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.

Signs of the Times

Our second sabbatical post concerns, well, the reader can decide what it concerns.

Last year, diagnostic quizzes were given to a large class of first year mathematics students at a Victorian tertiary institution. The majority of these students had completed Specialist Mathematics or an equivalent. On average, these would not have been the top Specialist students, nor would they have been the weakest. The results of these quizzes were, let’s say, interesting.

It was notable, for example, that around 2/5 of these students failed to simplify the likes of 81-3/4. And, around 2/3 of the students failed to solve an inequality such as 2 + 4x ≥ x2 + 5. And, around 3/5 of the students failed to correctly evaluate \boldsymbol {\int_0^{\pi} \sin 5x \,{\rm d}x}\, or similar. There were many such notable outcomes.

Most striking for us, however, were questions concerning lists of numbers, such as those displayed above. Students were asked to write the listed numbers in ascending order. And, though a majority of the students answered correctly, about 1/4 of the students did not.

What, then, does it tell us if a quarter of post-Specialist students cannot order a list of common numbers? Is this acceptable? If not, what or whom are we to blame? Will the outcome of the current VCAA review improve things, or will it make matters worse?

Tricky, tricky questions.

Feynman on Modernity

We plan to have more posts on VCAA’s ridiculous curriculum review. Unfortunately.

Now, however, we’ll take a semi-break with three related posts. The nonsensical nature of VCAA’s review stems largely from its cloaking of all discussion in a slavish devotion to “modernity”, from the self-fulfilling prediction of the inevitability of “technology”, and from the presumption that teachers will genuflect to black box authority. We’ll have a post on each of these corrupting influences.

Our first such post is on a quote by Richard Feynman. For another project, and as an antidote to VCAA poison, we’ve been reading The Character of Physical Law, Feynman’s brilliant public lectures on physical truth and its discovery. Videos of the lectures are easy to find, and the first lecture is embedded above. Feynman’s purpose in the lectures is to talk very generally about laws in physics, but in order to ground the discussion he devotes his first lecture to just one specific law. Feynman begins this lecture by discussing his possibly surprising choice:

Now I’ve chosen for my special example of physical law to tell you about the theory of gravitation, the phenomena of gravity. Why I chose gravity, I don’t know. Whatever I chose you would’ve asked the same question. Actually it was one of the first great laws to be discovered and it has an interesting history. You might say ‘Yes, but then it’s old hat. I would like to hear something about more modern science’. More recent perhaps, but not more modern. Modern science is exactly in the same tradition as the discoveries of the law of gravitation. It is only more recent discoveries that we would be talking about. And so I do not feel at all bad about telling you of the law of gravitation, because in describing its history and the methods, the character of its discovery and its quality, I am talking about modern science. Completely modern.

Newer does not mean more modern. Moreover, there can be compelling arguments for focussing upon the old rather than the new. Feynman was perfectly aware of those arguments, of course. Notwithstanding his humorous claim of ignorance, Feynman knew exactly why he chose the law of gravitation.

This could, but will not, lead us into a discussion of VCE physics. It suffices to point out the irony that the clumsy attempts to modernise this subject have shifted it towards the medieval. But the conflation of “recent” with “modern” is of course endemic in modern recent education. We shall just point out one specific effect of this disease on VCE mathematics.

Once upon a time, Victoria had a beautiful Year 12 subject called Applied Mathematics. One learned this subject from properly trained teachers and from a beautiful textbook, written by the legendary J. B. “Bernie” Fitzpatrick and the deserves-to-be-legendary Peter Galbraith. Perhaps we’ll devote some future posts on Applied and its Pure companion. It is enough to note that simply throwing out VCE’s Methods and Specialist in their entirety and replacing them with dusty old Pure and Applied would result in a vastly superior, and more modern, curriculum.

