WitCH 23: Speed Bump

Our second WitCH of the day also comes from the 2017 VCE Specialist Mathematics Exam 2. (Clearly an impressive exam, and we haven’t even gotten to the bit about using inverse trig functions to design a brooch.) It is courtesy of the mysterious SRK, who raised it in the discussion of an earlier WitCH.

Question 5 of Section B of the (CAS) exam concerns a boat and a jet ski. Though SRK was concerned with one particular aspect, the entire question is worth pondering:

The  Examiner’s Report indicates an average student score of 1.4 on part a, and comments,

Students plotted the initial positions correctly but significant numbers of students did not label the direction of motion or clearly identify the jet ski and the boat. Both requirements were explicitly stated in the question.

For part i, the Report indicates an average score of 1.3, and comments,

Most students found correct expressions for velocity vectors. The most common error was to equate these velocity vectors rather than equating speeds. 

For part ii, the Report gives the intended answer as (3,3). The Report indicates that slightly under half of students were awarded the mark, and comments,

Some answers were not given in coordinate form.

For part i, the Report suggests the answer {\sqrt{(\sin t - 2\cos t)^2 + (1 + \sin t + \cos t)^2}} (with the displayed answer adorned by a weird, extra root sign). The report indicates that a little over half of the students were awarded the mark, and comments,

A variety of correct forms was given by students; many of these were likely produced by CAS technology, including expressions involving double angles. Students should take care when transcribing expressions from technology output as errors frequently occur, particularly regarding the number and placement of brackets. Some incorrect answers retained vectors in the expression.

For Part ii, the Report indicates the intended answer of 0.33, and that 15% of students were awarded the mark for this question. The Report comments,

Many students found this question difficult. Incorrect answers involving other locally minimum values were frequent.

The Report indicates an average score of 1.3 on part d, and comments;

Most students correctly equated the vector components and solved for t . Many went on to give decimal approximations rather than supplying the exact forms. Students are reminded of the instruction saying that an exact answer is required unless otherwise specified.

Lots there. Get hunting.

WitCH 22: Inflecting the Facts

We’re back, at least sort of. Apologies for the long silence; we were off visiting The Capitalist Centre of the Universe. And yes, China was great fun, thanks. Things are still tight, but there will soon be plenty of time for writing, once we’re free of those little monsters we have to teach. (Hi, Guys!) In the meantime, we’ll try to catch up on the numerous posts and updates that are most demanding of attention.

We’ll begin with a couple new WitChes. This first one, courtesy of John the Merciless, is a multiple choice question from the 2017 VCE Specialist Mathematics Exam 2:

The Examiners’ Report indicates that 6% of students gave the intended answer of E, and a little under half the students answered C. The Report also comments that

f”(x) does not change sign at a.

Have fun.

VCAA’s Mathematical Reasoning

OK, Dear Readers, turn off the footy and/or the cricket. You have work to do.

We have written before of VCAA‘s manipulative “review” of Victoria’s senior mathematics curriculum, complete with scale-thumbing, push-polling and hidden, hand-picked “experts”. Now, according to their latest Bulletin,

[t]he VCAA will undertake a second phase of Stage 1 consultation …

Good. With any luck, the VCAA will subsequently get stuck on the nth phase of Stage 1, and Victoria can be spared their Potemkin Mathematics for another decade or so.

Still, it is strange. The VCAA has indicated nothing of substance about the results of the first phase of consultation. Why not? And, what is the supposed purpose of this second phase? What is the true purpose? According to the VCAA, one of two reasons for Phase Two is

to further investigate [t]he role of aspects of mathematical reasoning and working mathematically in each of the types of mathematics studies.

(The second reason concerns “Foundation Mathematics” which, try as we might, we just cannot pretend any interest.)

As part of this new consultation, VCAA has posted a new paper, and set up a new questionnaire (and PDF here), until 16 September.

