Towards Effective Remediation: Quantity and Pacing

I’ve been having conversations about arithmetic and similar topics (at the Achieving the Dream conference, and online at MATHEDCC).  In some cases, the conversation was the result of telling people about the New Life model (see https://www.devmathrevival.net/?p=1401).  In other cases, we had been discussing other issues.

So, I have been thinking about related issues.  As a result, I have some ideas of how to frame a conversation about developmental mathematics that might help us make progress.  To start with, we often describe developmental mathematics by using names of courses or by listing topics with implied outcomes.  In our New Life work, we actually started by examining the types of mathematics that students need to succeed, and dealt later with course names and lists of topics.

Our curricular designs are based on our assumptions and goals, which are often unstated.  One of the most problematic assumptions is:

It is effective to deal with 8 general topics, with 10 to 15 outcomes within each, in one course.

There are two fundamental problems with this.  First, the courses we design cover so much ‘material’ that we prevent the learners’ brains from dealing with the associations and connections that are part of learning; this results in most students focusing on just remembering what to do, rather than making sense of it.  Second, the design is based on the absence of prior learning (good and bad) in the learner; this is obviously not true in almost all cases.  Time is needed for us and students to identify where there are conflicts between prior learning and current need, and time is needed to deal with these conflicts.  The result is that we add another layer of ‘learning’, one that is weaker than prior learning; students after our courses are notorious for returning to wrong methods and ideas after our course is done … because we do not provide a method of correction.

We need to slow down; learning is much more complex than having a list of 80 to 120 outcomes.  Since we need to go slower, we must be strategic about what areas to focus on .. trying to do it all (or even most of it) means that we are willing to accomplish little of significance.

This strategic work should be based on our judgments as mathematicians about which mathematical ideas are most important in particular cases.  Do we want work with fractions, or do we want work with proportional reasoning?  If we want both, what are we willing to give up … percents or linear models (as examples)?

We need to do some critical thinking about our goals and purposes, and apply our problem solving skills so that our courses are effective learning experiences for our students.

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