I chose this class for a couple of reasons. First, I wanted to experience a MOOC. Second, I have had an interest in learning calculus and wanted a course that would be challenging; I wanted to put myself in the same position as my students. I have not been disappointed. This class has taught me a great deal about learning and teaching.

I think it is all too easy for us as educators to forget our purpose. Our purpose is not to dispense information. Our purpose is to help students develop understanding. My experience in this MOOC has taught me the difference.

If we assume that content or information is the independent variable and understanding is the dependent variable, a graph of our learning might look like this:

What I have come to understand is that this is normal. According to Brian Cox, “Everyone gets confused and stuck. Very few people understand difficult concepts at first.” When our rate of change of understanding has a zero or negative slope, we need time to develop a mental model that accommodates the new information. This is not revolutionary news – in fact it’s common sense. Don’t we talk about life’s “ups and downs?” What doesn’t make sense is how we respond as educators.

The problem we have as educators is we tend to teach at a constant rate of content delivery. We teach at a constant rate and expect our students to learn at a constant rate. This is unfair to both educator and student. What ends up happening when we teach at a fixed rate is we get variable learning. The “A” students are simply those that whose rate of change in understanding is equal to the rate of content delivery.

With today’s technology this doesn’t need to be the case. When a student reaches a point of cognitive disequilibrium, we should be able to suspend the delivery of new content and work on developing the necessary schema to understand the current concept. We have to build a ladder of abstraction ala Dan Meyer.

Remediation, additional time, or additional support might be necessary. When an acceptable level of understanding is achieved, the student can resume learning new content and the rate of change of understanding will become positive again.

Online environments are particularly well suited to this idea. Let’s say a course is traditionally offered in a 15 week format. Would it really be a crime if it took a student 20 weeks to master the material? Is that preferable to failing or dropping a course? It would require a new attitude toward education but it seems it is something to consider.

It has been said that reform is nothing more than improving a broken model. As we explore the possibilities of MOOCs and online learning, maybe we should be open to changes in the timing of our content delivery and the way we assess understanding.

As an endnote, I enthusiastically recommend the Calculus One offering from Ohio State University. Dr. Fowler and his staff do a great job. I am not only learning calculus, but I am also discovering a new interest in mathematics. I would say this course is an exemplary model for online content delivery.