Developmental Mathematics Revival!

All of The Above

Somehow, I am on my congressperson’s email list; fortunately, he does not produce too much spam. However, sometimes the emails sent from his office provide an interesting thought.

A recent email focused on energy policy, and touted an “all of the above” approach (exploration, federal lands, nuclear, coal, green, etc). I started thinking … policy is based on a goal (or problem) and reflects the understanding of how we can achieve a desired outcome (also known as progress). In the context of energy policy, ‘all of the above’ is a non-policy. It strikes me more as a desperate person thrashing wildly in the water to avoid drowning.

In developmental mathematics, though, we have been practicing “all of the above” for many years. We work from where we are, and we add ideas that sound productive. I think we appear to many others to be ‘thrashing wildly in the water’, and I know that some of us actually think this is accurate.

Is there an alternative? Yes, of course … though it requires going back to an empty page in many ways. We have a small set of basic questions that should guide (and somewhat determine) all of our work: What is important mathematics for all students? What does it mean to ‘learn’ this mathematics? How can we determine if a student has achieved this learning?

Our understanding of these questions is critical, for we know that various methodologies have different strengths … their impact on learning is different, and each is better suited to particular learning goals. For example, we generally give broad support to ‘problem solving using mathematics’, and this means capacity to transfer learning in our domain; research has determined how this outcome can be enhanced, and which methodologies are likely to be more effective. One specific point: Contrary to popular mythology, ‘drill’ is not ‘kill’ — repetition of skills forms a critical basis for development of problem solving; the problem is not ‘drill’ … the problem is ‘only drill’.

Think about this ‘all of the above’ idea. Take a look at totally new models (like New Life), and consider your own ‘answers’ to the basis questions. Our professional standards (Beyond Crossroads, http://beyondcrossroads.amatyc.org/) suggest that our work be focused on achieving our shared goals. “Thrashing wildly” in an “All of the Above” mode does not appear in the improvement cycle.

As long as we continue an “All of the Above” approach to our work, we actually achieve “None of These”.