Coverage vs. Mastery: Slowing Down with Dave Willard

A couple of weeks back, we had the opportunity to come together around math instruction at East Montpelier Elementary School for clinical rounds with Mahesh Sharma.  Mahesh worked with a group of fourth grade students who are taught math by Anne Carter and Dave Willard.  After working with the students, Mahesh remarked how well they did.  As I watched the class, I was seated next to a fifth grade teacher who was also favorably impressed.  Dave and Anne spent a little time with us afterwards reflecting on the changes that they made to their math instruction this year.  These changes were inspired by the training they received together last summer at "Lab School" - a week long course focusing on math instruction that was taught by Mahesh. 

Dave was adventurous enough to agree to let me capture some of his thoughts and ideas on the video embedded above (if you can't see the video, here is a link).  He's very articulate (even under duress), so be sure to watch Dave discuss how he changed from a "coverage" mindset to a "mastery" mindset this year.  And he feels that this change has made his students stronger math learners. 

At the heart of the issue is an idea that I've been calling "slow math" around my household where my third grade daughter races to memorize times tables, and rolls her eyes at me when I ask her about distributive property strategies or to explain why multiples of 8 are always even or why the "nines trick" works.  She feels that these kinds of questions just slow... her... down...  Unbearable mother than I am, in response, I say, "Good!"

Perhaps this could be a movement akin to the "slow food" movement that has gained traction across Vermont.  The idea is that quality takes time.  It's about nutrition, but it's so much more than that.  Nothing is simple.  It's about savoring the complexities that are inherent in a substance rather than simply making it palatable and wolfing it down.  It's about developing more sophisticated tastes.  It's about the importance of understanding where things come from.  It's about reflecting on what went into creating the meal.  Ultimately, it's about love and health and sustainability, rather than blind consumption.

Maybe I'm romanticizing (and I'm certainly a math nerd), but I feel we should demand a lot of ourselves and our students as consumers of math knowledge.  Math is not meant to be fast food.  "Fast math" does not sustain us, it just props us up for a while like a simple carbohydrate.  Then, it fails us miserably when we need to use it to do something challenging.  Unfortunately, fast math (like fast food) tastes good and is easily available.  We might even convince ourselves that fast math is somehow better.  We want it to be better.  Once kids get a taste for it (like my daughter), it's difficult to convince them that it's unhealthy junk.  Yet that is what we must do for their sake and for ours.

When it comes right down to it, "slow math" (like "slow food") is much more demanding, but it's not an impossibility.  It's not reserved for a select few.  We can all have it, if we take the time, and we will be stronger for the effort.  This is why when given the choice between "coverage" and "mastery," we must chose mastery.