Path Dependence

Q: Why are we so scared to change our default model for math instruction from direct instruction to something a lot more constructive?

A: Path dependence.

Wikipedia defines path dependence as follows:

Path dependence explains how the set of decisions one faces for any given circumstance is limited by the decisions one has made in the past, even though past circumstances may no longer be relevant.

Path dependence explains why computer manufacturers still use the QWERTY keyboard, and explains why the software we use dictates so much of our lives.

Path dependence is rampant in our schools - our discipline systems themselves include several path dependencies...but that's not what interests me the most. What I find most fascinating right now is our generally consistent approach to math education.

Here's the genesis of math education at No Excuses charter schools, as I see it:

The Setup: For years, math education had become increasingly 'progressive', asking kids to think about concepts deeply. They grappled with difficult problems. However, the thought that direct instruction would stifle their thinking or creativity stopped them from being directly taught some key math concepts or skills. Parents were frustrated: How could it be that their 4th grader didn't know how to add fluently?

Some teachers ignored the new wave of math instruction and just taught kids the way they knew best. One of the best such educators was Ms. Harriett Ball. She taught Dave Levin, who, together with Mike Feinberg, started KIPP. KIPP immediately saw incredible gains in math scores on the Texas state test. Dave went to NYC, where he started a school that got similarly high results.

This style of teaching was very heavy on the basics.I remember from the early-ish KIPP days that we used to share chants and songs and tricks, all with the goal of increasing our kids' procedural fluency. There was also an emphasis on "critical thinking", and though we spent a lot of time on it, it basically boiled down to a lot of word problems. We tried to make them relevant, though many ended up as pseudocontext with our own kids' names added to show them we cared about them.

(Aside: I still think most schools I have seen outside of No Excuses schools generally under-emphasize procedural fluency; it is certainly a key to understanding math down the road, as it frees up working memory to think at higher levels and make connections with new material.)

The gist is this: Our schools have distinguished themselves through the use of some form of direct instruction to fill gaps that were not being filled by other schools. Parents wanted our schools because they knew we would teach the basics. We have earned some accolades based on this style of teaching. It has served us well.

Zoom forward to 2013, and here's where we are:
Students at No Excuses schools still score relatively high on math tests. Though there is a very low sample size, I think it's safe to say that this is clearly the case more in states with easier math tests than in those states that moved toward a more rigorous assessment early on. At our school in Florida, we were not prepared for the rigor of the FCAT. Schools in Tennessee struggled when the test became more rigorous. Minneapolis struggled. KIPP Lynn seems to be a positive outlier here - their math scores are still good, partly because they have consistently focused on high-quality instruction.

The Common Core is coming. Rigor is going up across the board.

So we're trying to change up our instruction to meet these demands. It's great, and it's definitely best for kids. After all, how many people actually still believe a direct-instruction approach to math is really the best way to teach? Not many.

The problem is that we're going through some discomfort. We're afraid of what happens when our kids don't master the basics. We're afraid we'll end up like the schools our parents were running away from so many years ago. We're uncomfortable, because we've never taught like this before. A lot of this thinking is path dependent - because we began in states that emphasized low-level fluency, because we've developed curricula in this way, it feels very odd to depart from it.

But we shouldn't let this stop us from doing what we think is right. There are great examples out there - probably MORE great examples than there ever were of direct instruction lessons. We have Dan Meyer, Fawn Nguyen, and Kate Nowak. We have a whole community of teachers that has been thinking about this longer than we have. They tweet, they blog, and they share. We have tasks that are created to bring out the standards in Illustrative Math, and, as always, we have Marilyn Burns, Marcy Cook, Magdalene Lampert, and Deborah Ball.

This journey may not be easy - there will be a lot of bumps, and we'll all feel we're not quiet as good at our jobs as we once felt we were - but it is necessary. In the end, I look forward to the day where kids love math for math's sake, where the joy in our room reflects the joy of our discipline, and where we can bring the small pieces we've done very well and embed them in a rich, thought-provoking curriculum.