Normalizing a Bad Curriculum: Forty Five Years of Dev Math, Part IV

This is another entry in a series of posts looking back at developmental mathematics history. Previous posts dealt with origins, a golden age, and a missed opportunity … and now we look at the last half of the 1980s.

It might be difficult to believe that there was a time before people talked about standards. The first great effort on standards came from NCTM in 1989 (“Curriculum and Evaluation Standards”, summarized at http://www.mathcurriculumcenter.org/PDFS/CCM/summaries/standards_summary.pdf ) which was a follow up to “An Agenda for Action (http://www.nctm.org/Standards-and-Positions/More-NCTM-Standards/An-Agenda-for-Action-(1980s)/ ). Whether these standards were even discussed at a college was more a coincidence of faculty connections than any organizational cooperation.

The period we are talking about preceded these initial standards. However, collaborative activity across institutions and regions was increasing in the latter 1980s. It is not a coincidence that my first AMATYC conference was in 1987 (“Going to Kansas City” theme song). We, as a profession, were looking for stability and support. The AMATYC Developmental Mathematics Committee (DMC) had several active subcommittees on issues such as “Student Learning Problems” and “Minimal Competencies”, as well as “Handheld Calculators”. I served as the editor of the DMC Newsletter for several years, a newsletter produced by printing stuff on a dot-matrix printer and physically cutting & pasting to make the pages of the newsletter. Ah, for the good old days …

We entered this period having missed the great opportunity, which naturally led to the primary outcome of the time:

The existing pre-college and college curriculum was normalized and accepted as a “good thing”, or at least “the way it should be”.

Some of us knew that NCTM was working on their standards, though none of us were involved in any way (no community college faculty served on a team or as a writer). In this period prior to the first AMATYC work on standards, we explicitly supported the grade-course structure (from K-12) which had been our inheritance. When a problem was identified (such as low pass rates), our response was to double-down … we created split courses for beginning algebra, and split courses for intermediate algebra; we often added a basic math course separate from a pre-algebra course. This double-down trend resulted in horrific sequences for students. We often went from our old sequence of 3 courses to a system where some students took 9 terms or semesters of developmental mathematics. [These structures still exist, relatively intact, in some places … parts of California, for example.]

Another aspect of the ‘double-down’ response was an attempt to identify THE list of critical learning outcomes. The DMC “MinComps” (minimal competency) subcommittee worked by snail mail and annual meetings to identify the arithmetic skills that all students should possess. Although MinComps never achieved their goal of writing a position statement on this content, the group did have an impact on our courses and the textbooks used in those courses.

Never was our response to ask “What are the mathematical abilities which students need for college success and life success?” The response was ‘what outcomes should be in this course?’. There was a trend, especially during this time period, to have our textbooks converge to a common list of content topics and outcomes (very skill based). Workbooks were very popular in this period, often consisting of ‘name topic, state property, show example, give practice’. In some ways, the ‘programmed learning’ textbooks of a decade earlier were more supportive of student learning.

The content became the thing. When students did not succeed, we looked to identify a student learning problem. In some cases, we even tried to provide support to ‘overcome’ a student learning problem. Our efforts were directed at improving course pass rates … at the expense, frequently, of the sequence pass rate. Our friend ‘exponential attrition’ is very powerful … a sequence of 5 courses will always be worse than a sequence of 3 courses, unless we can realize close a 50% improvement in course pass rate. Going from 45% pass in all 3 courses to 67% pass rate in all 5 courses is not likely; if it has ever happened, you can be pretty sure that this improvement was temporary.

Since we were relatively ignorant of the sequence and attrition issues, we were pleased with longer sequences which reinforced the defective content we had inherited and then had normalized.

My younger colleagues will have a difficult time understanding the technological context for this work. When we had the “hand held calculator” subcommittee in the DMC, we were not talking about graphing calculators — the work was focused on basic calculators, with a recognition that scientific calculators were available. Our offices had computers (very slow) with no networking; I had a dial-up modem to connect to a nearby mainframe, but that was quite unusual. We often hand-wrote our tests (and it’s a miracle that any student could pass such tests!). Later in this period, we had the initial efforts to provide students with access to computers — often done in a separate computer classroom, not related to any math course. Homework, like our tests, were a hand written affair.

This technology did not cause any change in the content or delivery of instruction. If anything, the status of the technology was part of the set of forces which led to the normalization of the defective content in college mathematics. Our motto seemed to be “We don’t know if this stuff is really worth much, but at least we generally agree that it is what we should be doing because we are all doing roughly the same thing.” Many math faculty today continue to look at curriculum primarily from this lens.

The trend in this period to normalize the defective content contributed to our response in the next period (the early 1990s) when the NCTM standards suggested that such content was, indeed, defective. We had set up conditions which made us essentially immune to the valid critiques. That is where the next post will look at our history.

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history of developmental mathematics | Jack Rotman | April 1, 2017 4:11 pm

4 Comments

By schremmer, April 1, 2017 @ 7:40 pm

Re: “Our motto seemed to be “We don’t know if this stuff is really worth much, but at least we generally agree that it is what we should be doing because we are all doing roughly the same thing.” Many math faculty today continue to look at curriculum primarily from this lens.”

Only many? Where are the exceptions? I have yet to find a college textbook mathematically meaningful. And I have been around over half a century.
By Jack Rotman, April 3, 2017 @ 1:35 pm

Don’t confuse “textbooks” with “faculty”. Depending upon the institution, we would find 0% to 60% of faculty are critically looking at some part of their curriculum. The area most resistant to a critical analysis is CALCULUS, where many people want to continue creating their “Thomas experience” (even if they never used Thomas’s textbooks).
For textbooks, take a look at “Using and Understanding Mathematics” (Bennett & Briggs), which we use for our QR course. It’s a nice mix of applications and understanding.
By schremmer, April 3, 2017 @ 10:14 pm

Re. “Don’t confuse “textbooks” with “faculty”>”

Hard not to: what do these “other” faculty use for a textbook? How come Pearson and Cengage, although far behind, are making such a killing.? And, speaking of the “Thomas experience” (by the way, Thomas V or before-and-after?) No matter what, it was AWFUL. And, in addition, what book are they using these Calculus rebels? Stewart most probably (Cengage).

Re. “”, do I have to BUY this book sight unseen? In any case, I am willing to bet that it would not sustain any kind of real scrutiny: exactly what reality does “a nice mix of applications and understanding” cover? Applications preceding understanding? How many students on top of the leaning tower and letting something fall will derive … Don’t confuse inventing and learning.
By schremmer, April 6, 2017 @ 10:58 pm

Re. Using and Understanding Mathematics” (Bennett & Briggs)

Finally saw some of it on Amazon. Standard Pearson issue. I haven’t seen a student capable of reading this for many years. I wonder about the exams. But I don’t think this is the place to discuss it so I will stop right here.

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