This year, BC teachers (K-9) implement a new curriculum. For the past two years, much of my focus has been on helping teachers–in all subjects–make sense of the framework of this “concept-based, competency-driven” curriculum. This will be the topic of these next few posts.

In this series on curriculum, I’ll do my best not to use *curriculum*. There is no agreed upon definition. I imagine that if any educator in the “MathTwitterBlogoSphere” (#MTBoS) followed the link above, she’d be shouting “Those are *standards*, not curriculum!” Similarly, when #MTBoS folks talk about adopting curriculum, I’m shouting “That’s a *resource*, not curriculum!”

My union makes the following distinction: “Pedagogy is how we teach. Curriculum is what we teach.” *Curriculum* as *standards*. For the most part, this jibes with how *curriculum* is used in conversations with colleagues and is echoed in this Ministry of Education document. But Dylan Wiliam doesn’t make this distinction: “Because the real curriculum â€“ sometimes called the ‘enacted’ or ‘achieved’ curriculum â€“ is the lived daily experience of young people in classrooms, curriculum *is* pedagogy.” *Curriculum* as *experiences*. Or pedagogy.

Rather than *curriculum*, I’ll try to stick with *learning standards*, *learning resources*, or *learning experiences*.

Three elements–Content, Curricular Competencies, and Big Ideas–make up the “what” in each subject and at each grade level. Last summer, the Ministry of Education simplified this as the “Know-Do-Understand” (“KDU”) model. The video below describes how content (what students will know), curricular competencies (what students will do), and big ideas (what students will understand) can be combined to direct the design of learning activities in the classroom.

I imagined planning a proportional reasoning unit in Mathematics 8 using the KDU model and shared my thinking throughout this process.

Teachers can start with any of the three elements; I started by identifying content. (It’s a math teacher thing.) Then, I paired this content with a big idea. In English Language Arts and Social Studies, it makes sense to talk about you, as the teacher, making decisions about these combinations. In Mathematics and Science, this mapping is straightforward: algebra content pairs with a big idea in algebra, not statistics; biology content pairs withÂ a big idea in biology, not Earth sciences. (BC math teachers may notice that the big idea above is different than the one currently posted on the Ministry of Education website. It mayÂ reflect a big idea from a previous draft. I can’t bring myself to make that change.)

Identifying curricular competencies to combineÂ with content and big ideas is where it gets interesting. Here, my rationale for choosing these two curricular competencies was simple: problems involving ratios, rates, and percent lend themselves to multiple strategiesâ€¦ we should talk about them. The video makes the point that I could go in the opposite direction; if I had started with “use multiple strategies,” I likely would have landed at proportional reasoning.Â Of course, other curricular competencies will come into play, but they won’t be aÂ focus of this unit. This raises questions about assessment. (More on assessmentÂ in an upcoming post.)

Note that “represent” is missing from my chosen curricular competencies. Why is that? My informed decision? Professional autonomy for the win? Or my blindspot? A teacher who sees proportional reasoning as “cross-multiply and divide,” who is unfamiliar with bar models, or double number lines, or ratio tables, or who sees graphs as belonging to a separate and disconnected linear relations chapter wouldn’t think of connecting this content to “represent.” Making connections between these representations is an important part of making sense of proportional reasoning. Will this build-a-standard approach mean missed learning opportunities for students? This speaks to the importance of collaboration, coaching, and curriculum, er, I mean quality *learning resources*.

In early talks, havingÂ these three elements fit on one page was seen as a crucial design feature. Imagine an elementary school teacher being able toÂ view–all at once!–the standards for nine different subjects, spread out across her desk. As a consequence, the learning standards are brief. Some embracedÂ the openness; others railed atÂ the vagueness. In some circles, previous prescribed learning outcomes are described using the pejorative “checklist”; in others, there is a clamouring for “limiting examples.” (Math teachers, compare these content standards with similar Common Core content standards.)

I wonder if the KDU model *over*simplifies things. If you believe that there is a difference between *to know* and *to understand*, then you probably want your students to *understand* ratios, rates, proportions, and percent.Â For a “concept-based” curriculum, it’s light on concepts. Under content, a (check)list of topics. To that end, I fleshed out each of the three elements (below). But I have the standards I have, not the standards I wish I had. (Free advice if you give this a try: don’t lose the *that*Â in that stem below.)

kdu-proportional-reasoning.pdf

I wonder if the KDU model over*complicates* things. Again, U is for what students will *understand*. But “understanding” is one of the headers within the D, what students will *do*.

Despite this, I have found the KDU model to be helpful. In particular, it’s been helpful when discussing what it means to *do* mathematics. The math verbs that we’re talking about are *visualize*, *model*, *justify*, *problem-solve*, etc., not *factor*, *graph*, *simplify*, or *solveforx*. Similar discussions take place around *doing* science (scientific inquiry) and social studies (historical thinking).

More broadly, the model has been helpful in makingÂ sense of the framework of our new curriculum, or *standards*. It’s a usefulÂ exercise to have to think aboutÂ specific combinations–far more usefulÂ than:

Q: “Which competencies did we engage in?”

A: “All of ’em!”

We’re still some distanceÂ from “the lived daily experience of young people in classrooms” but it isn’t difficult to imagine learning experiences in which this specific combination of the three elementsÂ come together.