Developmental Mathematics Revival!

What is My Legacy?

When a person approaches the end of a job or career, whether as a transition to a new position or as a retirement, it is natural to examine and ponder what was accomplished. Perhaps there were awards received, new products introduced (‘courses’ in the college world), or new processes developed (‘pedagogy’ in the college world). As I approach my ‘inflection point’ (retirement), my thoughts have been on similar matters. However, I have a great colleague who asked an excellent question:

What is YOUR legacy?

Most of us would like to reflect on a set of positive accomplishments, and might consider that set to be our ‘legacy’. However, the concept of legacy suggests a carrying forward … an impact that extends past our personal inflection point. As ‘teachers’, we often view our impact on individual students to be a critical part of our ‘legacy’; certainly, knowing that we played a positive role in somebody’s education and achievement feels good — I just don’t think that ‘feels good’ is a basis for including this in our legacy.

I am also not using the word in the sense often cited in other contexts — business and leadership in particular, where ‘legacy’ refers to a future-oriented plan of creating impact and power. I am thinking more of legacy in reference to any long-term impacts that might be important to me personally.

To some extent, history establishes a person’s legacy. In ten years, what evidence or impact will there be?

Professionally, I have had goals involving the local curriculum and national curriculum at the college mathematics level. Establishing a legacy within these areas is difficult, it seems. Much of the work turns out to be temporary or unimportant aspects of courses or pedagogy — meaning that the 10 year impact (legacy) is approaching zero (from the positive side, at least).

How can we judge or establish our ‘legacy’ on important matters? I suspect that trying to estimate our own legacy is to engage in a flawed process, due to a variety of biases. Other people need to provide information. Sometimes, this validation comes through an awards process. On that front, I have received three teaching awards … AMATYC (national), MichMATYC (state), and college; the fact that the awards occurred in that order says something, though I am not sure what. In spite of those awards, I still have a critical view of my work as a teacher. Perhaps related to this, my goals for a ‘legacy’ have little to do with my teaching (though I obsess about my performance).

My goals are more about curricular impact. In developmental mathematics, my work has been directed at modernizing the curriculum while providing effective remediation within a shorter period (one or two courses maximum). At the college level, I have tried to get people talking — and doing something — about the very obvious problems with the college algebra – pre-calculus – calculus I to III ‘swamp’ of worthless artifacts from a by-gone era.

In some ways, people associate my work with ‘pathways’ in mathematics, and pathways has certainly been a big thing. This is an alignment concept, in general; in my view, alignment of math with program is an excuse to avoid doing any worthwhile mathematics while pretending that we are helping students by letting them get by with only the math they will encounter for their ‘program’ (as if they have a stable vision of what that is). In particular, the rush to use statistics as a gen ed math course is often based on questionable inputs concerning occupational needs combined with institutional avoidance of all things algebraic. If people think “pathways are part of your legacy”, I can only hope that they realize I do not support much of that work.

Within developmental mathematics, we have a tri-modal system: updated (like math literacy, quantway, foundations of math reasoning), eliminated (co-requisite), and traditional (same-old remedial courses). The presence of the updated curriculum, I’d like to think, is part of my legacy. Will it last 10 years to really be part of my legacy? Of course, we don’t know … things change, often in directions that can not be anticipated. I do know that a system with two conflicting designs (updated and traditional) is unstable and unlikely to be sustained in the long term. I am honestly quite dismayed by the proportion of our remediation which still consists of traditional courses for many students; not only does this harm students, it leaves the system easily attacked by the disruptive influencers who want to eliminate remedial courses. The fact that some proportion (whether it is 30% or 50%) refuse to update their remedial mathematics is likely to result in the total elimination of remedial mathematics in 5 to 10 years.

Certainly, within the college credit math courses (college algebra to calculus I-III) along with quantitative reasoning we, as a community of professionals, seem more concerned with improving pedagogy than we are with improving mathematics. Most of us do not include any numerical (computing) methods in the basic courses, and quite a few of us actually ban computing devices from those classes (like calculators). As AMATYC and MAA work on projects, each group seems to dance around the fundamental flaws in the curriculum in an effort to not ‘upset’ anybody. Sometimes, the reasoning for this awkward dance is that our colleagues are actively looking for pedagogy so that is what our publications and conferences should be about. Of course our colleagues are looking for pedagogical help — mostly because that is what we are offering. If we don’t offer definite curricular guidance, we will never know whether our colleagues are really interested. In spite of the lack of change, I remain convinced that many of us are ready to start the long process of discussion and dialogue concerning how we should change our broken mathematics curriculum in the first two years. Our colleagues may need a lot of encouragement and we need a large dose of patience; the process needs appropriate opportunities for meaningful critique and reflection combined with solid design work dealing with the needs of our students and their careers. The fact that this change process will take years and will be difficult at time is a poor excuse to avoid the problems (at the expense of our students).

As commented, judging one’s own legacy is difficult and perhaps a misguided effort. In spite of that, I wonder if I have a legacy that extends past my own institution in the time frame approaching the ten year standard. Perhaps I am looking for feedback on that, though other people will still be limited by the problem of predicting patterns in to the future. Part of my “legacy discouragement” is that the trends I see in mathematics do not encourage me to think an updated mathematics curriculum will survive a ten year standard.

Do you think the updated developmental mathematics curriculum will expand to encompass the majority of the colleges still offering remedial mathematics courses? Or, will we face the eventual condition where colleges offer either elimination options (corequisites) or traditional developmental courses (not updated)?