And now, Dear Readers, your work begins:

  • Please fill in the questionnaire.
  • Please (attempt to) read VCAA’s new paper and, if you can make any sense of it whatsoever, please comment to this effect below.

We suspect, however, that this is all a game, disguising the true purpose of Phase Two. It’d be easier to be sure if the VCAA had reported anything of substance about the results of Phase One, but we can still hazard a pretty good guess. As one of our colleagues conjectured,

“There was probably sufficient lack of support [in Phase One] for some radical departure from the norm, and so they will take longer to figure out how to make that happen.”

That is, although the VCAA’s nonsense received significant pushback, the VCAA haven’t remotely given up on it and are simply trying to wait out and wear down the opposition. And, since the VCAA controls the money and the process and the “experts” and the “key stakeholders” and the reporting and everything else except public sentiment, they will probably win.

But they should be made to earn it.

WitCH 21: Just Following Orders

This WitCH come courtesy of a smart VCE student. It concerns the newly instituted VCE subject of Algorithmics, and comes from the 2017 exam:

The Examiners’ Report indicates that half of students gave the intended answer of A, and notes

It is important for students to understand that Big-O notation describes an upper bound, and so is only used for analysis of worst-case running times.

Have fun.

WitCH 20: Tattletail

This one is like complaining about the deck chairs on the Titanic, but what the Hell. The WitCH is courtesy of John the Merciless. It is from the 2018 Specialist Mathematics Exam 2:

The Examiners’ Report notes the intended answer:

H0: μ = 150,   H1: μ < 150

The Report indicates that 70% of students gave the intended answer, and the Report comments on students’ answers:

The question was answered well. Common errors included: poor notation such as  H0 = 150 or similar, and not understanding the nature of a one-tailed test, evidenced by answers such as H1: μ ≠ 150.

Have fun.

WitCH 19: A Powerful Solvent

The following WitCH is from VCE Mathematical Methods Exam 2, 2009. (Yeah, it’s a bit old, but the question was raised recently in a tutorial, so it’s obviously not too old.) It is a multiple choice question: The Examiners’ Report indicates that just over half of the students gave the correct answer of B. The Report also gives a brief indication of how the problem was to be approached:

    \[\mbox{\bf Solve } \boldsymbol{\frac{1}{k-0} \int\limits_0^k \left(\frac1{2x+1}\right)dx = \frac16\log_e(7) \mbox{ \bf for $\boldsymbol k$}.\ k = 3.}\]

Have fun.

Update (02/09/19)

Though undeniably weird and clunky, this question clearly annoys commenters less than me. And, it’s true that I am probably more annoyed by what the question symbolises than the question itself. In any case, the discussion below, and John’s final comment/question in particular, clarified things for me somewhat. So, as a rounding off of the post, here is an extended answer to John’s question.

Underlying my concern with the exam question is the use of “solve” to describe guessing/buttoning the solution to the (transcendental) equation \mathbf {\frac1{2k}{\boldsymbol \log} (2k+1) = \frac16{\boldsymbol \log} 7}.  John then questions whether I would similarly object to the “solving” of a quintic equation that happens to have nice roots. It is a very good question.

First of all, to strengthen John’s point, the same argument can also be made for the school “solving” of cubic and quartic equations. Yes, there are formulae for these (as the Evil Mathologer covered in his latest video), but school students never use these formulae and typically don’t know they exist. So, the existence of these formulae is irrelevant for the issue at hand.

I’m not a fan of polynomial guessing games, but I accept that such games are standard and that  “solve” is used to describe such games. Underlying these games, however, are the integer/rational root theorems (which the EM has also covered), which promise that an integer/rational coefficient polynomial has only finitely many candidate roots, and that these roots are easily enumerated. (Yes, these theorems may be a less or more explicit part of the game, but they are there and they affect the game, if only semi-consciously.) By contrast, there is typically no expectation that a transcendental equation will have somehow simple solutions, nor is there typically any method of determining candidate solutions.

