I’m getting somewhat close to the end of my career, and I expect that AMATYC 2017 is the last AMATYC conference that I will attend. Most likely, it is natural for people to contemplate the arc of history at this point (whether this arc bends towards justice is another question). I will be writing a series of posts on the history of (my) developmental mathematics, which might be presented at a session in San Diego.
For me, the origins lie in a coincidence: having ‘trained’ as a high school math teacher, I was unable to find a teaching job that did not involve moving. I applied for a part-time job at the local community college, and in a fit of inexplicable errors, was hired. The job involved supporting the operations of the college’s “Math Lab”, where several remedial math courses were offered in a self-paced, mastery format. The time was the early 1970s.
In general, those remedial courses were intentional copies of K-12 courses from a short period prior to this time. We had middle-school math (basic math), beginning algebra, geometry, and intermediate algebra; soon after I started, we began offering a metric system course, a desk-top computer course, and a sequence of two statistics courses (which had a beginning algebra prerequisite … quite ahead of its time). The faculty in charge of the courses for students were, in general, current or former high school math teachers; familiarity with K-12 math was a high priority in hiring, and support for student success was not even considered.
The core of the ‘developmental math’ curriculum was the 3 course sequence aligning with grades 8, 9, and 11 .. basic math, beginning algebra and intermediate algebra. At this time, the mode for a student’s high school math was ‘algebra I’, with a fourth of recent HS graduates never having had any algebra course. Those on a ‘college-prep’ track certainly had more, but the community college policies were not targeted towards the college-prep students.
This was the time period when a pattern was started that still holds in many parts of the country:
Since most of the students graduating from high school had not taken ‘algebra II’, intermediate algebra is ‘college credit’ and often meets an associate degree requirement for general education.
The rationale for this policy lost its validity within about decade, as the majority of students began to graduate with algebra II credit on their transcript. Colleges have been slow to update their general education policies to reflect fundamental shifts in HS course taking behavior.
In terms of “hot topics” in developmental mathematics education, it was all about two systemic features:
- Curricular materials that required little reading and provided ‘clear’ examples with lots of practice.
- Alternative delivery methods, including self-paced and programmed learning.
The first element reflected the high-school context for the period prior to this … school textbooks were intended to be ‘teacher-proof’ (anybody could teach math), and the content was all about procedures to calculate answers in arithmetic and algebra. That context has changed in a basic way, as the result of the teaching standards over the past 30 years (NCTM, AMATYC, etc). Like the general education policy, math faculty have not altered the core focus of the curriculum; most current materials still focus on clear examples and lots of practice (though there is often more reading involved).
Our focus in alternative delivery methods, though cast in naive terms, was actually critical to trends that continue through today. Most of us find it funny that ‘programmed learning’ was a “Thing”; the central idea was to have an assessment ‘every page’ and the student was ‘branched’ to a different next page, depending upon their answer. In more recent times, this idea has been done in a more mature fashion with adaptive computer tutor designs.
The essential transaction that was being developed in these early days was “student — does math — correct OR recycles to re-learn it, repeat”. Faculty had a role, but this role was not seen as the most essential role for student learning. In contrast, much of our current professional development puts great emphasis on faculty interacting with students. Although there is an obvious and valid basis for this emphasis, I wonder if perhaps we would be better off focusing more on the student interaction with mathematics.
A subsequent post will look at the period of a few years following this ‘origins’ time of the early 1970s.
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