I’ve already posted Sai kumar Murali krishan’s Mathematica-VCE article, and fleshed it out a little. Here, I’ll give some of the back story, including a statement from Vinculum‘s editor, Roger Walter, and ending with a summary and a list of questions I sent to the MAV regarding the reviewing of Sai’s article, and to which I never expect to receive an answer. Throughout, I was curious whether the MAV would, once again, act in a gratuitously censorious manner, or whether they would now be wiser and publish Sai’s article; impressively, they accomplished both.
Last year, Sai was a student in my Monash Extension class. (It is irrelevant but ironic that Mathematica was used in this class in a limited but intelligent manner, for computing powers of large matrices, row reduction and the like.) The class was small and friendly, and fun, at least for me. I knew Sai well, and it’ll come as no surprise that he did very well in my class, but I had no sense of Sai’s Mathematica superpowers until the year had ended. Then John Kermond, Sai’s Specialist teacher, suggested I talk to Sai about Mathematica in VCE. Sai and I emailed back and forth a bit, and it became clear Sai had a very interesting story to tell.
I encouraged Sai to write up his gaming of VCE with Mathematica, with the goal of publishing in MAV’s journal Vinculum. Given the MAV’s previous conduct and general obsequiousness towards VCAA, some may suspect that goal was foolish or deliberate possum-stirring. With hindsight, it may have been the former but it was in no sense the latter.
There were a number of strong reasons to aim for Sai to write for Vinculum. First and foremost, Vinculum is the main senior school mathematics journal read by Victorian teachers, and was thus the natural home for an article such as Sai’s. Secondly, although Sai will clearly go far and needs absolutely no assistance from me, I thought it would be very good for Sai to have such a publication on his CV. Thirdly, I respected and continue to respect Vinculum‘s editor, Roger Walter, and I trusted he would see the importance of Sai’s article and would work hard to publish it. Finally, given the MAV had acted censoriously in the past and had been publicly called on it, I expected the MAV to be more circumspect in considering Sai’s article. On this last point, I was very wrong. Which is why we’re here now.
Sai quickly put together a very good draft, which I helped Sai tighten and polish. And, amusingly, I got Sai to tone down his language; Sai’s contempt for VCAA’s Mathematica crusade is significantly stronger than is indicated by the published article. Unfortunately, giving a clearer focus to Sai’s article also meant cutting out some very good material, on other clumsy and silly aspects of Mathematica in VCE. In particular, Sai put a lot of work into critiquing the sample Mathematica solutions provided by the VCAA, aspects of which Sai variously described, with supporting argument, as “contrived”, “incomplete”, “silly”, “bloated”, “obnoxious”, “abysmal” and “ludicrous”. (If he didn’t have better things to do, I’d retire and let Sai take over the blog.) I’m hoping to have Sai write a guest post on these solutions, and on other aspects of the Mathematica trial, in the near future.
In February, with a solid draft in hand, Sai submitted his article to Roger Walter, Vinculum‘s editor; I stayed in the loop, for the obvious reasons. The back and forth with Roger was sensible, efficient and amicable. Then, however, the MAV Publications Committee kicked in. What follows is a statement from Roger Walter, followed by my letter to the MAV (Publications Committee and CEO and President); that letter, as well as asking a number of questions, outlines the reviewing process and the frustration that it entailed.
And, failing any response from the MAV, that will end the story. I have heard nothing to indicate that the MAV is anything but satisfied with the manner in which Sai’s article was reviewed, which, if true, I find astonishing.
Statement from the Editor of Vinculum, Roger Walter (13/7)
I was very insistent that Sai’s article be published in Vinculum. This was partly my desire to publish, as far as is possible, all material that contributors have spent time and effort to put together, and partly because I was pleased to see a contribution from a student resourced from his experiences at secondary school. However, the main reason I pushed for publication was that the article itself had merit. This was for two reasons. Firstly, it was true, i.e. it clearly and accurately described the situation. Secondly, it was, at least in my mind, relevant – to both secondary teachers and to those who are responsible for planning our curriculum.