I find something generally unnerving about the exam question and, in particular, the Report. It exemplifies a dilution of language which is at least confusing, and I’d suggest is actively destructive. At its weakest, “solve” means “find the solutions to”, and anything is fair game. This usage, however, loses any connotation of “solve” meaning to somehow figure out the way the equation works, to determine why the solutions are what they are. This is a huge loss.

True, the investigation of equations can continue independent of the cheapening of a particular word, but the reality is that it does not. Of course, in this manner the Solve button on CAS is the nuclear bomb that wipes out all intelligent life. The end result is a double-barrelled destruction of the way students are taught to approach an equation. First, students are taught that all that matters about an equation are the solutions.  They are trained to give the barest lip service to analysing an equation, to investigating if the equation can be attacked in a meaningful mathematical manner. Secondly, the students are taught that that there is no distinction between a precise solution and an approximation, a bunch of meaningless decimals spat out by a machine.

So, yes, the exam question above can be considered just another poorly constructed question. But the weird and “What the Hell” incorporation of a transcendental equation with an exact solution that students were supposedly meant to “solve” is emblematic of a an impoverishment of language and of mathematics that the CAS-infatuated VCAA has turned into an art form.

WitCH 11: Impartial

The following WitCH comes from (CAS permitted) 2018 Specialist Mathematics Exam 2:

The Examiners’ Report indicates that about half of the students gave the intended answer of D, with about a third giving the incorrect answer B. The Report notes:

Option B did not account for common factors and its last term is not irreducible, so should not have Dx in the numerator.

Update (11/08/19)

The worst kind of exam question is one that rewards mindless button-pushing and actively punishes intelligent consideration. The above question is of the worst kind. It is also pointless, nasty and self-trippingly overcute.

As John points out in the comments, the question can simply be done by pressing CAS buttons. But, alternatively, the question also just appears to require, and to invite, a simple understanding of partial fraction form. Which brings us to the nastiness: the expected partial fraction form is not a listed option.

So, what to make of it? Not surprisingly, many students opted for B, the superficially most plausible answer. A silly mistake, you silly, silly student! You shoulda just listened to your teacher and pushed the fucking buttons.

The trick, of course, is that the numerator factorises, cancelling with the denominator and leading to the intended answer, D. The problem with the trick is that it is antimathematical and wrong:

  • As Damo notes, the original rational function is undefined at x = -1, which is lost in the intended answer.
  • As Damo also points out, there is no transparent, non-computational way to check that the coefficients in answer D would, as demanded by the question, be non-zero. 
  • It is not standard or particularly natural to hunt for common factors before breaking into partial fractions. Any such factors will anyway become apparent in the partial fractions.
  • To refer to the partial fraction form is actively misleading. Though partial fraction decomposition can be defined so as to be unique, in practice it is usually not helpful to do so, and the VCE Study Design never does so. In particular, if answer B had contained a final numerator of Dx + E then this answer would be valid and, in certain contexts, natural and useful.
  • The examiners’ comment on answer B is partly wrong and partly incomprehensible. One can pedantically object to the reducible denominator but if that is the objection then why whine about the Dx in the numerator? And yes, answer B is missing the constant E, which in general is required, and happens to be required for the given rational function. For a specific rational function, however, one might have E = 0. Which brings us back to Damo’s point, that without actually computing the partial fractions there is no way of determining whether answer B is valid.

But of course all that is way, way too much to think about in a speed-test exam. Much better to just listen to your teacher and push the fucking buttons.

WitCH 10: Malfunction

It’s a long, long time since we’ve had a WitCH. They have been not-so-slowly accumulating, however. And now, since we’re temporarily free of the Evil Mathologer, it is the WitCHing hour.

