Ed Barbeau’s Exams and Other Stuff

I’ve been slack on posting of late. To be frank, at the moment I seem to be a little tired from, and of, the crusading. I write this blog, of course, because I want to write it. I want to state clearly my thoughts, and I’m pleased and still very surprised that there is a small readership for these thoughts. Except for the instinctively lazy resistance to the hard work of writing, I enjoy it. But lately it feels more like I’m writing because I “should” be writing rather than because I want to from the gut, and it can be difficult to sustain that “should”. VCAA is currently offering a small, who-would-have-guessed flicker of hope, but the general trend in education, and everything, is clifflike downwards. Every institution appears to have been thoroughly and irredeemably rotted. The argument for sitting on the deck with a gin and tonic, resignedly watching the waters rise, seems a good one.

The feeling will pass, I think, and I’m not fishing for supportive comments. I know that, along with the many people who loathe this blog, there are a few who appreciate it. Both groups make me stronger. So, I’ll try to keep things ticking along while I get back into rhythm. I have one stewing, which involves making fun of Greg Ashman and should be enjoyable to write; hopefully tomorrow. And today’s is easy, and I think very worthwhile.

One of the surprising rewards for having started this blog is to have email-met and then have contributions from some of the big guys: Tony Gardiner and Ed Barbeau and, most recently, Hung Hsi Wu. These were/are mathematicians with a much longer and much more thoughtful commitment to educational reform. My jokes may be funnier and if you need a thug then I’m your man, but these guys are much more worthy of your attention.

Ed and I have been chatting a bit recently, about the TNDOTs and related matters. Ed noted that he was briefly involved in writing Ontario’s similar “Grade XIII” exams in the 1950s. The Ontario exams, which are indeed remarkable, are available on Ed’s website (go to “for teachers“, and scroll down a bit). Ed emailed me some background:

The year I wrote the papers (1956), the first examination was in analytic geometry and it was an unseasonably brutally hot day (June). For some reason, a lot of students found it very difficult and the complaints made it into the press. The Toronto Star had one of its reporters, who had recently graduated from Grade 13, write the examination and he added fuel to the fire by reinforcing the impossibility of the exam. There were calls to “adjust” the marks (which were probably ignored).

To give you a bit of context, Grade 13 was an additional high school year intended for university entrants (senior matriculation). Students who just needed an HS graduation diploma got a graduation certificate in grade 12 (as did everyone — junior matriculation). The only provincial examinations were at Grade 13; the Grade 8 and Grade 12 examinations were abolished earlier. (It is a little analogous with the British A-level, but far less specialized …)

The grade 13 papers were set by a committee of university professors and marked over the course of the summer by a combination of high school teachers and professors who met in a few locations around the province. According to my Grade 11 algebra teacher, each school had to provide a “confidential mark” for each candidate in each subject; an indication of how the student was expected to do. I do not know how it was fed into the system, but I suspect that its purpose was to recognize and compensate for anomalous results (which would of course depend on the track record of the teachers in evaluating their students).

Each year, the province published an examiners’ report for each subject that commented on the questions and their answers, how the students did and what were common pitfalls, etc. The English one was very long and detailed and typeset, containing some of the answers submitted along with comments of the examiners. The mathematical ones were more modest on mimeographed sheets.

The Grade 13 “departmentals” were abolished in the mid 1960s, I believe in part due to the magnitude of the task as more students stayed in high school to Grade 13 and in part to the changing mores about formal examinations. The original University of Waterloo competition was established by a group of teachers (who subsequently became part of the mathematics faculty at the U of W) who deplored the abandoning of the departmentals and wanted to replace them by a voluntary exam that students might use to support a university application for a scholarship.

More broadly, Ed Barbeau’s webpage contains an astonishing amount of material: short articles, newspaper articles, competition papers and so forth. The work of a lifetime and enough for a lifetime, and not forgetting Ed’s many books. Ed notes that the various articles on problems are not written as or intended to be lesson plans. Rather, they are the mathematical story from which a lesson or sequence might be constructed:

My general philosophy of educating the young is that wherever possible you should base your instruction on some task, problem or challenge with gets the pupils into the mathematics and provides experience. In my own limited experience, I have found the results gratifying and the purpose of much of the stuff on the website is to provide situations that lend themselves to this. However, they are not recipes, because in a given situation it is up to the teacher to read the situation and decide how much “scaffolding” (to use an “in” word is necessary); my vignettes give a lot of detail that should be regarded merely as background.

I’ve also added Ed’s page to the Good Resources post, which readers should always keep mind when hunting for good stuff.