To me, two important statements were made (among others). One was that Mathematica was extremely powerful: too powerful for VCE, in fact, as it meant that students could answer questions without understanding the mathematics involved – an understanding which would be important for their future studies. The other is that Mathematica, being so much more powerful than the CAS calculators used by the majority of students, has the potential to create a non-level playing field. It is important that both teachers and those responsible for our curriculum are aware of this, if they aren’t already.
One of the things I try to do as editor, particularly in the editorials I write, and the material that is published, is to make educators think about what they are doing in their classes. I hope that if nothing else, this article achieves that. Also, as editor, I need to be impartial, and publish according to relevance and reality, regardless of my personal opinions, and the opinions and policies of other organisations. This impartiality is not always easy, but is relevant in the case of this article, and many others.
Letter From Marty to the MAV (13/7)
Dear Publications Committee, I am writing to you in regard to the article Mathematica and the Potential Gaming of VCE, by Sai kumar Murali krishnan (cc-ed) and just now published in the Term 3 issue of Vinculum.
By way of background, it was at my suggestion that Sai wrote his article and submitted it to Vinculum. I also consulted with Sai during what turned out to be the lengthy and erratic reviewing process. Now, with Sai’s interest and agreement, there are a number of questions I wish to ask about that reviewing process. I am willing to publish any response by the Publications Committee or the MAV on my blog. I will interpret a lack of reply by Friday, 17 July as a decision to not comment.
Kind Regards, Marty Ross
******************************************
Sai initially submitted his article to Roger Walter, the editor of Vinculum, in mid-February of this year. After some back and forth, by early March Roger and Sai considered the article polished and ready for the Term 2 issue of Vinculum. The Publications Committee, however, objected. In late March the Publications Committee demanded that the following two paragraphs, the final paragraphs of Sai’s article, be cut:
To the extent VCAA is aware of these issues, there is reason to doubt that they are sufficiently aware, or at least sufficiently concerned. VCAA, after all, has created and continues to maintain this strange and uneven playing field. As further evidence, VCAA provides sample Mathematica solutions, and it is telling that these solutions are clumsy, uninventive and calculator-mimicking, suggesting a limited understanding of Mathematica’s capabilities.
Whatever naivety may exist, I believe it is unlikely to last. Nothing precludes the marketing of Mathematica packages designed specifically for VCE testing and, if Mathematica becomes widely available in VCE, I believe this commercialisation is inevitable. Such a development would turn VCAA’s implementation of Mathematica, which is already very problematic, into an obvious farce.
Q1. Was there any reason for these cuts, beyond members of the Publications Committee being “not happy with comments about the VCAA”? Does the Publications Committee generally regard such unhappiness as sufficient reason to censor an author?
Q2. Given that the criticism of VCAA was objectively valid and directly relevant, and given the potential commercialisation of Mathematica in VCE is an obvious and significant concern, will the Publications Committee now acknowledge there was no editorial or policy reason for demanding these paragraphs be cut? If not, will the Publications Committee now, finally, state any such reason?
Reluctantly, Sai then accepted these unjustified cuts, together with a new conclusion, with the understanding that publication could go ahead in Term 2, and with no further requests for substantial changes. Almost immediately, however, the Publications Committee demanded this second version of Sai’s article be held over until the Term 3 issue of Vinculum. The reason given to Sai for this delay was the Publications Committee “wanted time to consider the rest of the article and the conclusion”.
Q3. Will the Publications Committee now acknowledge that demanding a substantial and unjustified cut, and then subsequently demanding further time for review was a flawed and unfair process? Will the Publications Committee now acknowledge that in these circumstances, and in any circumstances, such a demand for further time should be accompanied by clear and substantive reasons, reasons that were entirely absent in this instance? Will the Publications Committee now indicate what specific parts of the article needed to be considered further, and why?
In mid-April the Publications Committee contacted Sai about further revising the second version of his article. The Publication Committee failed to indicate, much less argue for, a single flaw in this version. Rather, the Publications Committee requested that Sai add to his article, that the article also indicate what teachers could do in “using calculators and technology to support rather than bypass technology [sic]”. To this end, the Publications Committee also indicated they had contacted an MAV consultant familiar with Mathematica “to help [Sai] complete the article”.