Due mostly to the hard work of Damo, all of the outstanding WitCHes have been resolved, with the exception of WitCH 8. That one will take time: it’s a jungle of half-maths. Our new WitCHes are not so tricky, although there is perhaps more to be said than indicated at first glance.

The first of our new batch of WitCHes is from the VCE 2018 Specialist Exam 1:

The Examiners’ Report gives the answer as \int_0^{\frac34}\left(2-t^2\right)dt. The Report also indicates that the average score on this question was 1.3/5, with 98% of students scoring 3 or lower, and over a third of students scoring 0.

Happy WitCHing.

The Story of an Unqualified Teacher

This final sabbatical post is a story from 1965. It is the story of Marian, who found herself as a single mother with two young children, in Australia with no extended family, and in need a job. It is quite a remarkable story, not least for Marian’s skirmish with the Victorian Universities and Schools Examinations Board, the pre-pre-precursor to the VCAA. The story is taken from Marian’s memoirs.

 

A New Profession

Near the end of the school year in 1964, I began seriously looking for a job starting in the New Year. In late November, I asked Eileen about the possibility my getting a job at the local Macleod High School where she was teaching. After making inquires, she told me that there would be no vacancies in the Science department. So I went out a bit further into the suburbs and applied to the principal at Watsonia High School. I was interviewed by the headmaster who was a very kind and fatherly type of man, not at all threatening. He asked me lots of questions about my education and work experiences. I played up my studies of the sciences and my teaching experiences within hospital settings. He and I both understood that I was not a qualified teacher and I had the feeling that he was reluctant to hire me. However part of his job, as a principal employed by the Victorian Education Department, was to cover all of the subjects and classes in his school and it seemed to me that they didn’t care how he did it. I soon learned that there were many schools in the same predicament. They also hired unqualified staff just to keep their schools functioning, at least at some basic level. Watsonia High was a new school and had been open for only a few years. 1965 was the first year that they would be offering year eleven subjects. It would be several more years before students could complete year twelve at that school. When the headmaster said I could have the job teaching year eleven Biology, as well as junior science and mathematics, I swear I heard him say a prayer. I know I did.

He handed me a copy of the Biology syllabus which was set by the Education Department of the State of Victoria. That was my complete introduction to the Victorian Education system. I knew absolutely nothing about how the local school related to the Education Department. What I would be teaching, other than Biology, remained a mystery until the following February when the school year actually started. As Biology had not previously been taught at the school a copy of the student text book was not yet available and materials and equipment for teaching the subject were extremely limited or completely absent. It would have been a huge job for a qualified teacher to set up a new department in the school and here was I, an absolute novice, being thrown in at the deep end. I felt I could not complain because I had known that I was applying for a job for which I was not qualified. It was because I was not qualified, that I did not even know what kind of help to ask for. 

My Life as a New Teacher

My life as a schoolteacher began in February 1965. My first actual teaching experience on the first day of school was fronting a mathematics class of forty seventh grade boys and girls. I really had no idea of what to do but that didn’t stop me. I plowed in and opened the maths book at page one which just happened to be on operations with fractions. I wasn’t even aware that working with fractions was still in my memory bank. Discovering that I still remembered much from my own education came as a surprise and gave me some much needed confidence. Those were the days in the state of Victoria where temporary teachers made up a fair section of all teaching staffs. As well, the class sizes were ridiculous. I ended up with one grade eight general science classes which was composed of fifty students. The worst part of trying to teach science to such a large group was in supervising the lab work and finding enough equipment for all of the students. What I considered my real work and my real interest was teaching Biology to fifteen lovely teenagers. I really enjoyed those boys and girls and I so wanted to do the very best I could for them. No one on the staff, neither the principal or other science teachers, assisted me in any way whatsoever. I had to learn routine school procedures plus the requirements of my own discipline, including the laboratory procedures. I did know that these older students would sit for an external exam at the end of the year. That really did not worry me. I knew I could well and truly handle the subject matter and I knew that I would do everything I could to help those students gain a pass, so that they could go on to year twelve. In addition to my teaching duties, by virtue of my nursing credentials, I was appointed the job of ‘first aid’ to the entire student body of approximately three hundred plus students. It was a natural enough appointment considering my background but I often wondered what schools did where there was not a trained nurse on the staff. I did not get paid extra for that job. In a way, it made me feel better about my teaching appointment, as it was a part of the job that I really was qualified to do.