Here, we just want to mention one extended topic in that curriculum: dynamics. As it was once taught, dynamics was a deep and incredibly rich topic, a strong and natural reinforcement of calculus and trigonometry and vector algebra, and a stunning demonstration of their power. Such dynamics is “old”, however, and is thus a ready-made target for modernising zealots. And so, over the years this beautiful, coherent and cohering topic has been cut and carved and trivialised, so that in VCE’s Specialist all that remains are a few disconnected, meat-free bones.

But, whatever is bad the VCAA can strive to make worse. It is clear that, failing the unlikely event that the current curriculum structure is kept, VCAA’s review will result in dynamics disappearing from VCE mathematics entirely. Forever.

Welcome to the Dark Ages.

VCAA Puts the “Con” into Consultation

As we have written, the Victorian Curriculum and Assessment Authority is “reviewing” Victoria’s senior secondary maths, which amounts to the VCAA attempting to ram through a vague and tendentious computer-based curriculum, presented with no evidence of its benefit apart from change for the sake of change. Readers can and should respond to the VCAA’s manipulative questionnaire before May 10. In this post we shall point out the farcical nature of VCAA’s “consultation”, as evidenced by VCAA’s overview and questionnaire.

The overview begins by framing VCAA’s review with the following question:

What could a senior secondary mathematics curriculum for a liberal democratic society in a developed country for 2020–2030 look like?

This is peculiar framing, since it is difficult to imagine how a society being “liberal” or “democratic” or otherwise has any bearing on the suitability of a mathematics curriculum. Why would a good curriculum for China not also be good for Victoria?

One could easily write off this framing as just jingoistic puffery; neither word reappears in VCAA’s overview. It is, however, more insidious than that. The framing is, except for the odd omission of the word “suitable”, identical to the title of the Wolfram-CBM paper promoting “computer-based mathematics” in general and Wolfram-CBM in particular. This paper is the heavy propaganda gun VCAA has procured in furtherance of its struggle to liberate us all from the horrors of mathematical calculation. Though the Wolfram-CBM paper never states it explicitly, this makes clear the purpose of the framing:

“[L]iberal” and “democratic” and “developed” amounts to “rich enough to assume, demand and forever more have us beholden to the omnipresence of computers”.

The VCAA overview continues by noting the VCAA’s previous review in 2013-2014 and then notes the preliminary work undertaken in 2018 as part of the current review:

… the VCAA convened an expert panel to make recommendations in preparation for broad consultation in 2019.

Really? On whose authority does this anonymous panel consist of experts? Expert in what? How was this “expert panel” chosen, and by whom? Were there any potential or actual conflicts of interest on the “expert panel” that were or should have been disclosed? How or how not was this “expert panel” directed to conduct its review? Were there any dissenters on this “expert panel”?

The only thing clear in all this is the opacity.

The overview provides no evidence that VCAA’s “expert panel” consists of appropriately qualified or sufficiently varied or sufficiently independent persons, nor that these persons were selected in an objective manner, nor that these persons were able to and encouraged to conduct the VCAA review in an objective manner. 

Indeed, any claim to breadth, independence or expertise is undermined by the constrained formulation of the questionnaire, the poverty of and the bias in the proposed curriculum structures and the overt slanting of the overview towards one particular structure. Which brings us to the issue of consultation:

There is no value in “broad consultation” if discussion has already been constrained to the consideration of three extremely poor options.

But, “consult” the VCAA will:

The VCAA will consult with key stakeholders and interested parties to ensure that feedback is gained from organisations, groups and individuals.

Well, great. The writer of this blog is a keenly interested stakeholder, and an individual well known to the VCAA. Should we be waiting by the phone? Probably not, but it hardly matters:

The VCAA has provided no indication that the consultation with “key stakeholders” and “interested parties” will be conducted in a manner to encourage full and proper critique. There is very good reason to doubt that any feedback thus gained will be evaluated in a fair or objective manner.

The overview then outlines three “key background papers” (links here). Then:

… stakeholders are invited to consider and respond to the consultation questionnaire for each structure.

