Plane thoughts – part 2

I recently participated in a meeting for the EdCan Network, part of the Canadian Education Association, in Mississauga. I knew we’d be talking about some heavy issues regarding education in Ontario, especially K-12 education. I spent my time on the flights down and back writing some thoughts I’d been wrestling with. I’m planning to share those thoughts in small posts for a little while. Here’s the second entry.

Our curriculum is a Least Common Multiple curriculum. Consider all of the different factors that are components of the complete educations for each child. Our exhaustive curriculum tries to include all of those factors in every child’s education. This is unnecessary and inefficient, and frustrating for the students. This is the Just-In-Case curriculum.

We need a Greatest Common Divisor curriculum. We should identify the factors that are in common between every child’s educational needs and include only those in the compulsory curriculum. This minimalist approach would leave room for children to explore and specialize without wasting their time on irrelevancies. This is the Just-In-Time curriculum.

Consider how schools would be different with narrow curricula and expansive opportunities. A small core and room to explore.

 

Different kinds of Thinking: Ontario Math Achievement Chart

I’m evaluating some student work today and I’m struggling with the Achievement Chart for Mathematics (see page 28). In particular, this part of the Thinking category is bothering me:

An excerpt from the math achievement chart for Ontario

Take a look at the first point in “Use of planning skills”, called “understanding the problem”, which includes “formulating and interpreting the problem” as an example of that skill.

Now look at “Use of processing skills” point “carrying out a plan”, which includes “modelling” as an example of that skill.

Are these different? In my mind (up until now, at least), “formulating and interpreting the problem” has meant representing a situation mathematically so that we can apply our other math skills to solving it. Isn’t “modelling” in the context of “carrying out the plan” sort of the same thing? Representing components of the problem mathematically? Is the difference justĀ when it happens (i.e. formulating/interpreting is initial planning, and modelling is during the act of solving)?

I’m not trying to be pedantic here; I’m having trouble distinguishing between the different components of Thinking when I’m trying to assess and evaluate my students’ work. I could use some external thinking on this issue (and math evaluation in general, I suppose).

Please comment; I’d love to talk to you if you have ideas about this stuff.