There were a couple of men on the staff who deeply resented not only us temporary teachers but the fact that women actually held any teaching positions at all. One man teacher, fortyish, blatantly stated that women should not be allowed in any work force but rather should be at home full time. Misogyny was alive and well in Australia. He was quite serious and this, in spite of the fact that, when I started teaching in 1965, women did not receive equal pay even though they did the same jobs as the men. He didn’t want us to be paid at all. A couple of years later Australia joined the real world and women were awarded equal pay. A couple of the teachers tended to look down their noses at us temporary teachers but I was amazed at the thickness that my skin developed over the next years. I was not doing the job because I wanted it but because I needed to work to support myself and my sons. I was determined I was going to do whatever I had to do to manage that. After all I did not create the system that employed me and if they were willing to pay me for teaching in their school then I would do my very best.

I Hate this Job

After the initial pleasantries of meeting the students and the novelty of my Yankee accent wore off I found the large classes of boys and girls, aged twelve and thirteen, hellish. I often found myself at my wits end trying to keep classes of forty to fifty students interested and attentive. It is a fact that in that first year at Watsonia High School I said to myself (and sometimes aloud) every single day, “I hate this job, I hate this job’ and I absolutely meant it. However, I stuck it out, taking one day at a time, knowing that I had to work at something and no other job would allow me the luxury of being at home when my sons were home from school. At that time, as far as I was concerned, that was the only good thing about the teaching profession. I did however get a lot of enjoyment from the company of most of the other staff members. It was nice being out in the world again, meeting and interacting with intelligent adults. I got along very well with everyone who wanted to be friendly. It was not only the days before equal pay it was also the days before anyone ever talked about or recognized any such thing as single mothers. Out of a staff of fifty teachers only two of us fit that category and I generally escaped overt ridicule because I was an American and every one agreed they were weird.

Teaching for a Living

I worked extremely hard over the next couple of years but, by far, that first year was the hardest and steadiest of grinds. I tried to learn every thing I could about the noble art of teaching. I went to every seminar and tutorial which became available. I bought many books on subjects which I thought might enable me to become somewhat proficient as a teacher. I tried to learn class discipline from reading books and articles because, god knows, the senior teachers at the school, although they were quite friendly, seemed to be quite ready to see me sink or swim in my own good time. The prescribed laboratory work for the Biology students was very minimal to what it became in later years. However, since this was the first year the subject had been taught in the school, I had to start from scratch in setting up the materials for the course. So, although the actual course work was quite basic, I spent endless amounts of time trying to scrape together materials and equipment and, where these were not available in the Science Department, I had to chase around to find out where I could get the necessities. One good example of how I struggled was just one demonstration (when a word from a senior science teacher might have saved me much anxiety). I was required to dissect, as a class demonstration, the reproductive system of a female mammal. In order to complete this required part of the syllabus, one of the students brought in a freshly killed rabbit and the students and I suffered through the dreadful smell of dissecting it. Much later I learned that many such preserved specimens were available to be purchased from certain universities or supply houses. I probably could have ask for a lot more help but it was not in my nature to impose on other people. Besides I had no wish to flaunt my inadequacies.

My first year of teaching coincided with the advent of the “New Mathematics”. I was on a par with other junior school mathematics teachers in learning something which was new to them as well. We were all equal when we attended the classes teaching us the basics of this new approach to mathematics.

