In the classic problem solving methodology, the intense effort is placed in two early stages — understand the problem, and make a plan. In the case of mathematics (especially developmental mathematics), we have seen much hand-wringing and gnashing of teeth, often accompanied by saber-rattling, about ‘the problem’. However, a problem can only be defined by comparing the current condition to the desired condition. Looking at data is a first step, but can often lead to short-sighted efforts that do not solve any significant parts of the problem.
Here is one overview of a plan for mathematics in community colleges (focusing on developmental mathematics, though not restricted to that):
- All math courses must provide good mathematics (appropriate and powerful concepts to deal with quantitative situations).
- All math courses must prepare students for mathematical needs that they will encounter in college.
- Community college mathematics is not a repeat of school mathematics.
- Community college mathematics is compatible with, and supportive of, university mathematics.
- Reasoning and problem solving are central goals of mathematics as part of a general education.
- Remediation is needed for some students, ideally limited to one course or a fast-track experience for most of those students.
- Any student might be inspired to higher goals, and many are capable of additional mathematics in a reasonable amount of time.
If a “solution”, whether modules or online homework or emporium model, only deals with the patterns of the data, then the solution will not solve anything important. In some cases, the ‘pass rates’ might rise temporarily or even long-term; however, there is still likely to exist a substantial gap between a larger plan for mathematics and what is actually delivered to students. If the traditional mathematics does not contribute to a larger plan (which is my view), then a solution plan involves much more than the delivery system and much more than course organization.
In the case of developmental mathematics, we have a historical artifact which is based on a premise that we need to provide the same mathematics that students should have learned in high school. Such an approach is arbitrary, unrelated to mathematical needs, and dooms our courses … and dooms our students … at the system level. Having a sequence of 4 courses in developmental mathematics guarantees that less than 20% of the students will reach college work, based on an unreasonably high 80% pass rate and 80% retention rate. The response, based on ‘the data’, is to get students to their exit point in this ‘school mathematics’ as quickly as possible (modules); is our plan for mathematics that students should be shoved off the train as soon as possible … or do we want to have an opportunity to inspire students?
The emerging models — AMATYC New Life, Carnegie Pathways, and Dana Center Mathways — are based on a larger plan. However, many of us are looking at them as responses to ‘the data’. For these models to work well, the faculty and colleges involved need to have a deeper understanding of a plan for mathematics. Hopefully, you will see much in the plan outlined above that you can agree with. One of our basic problems is that policy makers do not have this larger plan for mathematics in mind; they, naturally, focus on the data. We, and our professional organizations, need to articulate a larger plan so that we can better serve our students.
One of my colleagues said, back in 2008, that pass rates are the least of our problems in mathematics. I agree. We need to have a plan for mathematics, and build new curricula to support that plan.
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