As some relief from the heavy lunacy of the AMT debacle, here is a light little story, a lead-in to a second little story to come soon. A couple weeks ago, we were contacted by Simon the Likeable, asking if we had any “old (or new) texts” containing an introduction to matrices suitable for not-so-strong Year 10 students. Simon wanted to avoid using the school’s current Year 11 text, which the students would use next year, but also his inclination was to use an older text.

As matrices are a more modern topic, our old Year 10 (Form 4) texts contained nothing of much use. We did, however, find some good treatments in old Victorian Year 11 texts, including two books by “Bernie” Fitzpatrick and G. L. Watson.* These books were published in 1971 (left) and 1985 (right), with the books’ treatment of matrices close to identical. The later treatment is slightly gentler (and slightly marred by the briefly popular superscript notation for negatives: ^{–}5 instead of -5); we sent that version to Simon the Likeable. Beyond that, there are a couple things worth noting about these texts.

First of all, the texts are very good, *much* better than current texts. They are not great, memorable texts, but they are clear and solid.** Words are used sparingly and carefully. The examples and exercises are well chosen. There are no neon colours to blind the reader, and no idiotic photographs or monkey calculator nonsense to distract from the mathematics. Even the treatment of matrices, which is difficult to get too wrong in an introduction, is clearly better in these earlier texts than in current ones. Bernie Fitzpatrick is of course a legend of Australian textbook writing.*** So the quality of the texts is perhaps due to both the times and the author(s). And, if you hunt hard enough at enough Sunday markets, you can get these books for a dollar.

The second thing to note is that, simply because of their age, the textbooks can end up being very funny. Which is the main impetus for this post (although we’ll also get back to the first point in a future post). The following is an example from the texts (the same in both), the second on multiplication of matrices. It made us laugh, at least.

*) All due apologies are extended to G. L. Watson for our title. But, Bernie was/is the more famous guy, and was perhaps more the driving force behind these books. And we couldn’t resist the ring of the title.

**) A later edition of the 1971 text, together with its companion, were our textbooks in Year 11. We remember liking the texts, more than previous years’, although we didn’t love them.

***) Bernie’s *Pure Mathematics *and *Applied Mathematics*, co-authored with should-be-legend Peter Galbraith, were our Year 12 texts. These books we loved, and love. They were a hundred miles better than anything we had seen, or have seen.

Modern day textbook writers (or is it the publishers?) don’t seem to understand the seductive details effect.

Thanks, Cathy. Is “seductive details effect” a discussed thing? As for who is to blame, no one person could make the current texts as bad as they are: it has to be a team effort.

Well I learned about it in my B.Ed (about 15 years ago). I think it is probably comes under the umbrella of cognitive load theory.

And as far as the production of high school textbooks goes, the only time that I’ve seen it up close and personal (but still not directly involved) the publisher plonked in a whole heap of random photos (cows, coffee beans, paddle boarders) that were not even tangentially related to the text anywhere there was free space.

Thanks Cathy. It also comes under the umbrella of common sense (as does cognitive load theory). The vast majority of education publishers are leeches, pure and simple.

Indeed. I only did the B.Ed (as one half of a double degree) because it was impossible to get registration as a maths teacher without it. It completely lived down to my expectations.

I used to have all the Modern Maths books from the 70’s as I had used them as a student. I used them in my teaching too but then I left teaching for a different career, and they were most likely donated somewhere. I now have one, the partner to the picture shown. They are very hard to find. If anyone has info about any that ate available, I would like to know as I am trying to re-enter the profession…

Thanks, PR. I neglected to mention that pretty much the

onlyway to get these old textbooks is by hunting in Sunday markets. Or, by waiting for teachers to retire and then pouncing. Old textbooks, unless they’re really old, are regarded as worthless, and so used bookstores won’t bother with them.Sometimes I use ideas from (very) old school mathematics text books. Attached is a lesson that I used this week.

However, as I rummaged through my collection, I was struck by the fact that matrices do not appear in them. I started to wonder: When did matrices appear in school mathematics? I did not meet them at school.

8-algebra-todhunter3

I think In Victoria they appeared around 1970, but I’m guessing.

It is a fact that they were on the VUSEB (*) Pure Mathematics exams from at least 1967 (and I suspect earlier than 1967).

* The noble ancestor of VCAA.

Thanks, BIB. Interesting. Why do you suspect earlier?

I can’t find them in the 1966 papers from Victoria, but that doesn’t mean they weren’t part of the course.

Not everything has to be assessed every year.

EDIT: In the book “Exercises for Matriculation – Calculus and Applied” which includes questions from 1961 to 1964 matrices do not appear either.

OK, maybe the curriculum changed as of 1967. I don’t have papers (or syllabi) prior to 1967.

@Marty: My suspicion was just a hunch. Wrong by the looks of it. More like a junch.

Yes, it looks like the mathematics curriculum changed in 1967:

“The MAV had responded to the new conditions by putting in place a Curriculum and Research Group to keep abreast of current thinking in mathematics education, and this group conducted summer schools to provide assistance for inexperienced teachers. A tertiary committee was formed in 1961 and this group set about the task of preparing new syllabuses which were to be adopted by VUSEB to commence in 1967. On a wider front the MAV responded by founding, in 1965, the School Mathematics Research Foundation (SMRF), based at Monash University.”

Quoted from page 10 of attachment, downloaded from here:

chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://vuir.vu.edu.au/25717/1/TECHNICALREPORT16_compressed.pdf

TECHNICALREPORT16 – The Emergence of a Discipline-Mathematics Education

That might depend on which state you are in.