Staff Interactions

There was the most minimal supervision of my work that one could imagine. I am certain that the headmaster visited my classroom no more than twice in that first year and even then he had nothing to say to me concerning my teaching, either good or bad. Nothing. In one staff meeting he made a point of mentioning my name. He had asked for some written information from each of the teachers and he reported that I was the only member of staff to complete the task. At the time I felt embarrassed, fearful that I appeared sycophantic. I mention this incident only to demonstrate how keen I was to do whatever was required of me. The headmaster had what I considered a bad approach to the staff in that he often remarked, critically, that he had seen or heard a teacher do this or that. But he never said who he was talking about. At first, I used to think to myself, ‘is he talking about me?’ I would wrack my brain trying to recall recent incidences and I would worry about it. After he did this several times I quietly let myself off the hook. I decided if he had something to say to me he should say it to me personally. As for his generic remarks in future staff meetings, I just said to myself, ‘he doesn’t mean me’ and I immediately put whatever he had said out of my mind. I do believe I was being watched, or listened to, plenty of times when I was not aware of it. I base this on one incident which occurred in a staff meeting chaired by the assistant headmaster, the physics teacher. In speaking to the staff he chose to quote something I had said to my students when teaching them about Mendel’s experiments in genetics. It was clear he been listening to my lesson from the preparation room which separated the two science classrooms. I suppose I should have felt flattered.

During the school year all fifty teachers on the staff had to endure several days of visits by several men, ‘inspectors’, from the central office of the State Education Department. They were the closest things to gods that I had ever run into. Everyone, even senior teachers, would shake in their shoes. I suppose some teachers’ promotions depended on the assessments made but that certainly was no concern of mine. I was at the bottom of the totem pole with every prospect of staying there. They came to our school, usually three or four, in a bunch, all dressed in dark suits, and looking exceedingly furtive, rarely saying anything, and making everyone nervous as hell. Then they left, not to return for another year. They sat in on a couple of my classes and at least one Biology class. They ask to see a couple of the students’ practical books which recorded results of experiments we had completed. At no time did they say anything to me regarding my teaching, either constructive or critical. If they said anything to the headmaster, he never mentioned it to me. I never went crying to the headmaster or anyone else when things got tough. I worked things out by myself and I was determined not to show any anxiety or distress. By the end of the school year no one was happier than I to see the summer holidays roll around. I still hated the job but I had become very fond of my fifteen Biology students and I was even finding that the younger kids could be lots of fun, at times. However, I still had no real love for the job and I continued solely out of necessity.

Fighting the Good Fight

My Biology students had taken their final exam in November and, according to the system, as their regular teacher, I had nothing to do with setting the exam, supervising or correcting it. This was all done by specially chosen people within the Education Department. One of my Biology students had become very friendly with me and my sons and he visited us often during that holiday period. From him I learned that the exam was not too difficult and he felt he had passed it. Results were routinely sent to the students during the following January. One day this young man came to the house visibly upset because, when he got his exam results, he found he had not passed Biology. Not only that, he had checked with the other students and none of them had passed either. One of the parents had phoned the Department to question the results. He was told that his daughter had passed the exam but the practical work, as evidenced by the submitted ‘prac’ books, was not of a passable standard. I was shocked. I knew I had followed the syllabus to the letter. I had taught every required topic and completed every experiment as laid down in the syllabus. I had been much too new to the business to try anything tricky or try to cut corners. I knew it was essential that I teach the subject as prescribed. It took me about ten minutes to absorb the shock and then I realized I had to do something. But what? The school was still closed for the holidays and I did not know how to get in touch with the headmaster at his home. So I decided the only thing I could do was to go to the source of the problem. Since the exam was set and corrected by people working in the main offices of the Victorian Education Department in the city, I determined that was where I had to go. I did not bother to make a phone call or arrange for an appointment. I was angry as well as mystified and I was determined my students were not going to suffer if I could help it.