Simply, this is false. Question 1 of VCAA’s questionnaire asks

Which of the proposed structures would you prefer to be implemented for VCE Mathematics?

Questions 2-8 then refer to, and only to, “this structure”. It is only in the final, catch-all Question 9 that a respondent is requested to provide “additional comments or feedback with respect to these structures”. Nowhere is it possible to record in a proper, voting, manner that one wishes to rank the Wolfram-CBM Structure C last, and preferably lower. Nowhere is there a dedicated question to indicate what is bad about a bad structure.

The VCAA questionnaire explicitly funnels respondents away from stating which structures the respondents believe are inferior, and why.

The good news is that the manipulativeness of the questionnaire probably doesn’t matter, since the responses will be presumably just be considered by another VCAA “expert panel”.

The VCAA overview gives no indication how the responses to the questionnaire will be considered and provides no commitment that the responses will be made public.

The VCAA overview goes on to provides outlines of the three structures being considered, which we’ll write upon in future posts. We’ll just comment here that, whereas Structures A and (to a lesser extent) B are laid out in some reasonable detail, Structure C looks to be the work of Chauncey Gardiner:

What is written about Structure C in the VCAA overview could mean anything and thus means nothing. 

True, for a “detailed overview” the reader is directed to the Wolfram-CBM paper. That, however, only makes matters worse:

A 28-page sales pitch that promotes particular software and particular commercial links is much more and much less than a clear, factual and dispassionate curriculum structure, and such a pitch has absolutely no place in what VCAA describes as a “blue-sky” review. By giving prominence to such material, the VCAA fails to treat the three proposed structures in anything close to a comparable or fair manner. 

If there were any doubt, the overview ends with the overt promotion of Structure C:

The distinctive proposal … contain[s] aspects which the Expert Panel found valuable … There was support for these aspects, indeed, many of the invited paper respondents [to the 2018 paper] independently included elements of them in their considerations, within more familiar structures and models.

Nothing like putting your thumb on the scales.

It is entirely inappropriate for a VCAA overview purportedly encouraging consultation to campaign for a particular structure. A respondent having “included elements” of an extreme proposal is a country mile short of supporting that proposal lock, stock and barrel. In any case, the cherry-picked opinions of unknown respondents selected in an unknown manner have zero value. 

Though woefully short of good administrative practice, we still might let some of the above slide if we had trust in the VCAA. But, we do not. Nothing in VCAA’s recent history or current process gives us any reason to do so. We can also see no reason why trust should be required. We can see no reason why the process lacks the fundamental transparency essential for such a radical review.

In summary, the VCAA review is unprofessional and the consultation process a sham. The review should be discarded. Plans can then be made for a new review, to be conducted in the professional and transparent manner that Victoria has every right to expect.

Reviewing the VCAA Review – Open Discussion

The VCAA is currently conducting a “review” of VCE mathematics. We’ve made our opinion clear, and we plan to post further in some detail. (We’ll update this post with links when and as seems appropriate.) We would also appreciate, however, as much input as possible from readers of (especially critics of) this blog.

This post is to permit and to encourage as much discussion as possible about the various structures the VCAA is considering. People are free to comment generally (but carefully) about the VCAA and the review process, but the intention here is to consider the details of the proposed structures and the arguments for and against them. We’re interested in anything and everything people have to say. Except for specific questions addressed to us, we’ll be pretty much hands-off in the comments section. The relevant links are

Please, go to it.

The Wolfram at the Door

(Note added 20/4: A VCAA questionnaire open until May 10 is discussed at the end of this post. Anyone is permitted to respond to this questionnaire, and anyone who cares about mathematics education should do so. It would be appreciated if those who have responded to the questionnaire indicate so in the comments below.)

Victoria’s math education is so awful and aimless that it’s easy to imagine it couldn’t get much worse. The VCAA, however, is in the process of proving otherwise. It begins, and it will almost certainly end, with Conrad Wolfram.

