point, Laura. Both things might be a problem — placement AND the prealgebra class.
The transition to algebra is difficult for a number of students, and for the kinds of reasons you list. I think we would have a stronger course, and a stronger rationale, if our courses dealt with those issues along with a reduced range of mathematics presented for reasoning not procedures.
By Peter Brown, March 24, 2012 @ 6:01 pm

Hey Jack. I would argue, with some factual basis that 1/3 of pre algebra students should be in algebra, 1/3 should be in a 2 credit hour pre algebra course, and 1/3 need a full 4 credit semester of pre algebra. We are looking at the compass diagnostic test. Have you ever looked at that?
By Jack Rotman, March 26, 2012 @ 12:52 pm

Peter:
No, have not looked at the Compass diagnositcs … a little at the Accuplacer diagnostics.
The most common use of such diagnostic tests is to interface with a modular program design based on traditional content (procedures, correct answers). I do not think that methodology serves our students very well. The basic point is — let’s not assume that the course before beginning algebra is a good preparation for algebra.
Jack

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