I reached the Department in the center of Melbourne during the middle of the morning and the place was a hive of activity, absolutely teeming with energy. There were loads of people running around like a bunch of mice, in and out of offices, up and down hallways, occasionally one of them stopping for a quick word with someone, then quickly running off again. It reminded me of a scene from Alice in Wonderland. As I watched their hyperactivity I felt reassured because it looked to me like they didn’t know what they were doing. Their kinetic behavior suggested indecision and confusion. They wouldn’t have looked any different if they had been told that the world was coming to an end and they were trying to find a place to hide. Watching them gave me courage, if I needed it. I waited for a very long time before I was finally ushered into the office of a properly suited male. I told him my story and explained that I could not understand why all of my students had been denied a pass in my subject. He had some records in front of him and he said (with a straight face) the students were failed because the practical work was not corrected properly. WHAT!! ?? I could not believe my ears. Not a word about the work completed, nothing about the content of the prac books, and nothing about the results of the students’ three hour exam. Their only criticism was the lack of corrections by me. Assuming I had made mistakes, how the hell could they make my students pay for it by failing them? If I had neglected to correct a statement or allowed misspelling of words to go unchecked, so what? Now they were going to fail the entire Biology class because of something I did or did not do with their practical reports. I saw this as raw injustice and whenever I come into close contact with blatant unfairness, I see red. I started by giving this man some home truths, saying what I honestly felt. I reminded this man that I was hired by the Victorian Education Department as an untrained teacher just one year ago. The school itself had not been set up for teaching Biology. I was not only setting up the department but also learning the job as I went. That was no secret. No one at the school had instructed me on how precise the corrections of the practical work had to be. No one supervised my work or the work of my students. Now at the end of a very gruelling year, if the practical work had not been properly corrected, then sack me, boot me out of the job, but for gods sake don’t ruin a year of these young students’ lives because of something I had or had not done. Amazingly, the man did not even make a pretence of arguing with me. The logic of my argument was sound and he knew it and, although he could not give me a decision immediately, he said he would get in touch with the school. I left that office and that building feeling quite satisfied. They were not going to get away with this. I knew it and so did that man I had just spoken to. As for my future as a teacher, I could not have cared less. I was not doing the job for the love of it and if they fired me, so be it. I would survive without the stupid system that not only set me up for trouble but worse still treated these young people with such disdain.

As it turned out the matter was dealt with quite promptly. A few days after my complaint session my young student came to the house to tell me that he had received another letter from the Education Department stating that he had passed Biology after all. In fact, eight of the fifteen students had passed, based on the exam results. This better than 50% pass rate was considered a good result in a very new, barely established, state school where students were not screened out, as is the practice in most, if not all, elite private schools. On the first day of the new school year in February, I made a point of approaching the headmaster to tell him what I had done. He was quite satisfied and told me if I had not gone to the Department he would have done so himself.

So all was well that ended well and my eight successful students went on to do year twelve Biology at nearby Macleod High School and most went on to do University courses. As for me I was relieved of teaching Biology when the school hired an ambitious university trained male teacher. He had a very big head and was sure he was God’s gift to the teaching profession. This well qualified male was given a whole year in which to set up the Biology Department in preparation for expansion to teaching Year 12 the following year. No such consideration was ever even hinted at when I started the department the year before. It just proves some people have clout and some don’t. In those days it certainly helped to be a male. I spent nine years altogether teaching in that school and as the years went by I enjoyed it more and more. The year eight students who had given me so much grief in my first year eventually gave me endless pleasure and many laughs. I was always aware of being an untrained teacher but through the years I learned a lot and after nine years in the State system I spent another six years at a Catholic Girls’ School which was a wonderful experience as well. I always worked hard, being employed as a teacher, but I also had a lot of fun with the students and fellow teachers.

 

My mother, Marian Ross, is now 90, and is still going sort of strong. She is as principled, as fearless and as good-hearted as she was in 1965.