Guest Post: Ed Barbeau – Exercises that Schmeck

Ed Barbeau took up my recent offer for readers to write something for the blog, and has contributed the following, typically excellent, article. 

 

EXERCISES THAT SCHMECK

Whatever your approach to mathematical pedagogy in the schools, it appears that the pupils have to work through a lot of sludge. At the end of a section in a textbook, they might be faced with a large number of similar low level exercises that are essentially rote and restricted in their application. Continue reading “Guest Post: Ed Barbeau – Exercises that Schmeck” →

The Problem of Conceit and the Importance of Conception

A couple weeks ago, I wrote about my brother Jeff happily declaring women to be objects, and the philosopher Frege’s attempts to untangle concepts from the objects to which those concepts may apply. The point, apart from the self-indulgent pleasure of reminiscing and of pondering such things, was to raise the question of the meaning and the value of categorisation: how do we distinguish this from that and what is the value in doing so? The broader purpose of that post was to provide a (gratuitous and elaborate) introduction to two posts on Ashman and his dismissal of conceptual understanding. And, here we are, with Post Number 1.

Continue reading “The Problem of Conceit and the Importance of Conception” →

The Concept ‘Horse’ is an Object

JEFF

Once, when I was a teenager, I was hanging out with my brother Jeff and some of his university acquaintances. The conversation was meandering, in the solving the world manner that students have always loved. At some point, a girl made the very standard complaint,

“Women are being treated as objects.”

My brother, employing his famous Jeffersonian diplomacy, responded,

“But women are objects.”

And the fun ensued. Continue reading “The Concept ‘Horse’ is an Object” →

David and Gareth’s Extension Book Is Out

Cambridge has just published Enrichment Mathematics for Secondary Students (22/01/26 – link fixed). Cambridge describes the set as “an inspiring and challenging new series for ambitious 7-10 maths students and teachers”, and I strongly agree (except for their use of the term “maths”). I don’t know of any other text, anywhere, that is as good at covering secondary pre-calculus curriculum material, and should-be-curriculum material, at such a deep level. Continue reading “David and Gareth’s Extension Book Is Out” →

Terry Mills’ VCAL Problems

When not making annoying non sequitur comments on the blog, Terry Mills works very hard to be a very good teacher. This includes hunting for and working hard to create mathematical resources for his students. One such is a list of problems compiled by Terry. Prompted by Sunday’s problem-solving post, Terry reminded me yesterday of his collection. As Terry put it,

A few years ago I taught a class of VCAL students; VCAL was the predecessor of Foundation Mathematics. I was told that these students are not interested in mathematics; they all want to go into a trade; so teach them something about building.

I met the students and indeed many did want to go into a trade: building, electrician, beauty therapy, or hospitality. Some were there because they had never been successful in mathematics. Some came to Australia as refugees and did not speak English very well.

What did they have in common? Nothing!

So I decided to give classes devoted to solving problems.

Attached is what grew out of my experience.

Many of Terry’s problems are not “problems” in the sense of Sunday’s post (although what constitutes a “problem” is very much in the eye of the beholder). But, whatever one calls them, it seems to me be a very nice collection, very suitable for the students it would suit.*

*) Terry i forgiven for Questions 31 and 32 (just).

How Does One Teach Problem-Solving?

Yes, it is Problem Season here in Crapland. Yesterday there was a new TNDOT, with a couple others still outstanding, and there are more problems, below. But I am less interested in solutions to the problems below than I am in how one might teach them, if that is even the proper phrasing. How, generally, does one teach the techniques, or perhaps the art, of problem-solving? Continue reading “How Does One Teach Problem-Solving?” →

Notch 9: Ed Barbeau’s Classroom Problems, and His Request

Ed Barbeau is a Canadian maths ed legend, and an occasional commenter here. I previously noted Ed’s astonishingly extensive website, which is also listed in the Good Resources post, and I posted a long comment of Ed’s on gifted education.

Ed has recently compiled a list of classroom problems, accompanied by discussions, which he has used “positively” in classrooms. He is now requesting teachers will also give them a try and see how they go, and let Ed know how they go: Ed wants your feedback. 

Ed’s document of problems is here (and is embedded below), and you can email Ed. to provide feedback. (Of course everyone is also free to comment below.) Ed also makes it clear that he is happy for the document to be passed around further afield.

What follows are two (slightly edited) introductions: a short one, which Ed used to introduce the problems on an email group; then the longer introduction from the document, which is worth reading in itself. Continue reading “Notch 9: Ed Barbeau’s Classroom Problems, and His Request” →

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.

Continue reading “Ed Barbeau’s Exams and Other Stuff” →

Notch 8: Battling Away at Prince Alfred College

Anthony Harradine is tireless in trying to save Australian Maths Ed. He is responsible for MathsCraft and Numerical Acumen, and all manner of things. Anthony invariably takes a positive, Nice Guy approach to all this. Nonetheless, we get along very well.

Continue reading “Notch 8: Battling Away at Prince Alfred College” →

Notch 7: Ed Barbeau on Gifted Education

A very pleasing irony of writing this thoughtless and classless, “We’re all doomed” blog is that it has resulted in my being introduced to thoughtful and classy heroes like Tony Gardiner, mathematical stars who have been working tirelessly for decades that we not be doomed. The most recent introduction is to Edward Barbeau, a star of Canadian mathematics education. Tony Guttmann, AKA Mr. Very Big, alerted me to a long comment Ed contributed to a maths-ed discussion, on gifted education. Ed has kindly permitted me to reproduce his great comment here. Continue reading “Notch 7: Ed Barbeau on Gifted Education” →