There's a difference between curriculum and pedagogy. Curriculum is all about what we teach. Pedagogy is about how we teach it.
There's also a difference between knowing how to do something and understanding what you're doing. In mathematics there are all kinds of "how-to", or computation skills, that kids learn and promptly forget right after the test; sometimes they forget before the test. The thing is though, it's difficult to forget something once you understand it.
A few weeks ago I was part of a panel on the Richard Cloutier Reports show on CJOB radio here in Winnipeg. There were four of us: myself, Paul Olson (President of the Manitoba Teacher's Society), Robert Craigen (Associate Professor of Mathematics, University of Manitoba) and Anna Stokke (Associate Professor of Mathematics, University of Winnipeg). Robert and Anna are one-half of the group behind the wisemath blog.
There are some things we agree on:
- All kids can and should learn basic computation skills (how to add, subtract, multiply and divide).
- It's important for kids to understand what they're doing, not just to be able to perform by rote.
- Manitoba's recent poor performance on the Pan-Canadian Assessment Programme test is not good news and we have some work to do in mathematics in Manitoba.
- We'd like to see Manitoba place at the top of future national and international tests of this sort.
Some things we disagree on. I believe:
- Learning with understanding should precede the learning of rote algorithms in mathematics.
- To say Manitoba has placed 10th out of 11 provinces and territories in the 2010 PCAP test is a gross oversimplification of the the data represented on page 24 of the report (pdf). (Those confidence intervals are important. A repeat of the same test would likely have Manitoba place somewhere between 6th and 11th place. This isn't good news, but it's a little more nuanced than "10 out of 11". People knowledgeable about mathematics should be helping the public understand these nuances and promote informed discussion.)
(1) I believe Robert and Anna conflate curriculum and pedagogy and are reading the Manitoba Curriculum documents as pedagogical texts when they were never intended to be read that way. Curriculum tells us "what" to teach, not "how" to teach.
(2) Robert and Anna believe the teaching of algorithms should be student's entry point to learning the basic operations (+, -, x, ÷). I believe the algorithms should be closer to the end-game of learning the basic operations.
John Scammel blogged about his take on the views expressed on Robert and Anna's blog. John points out in the comments the clear distinction the wisemath blog draws between Mathematicians and Mathematics Educators and the populations we teach. In K-12 classrooms we teach all students. The student body in University is different. Students taking math at University want to be there. That's not true of many students in the K-12 sector; the challenges are quite different.
On further reflection, there's a third difference: public (and private) debate should be open and sidestep insult.
The wisemath site seems to reject any comments that debate the blogger's views.
What I've read in the comments on John's blog and on Anna's blog (The last sentence of the last paragraph was recently edited; it used to say all future mathematics education research has no merit as a result of the issues Anna took with the article she blogged about. I regard this edit as a positive evolution in her thinking.) seems to hold K-12 teachers in a disdainful light.
Here's the audio from the CJOB panel we sat on together. It was a 2 hour broadcast, without commercials it's about 58 min. I took out the commercials. We talked about much more than was broadcast in the moments we were "off air". That was also an interesting conversation; unfortunately we didn't capture it. Next time I'll bring along my mp3 recorder. ;-)
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