Curriculum Coherence

Matt Larson wrote a great article last month as the NCTM President’s Message titled “Curricular Coherence in the Age of Open Educational Resources“. He argues that, without serious effort and collaborative work in professional learning communities, using online tasks and activities is likely to lead to an inconsistent experience for students that undercuts curricular coherence.

I’ve never had access to a coherent, high-quality curriculum. I have always had to supplement with resources that I’ve either found on the internet or created myself. It’s easy to be defensive and argue that Matt is wrong — that there are lots of high-quality resources on the internet and that many teachers have the expertise to put them together into an effective curriculum.

Case Study
I wish I had time to do that on a regular basis. Too often I don’t. I am teaching expected value in Precalc right now. So I went to my usual haunts for resources. A few tasks from Illustrative Mathematics, some questions I threw together based on the Wheels of Fish, Chips, and Peas that Darryl and Bowen used at PCMI, a Yummy Math lesson I just found on two point conversions, something cool from Dan Meyer, something else cool from Dan Meyer, and some Mathalicious lessons in their probability unit.

It’s a bit of a mess. There’s high-quality stuff in there, but I’m having trouble sequencing it, figuring out the best places to deliver explicit instruction, and using consistent representations across tasks. I think kids will have some good opportunities for learning — there are benefits to seeing a concept in a wide range of contexts. But this is far from an ideal unit.

Counterpoint
This is my first time teaching expected value; I am particularly in need of high-quality curriculum for that unit. That’s less the case for quadratics. I’m teaching graphing quadratics in Algebra II right now; I’ve taught this unit before, as well as introduced quadratics in Algebra I. I have a much better idea what a learning progression looks like, and instead of scrambling for anything to work with, I’m trying to supplement what I’ve done before with some more high quality activities. In this case, I’m plugging in the great Desmos lesson Build a Bigger Field, and then on the following day teaching the Mathalicious lesson Prescripted. These two lessons get at a challenging idea — writing a quadratic model for a particular situation of the form y=x(a-x), and analyzing that function to learn something about the situation.

This feels like a much stronger curricular choice. I’m definitely lacking in meaningful application tasks for quadratics. The activities complement each other well, fill a gap in my prior curriculum, and I have the chance to put some effort into figuring out how I will teach them and link them together.

I love all of the resources that exist through online communities; I’m sure that, no matter what curricula I have access to in the future, I will keep using many of them. But Matt’s right — it’s easy to divorce the potential of great online activities from the reality, and to mistake a lesson that’s cool and fun for one that leads to meaningful student learning. I have trouble doing this. But no single lesson, no matter how amazing it is, is likely to make or break a student’s understanding of some topic in math. That happens with lots of effort, over time, as ideas build on previous knowledge and connect to the broader curriculum.

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