We’ve long hoped to write about Wolfram, the slick salesman for Big Brother‘s Church. Conrad Wolfram is the most visible and most powerful proponent of computer-based maths education; his Trumpian sales pitch can be viewed here and here. Wolfram is the kind of ideologue who can talk for an hour about mathematics and the teaching of mathematics without a single use of the word “proof”. And, this ideologue is the current poster boy for the computer zealots at the VCAA.

The VCAA is currently conducting a “review” of VCE mathematics, and is inviting “consultation”. There is an anonymous overview of the “review”, and responses to a questionnaire can be submitted until May 10. (Below, we give some advice on responding to this questionnaire. Update 25/4: Here is a post on the overview and the questionnaire.) There is also a new slanted (and anonymous) background paper, a 2017 slanted (and anonymous) background paper, a 2014 slanted (and anonymous) background paper, and some propaganda by Wolfram-CBM.

In the next few weeks we will try to forego shooting Cambridge fish in the barrel (after a few final shots …), and to give some overview and critique of the VCAA overview and the slanted (and anonymous) background papers. (We hope some readers will assist us in this.) Here, we’ll summarise the VCAA’s proposals.

The VCAA has stated that it is considering three possible structures for a new VCE mathematics study design:

  • Structure A.1 – the same warmed over swill currently offered;
  • Structure A.2 – tweaking the warmed over swill currently offered;
  • Structure B – compactifying the warmed over swill currently offered, making room for “options”;
  • Structure C – A “problem-centred computer-based mathematics incorporating data science”.

What a wealth of choice.

There is way, way too much to write about all this, but here’s the summary:

1. Structure C amounts to an untested and unscripted revolution that would almost certainly be a disaster.

2. The VCAA are Hell-bent on Structure C, and their consultation process is a sham. 

So, what can we all do about it? Pretty much bugger all. The VCAA doesn’t give a stuff what people think, and so it’s up to the mathematical heavy hitters to hit heavily. Perhaps, for example, AMSI will stop whining about unqualified teachers and other second order trivia, and will confront these mathematical and cultural vandals.

But, the one thing we all can do and we all should do is fill in the VCAA’s questionnaire. The questionnaire is calculatedly handcuffing but there are two ways to attempt to circumvent VCAA’s push-polling. One approach is to choose Structure C in Q1 as the “prefer[red]” option, and then to use the subsequent questions to critique Structure C. (Update 25/4: this was obviously a poor strategy, since the VCAA could simply count the response to Q1 as a vote for Structure C.) The second approach is to write pretty much anything until the catch-all Q9, and then go to town. (20/4 addition: It would be appreciated if those who have responded to the questionnaire indicate so below with a comment.)

We shall have much more to write, and hopefully sooner rather than later. As always, readers are free to and encouraged to comment, but see also this post, devoted to general discussion.

The VCAA Dies Another Death

A while back we pointed out two issues with the 2018 Specialist Mathematics Exams. The Exam Reports (though, strangely, not Exam 1) are now online (here and here). (Update 27/02/19: Exam 1 is now also online.) Ignoring some fresh Hell suggested by the Exam 2 Report (B2(b), B3(c)(i), B6(e)), how did the VCAA address these issues?

Question 3(f) on Section B of Exam 2 was a clumsy and eccentrically worded question that covered material outside the curriculum. Unsurprisingly the Report made no mention of these issues. But, what about a blatant error by the Examiners? Would they remain silent in the face of such an error? Again?

Question 6 on Exam 1 (not online) required students to find the “change in momentum” of an accelerating particle. Unfortunately, the students were required to express this change in kg m s-2. The Exam had included the wrong units, just a careless typo, but a blatant error. The Report addressed this blatant error with the following:

Students who interpreted this question as asking for the average rate of change of momentum to be dimensionally consistent with the units and did this correctly were awarded marks accordingly.

That’s it. Not an honest word of having stuffed up. Not a hint of regret or apology. Just some weasely no-harm-no-foul bullshit.