# This is what I’ve been saying…

I ran across this from Koeno Gravemeijer, quoted by Jeffrey Choppin in the Mathematics Education Research Journal:

Older design principles take as their point of departure the sophisticated knowledge and strategies of experts to construe learning hierarchies… The result is a series of learning objectives that can make sense from the perspective of the expert, but not necessarily from the perspective of the learner.

This is where I have struggled with the Common Core State Standards. That business about complex fractions last spring? This is what I was talking about. My recent fussiness with Hung-Hsi Wu? Ditto. Even that business about logs and quotients; it was about the difference between the views of mathematics content seen by experts and by novices.

### 3 responses to “This is what I’ve been saying…”

1. Laura

So, are you saying that the Common Core was developed by “experts” and is therefore non-sensical to the novice (teachers/students)? Or that it was designed by the perspective of the “learner” and therefore does not address the hierarchies future experts might need? I’m trying to follow your thoughts on this and I’m confused.

2. Christopher

Not the whole thing, Laura, but yes. I do think that many of the distinctions that get drawn in CCSS reflect an expert’s viewpoint rather than one that would be sensible to learners. And furthermore, I think that’s what Wu was praising in the article that sent me on my two-week Daily Wu bender.

Consider Wu on fractions. He seems to be arguing that the multiple interpretations of the symbol “2/3” are incomprehensible and meaningless, when in fact they are at the very core of how people use and talk about fractions. Viewing a fraction as an ordered pair is an expert viewpoint. Making sense of when a fraction represents a part-whole relationship, when it represents a part-part relationship, when it represents a number and when it represents a comparison of two numbers? These are things novices (e.g. elementary and middle-school students) need to sort out.

Consider complex fractional unit rates. I argued in a series of posts that sixth-graders can handle 1/2 mile in 1/4 hour just fine without needing to think of this as (1/2)/(1/4) miles per hour. The distinction between these two ways of notating a rate is purely the creation of experts and not at all relevant to the development of 12 year-old learners.

3. Christopher

Looking back at the beginning of the Gravemeijer quote, I notice a possible source of confusion. I would say (again in disagreement with Wu) that CCSS is designed using “older design principles”.