Yes, the “if any” is implicit. Unlike our recent Who Should People Read post, this one is not intended to produce a list of “useful resources”. Rather, akin to this post, it is a challenge to come up with anything. But first, a story. Continue reading “What Are the Proper Uses of “Technology” in the School Mathematics Classroom?”
This post will take the form of Betrayal, with a sequence of five stories going backwards in time.
Last year, I was asked by an acquaintance, let’s call him Rob, to take a look at the draft of a mathematics article he was writing. Rob’s article was in rough form but it was interesting, a nice application of trigonometry and calculus, suitable and good reading for a strong senior school student. One line, however, grabbed my attention. Having wound up with a vicious trig integral, Rob confidently proclaimed,
“This is definitely a case for CAS”.
It wasn’t. Continue reading “The CAS Betrayal”
About a decade ago, the New York Times ran an opinion piece in which the authors argued for a renewed emphasis on the traditional algorithms for arithmetic. In particular, the authors claimed and lamented an increasing use of calculators as a supposed alternative to proper instruction in the algorithms:
The idea is that competence with algorithms can be substituted for by the use of calculators, and reformists often call for training students in the use of calculators as early as first or second grade.
Keith Devlin wrote a snarky response, including an accusation of straw manning: Continue reading “Original Digital Sin”
To be more precise, what does “digital technology” mean and, precisely as possible, how is Digital Technology X used in Year Y of schooling? If you confused, then why not find out more about this here.
It is now impossible, of course, to write a document on education without genuflecting to the God of Technology. The repetitious chanting of “technology”, like a wired Tibetan monk, is the way people with no sense of the past or the present indicate how hip they are with the future. But, what do they mean? What technology are they talking about? It is a serious question, of which we only vaguely know the answer. We want help.
Of course by “technology”, the Education Experts are never intending to refer to something like blackboards and chalk. They would not even recognise such primitive devices as products of technology, although of course they are. No, what the EE mean by “technology” is electronic devices, mostly computers and computer programs, and preferably devices that are internetted. So, calculators and electronic whiteboards and Mathletics and Reading Eggs and iPads, and so forth.
The question is, precisely how are these devices used in specific classrooms? For example, are calculators used in Year 5 to perform arithmetic calculations, or to check calculations that have been done by hand? Is Mathletics used in Year 7 to teach ideas or to test knowledge and/or skills?
The same question applies to all subjects. Are word processors used in Year 6 to check and/or teach spelling and grammar? Are iPads used in Year 8 to check the definitions of words?
We want to know as much as possible, and as specifically as possible, what electronic gizmos are being used, and with whom and how.
This post is tricky. It is not about us, but there is context, and that context should be kept in mind.
Many readers of this blog will be aware of the long relationship we have had with the Mathematical Association of Victoria. It dates back to 2001, when we first came up with the weird idea that mathematics teachers may be interested in learning some maths beyond the thin gruel they were typically served while at university. That idea morphed into 15+ years of teaming up with the Evil Mathologer, of presenting under the banner of and as a consequence of the MAV, of spreading ideas and rousing the rabble. It was quixotically stupid and exhausting and incredibly rewarding. The prehistory of this blog is an interesting story, which is probably of interest to no one.
Fewer readers of this blog will be aware that our association with the MAV ended a few years ago, when the MAV threatened to (and arguably did) censor the abstract of our (invited) keynote. That story may be of more interest, and we hope to write on it in the near future.
In summary, and notwithstanding our long association with and our gratitude to the MAV, we have no love for the MAV in its current form. That is the context. Now for the post.
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A few months ago we heard that an article was rejected for publication in the MAV’s teachers’ journal Vinculum. The manner of and the reason for that rejection sounded very strange, and so we began to ask questions. As indicated below, the MAV has not been particularly forthcoming, but this is our current understanding of the story:
1) An opinion piece was submitted to Vinculum. In the piece, the author argued that all VCE mathematics exams in Year 12 should be calculator-free.
2) Roger Walter, the editor of Vinculum, accepted the piece for publication and included it to be published in the next issue.
3) Peter Saffin, the CEO of the MAV, overruled the editor, instructing Walter to retroactively reject the piece.
4) Saffin’s stated reason for the rejection was that the author’s position was in conflict with the VCAA’s strong advocacy of calculator use.
That is the bare bones of the story. Here is a little flesh (once again, as we understand it):
a) The author of the article is a long-standing member of the MAV, a respected gentleman who has devoted decades to Australian mathematics education generally and to the MAV specifically.
b) The author’s piece was topical, well-written and not flame-throwing.
c) In early September we contacted Michael O’Connor, the President of the MAV, seeking information and clarification. After a back and forth, the President declined to confirm or deny point 3, declaring that as a member of the public we had “no need to know”, and that “even MAV members would have to show sufficient reason”. O’Connor citied his “duty of care towards MAV staff and volunteers”. Similarly, O’Connor declined to confirm or deny point 4.
d) To our knowledge, no MAV editor has ever previously been overruled in such a manner, by anyone.
e) The author has not contested the rejection.
f) Notwithstanding (d), O’Connor indicated that “proper processes have been followed”.
g) O’Connor indicated that he is “expecting there to be a policy discussion at the next publications meeting”.
h) At this stage, the rejection of the article has not been rescinded.
i) At this stage, no one at the MAV, nor the MAV as a body, has apologised to the author for the rejection of the article or the manner of that rejection.
j) In late September we replied to O’Connor, critiquing various aspects of this incident and his characterisation of it. O’Connor indicated his intention to respond.
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That then is the post. O’Connor and Saffin were invited to comment on a close version of the above. O’Connor reiterated his intention to reply and suggested our posting now was “premature”, arguing that the MAV had not had “sufficient time to perform due diligence”. Saffin did not reply as of the time of posting.
We will update the post if and when any new information comes to hand.
UPDATE (05/12/19): In response to a query in the comments of another post, here is a brief and empty update:
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 
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.