Q4. Was the intent of the Publication Committee at that stage simply to dilute the clear content and message of Sai’s article? Will the Publications Committee now acknowledge that the suggested expansion of Sai’s article was unnecessary and unhelpful, at best orthogonal to the clear content and message of his article? Given this orthogonality and the absence of any claim of error in Sai’s article, will the Publications committee now acknowledge that at that stage they simply should have apologised to Sai for the needless delay and have accepted the second version of Sai’s article?
Q5. Does the Publication Committee understand the distinction between offering “help” and attempting to impose it, and will the Publications Committee now acknowledge the extraordinary presumptuousness of initiating “help” before having even canvassed the idea with Sai? Sai quickly replied to the Publications Committee, rejecting this proposal, and making it clear that his article should be accepted or rejected as is. Sai also clearly and carefully detailed the flaws and frustrations of the review process to that stage.
Q6. Why did the Publications Committee not respond to the concerns raised in Sai’s email? Why did the Publications Committee still decline to publish Sai’s article, still without providing a single reason beyond a vague and unjustified “too negative”?
Over Roger’s objections, the Publications Committee continued to refuse to publish the second version of Sai’s article. In an attempt to placate a member of the Publications Committee, Roger suggested “a possible insertion which … doesn’t need to be at the end”:
Technology, including Mathematica, calculators, spreadsheets and the many online programs, have tremendous potential to assist students with learning, understanding and applying mathematics. What is important for educators is to be careful that students are not using this technology to bypass learning and understanding mathematics.
Although Roger’s proposal was clearly well-intentioned, Sai considered, and considers, Roger’s paragraph to be clumsy, unnecessary and forced, particularly as a concluding paragraph. He also didn’t believe for a minute the inclusion of this paragraph would placate the objecting member. Nonetheless, Sai was willing to consider it, and asked Roger: IF Sai agreed to this third version, with the original conclusion cut and this new conclusion properly incorporated, would that THEN be acceptable to the Publications Committee? Sai never received an answer.
Q7. Why did Sai never receive an answer to this question, on a proposal originating from discussion within the Publications Committee? Does the Publications Committee now acknowledge that this failure to respond was rude and unprofessional? In early May, Sai received the following communication from the Publications Committee:
The MAV are continuing internal discussions regarding the publication of the Mathematica article in alignment with MAV’s publication policy. It is expected that a decision may be provided by the end of Term 3.
Q8. Why, after months of failing to indicate a single flaw in Sai’s article, did the Publications Committee consciously and pointedly fail to tell Sai anything about any further “internal discussions”? What, precisely, in the “publication policy” necessitated that Sai was given no opportunity to comment on these “internal discussions” and, in particular, why was Sai given no opportunity to confirm or correct the version of his article then being considered?
Sai responded, indicating his frustration with the further delay and lack of communication. The Publication Committee responded:
1. Mathematica article is not to be included in Term 3. Pending subcommittee decision, it will be published in Term 4.
2. MAV are ‘continuing internal discussions regarding the publication of the Mathematica article in alignment with MAV’s publication policy. It is expected that a decision may be provided by the end of Term 3”.
Q9. Why was there a loud and definitive, and subsequently false, statement that Sai’s article would be further delayed until Term 4? Why was this further delay left unexplained?
Q10. Why did the Publications Committee not inform Sai of this “subcommittee” directly and immediately upon its formation? Who were the members on the subcommittee, what was the role of the subcommittee, and who determined this membership and role? On what formal basis and with what justification did the Publications Committee deprive Sai of this information?
Q11. Was the subcommittee properly informed that Sai had never agreed to Roger’s inserted paragraph being the conclusion to Sai’s article, and if not then why not? If, as appears to be the case, the subcommittee was not informed of this, will the Publication Committee now acknowledge that this lapse was a very serious error, and will the Publication Committee now apologise to Sai for this error?
Q12. What summary and/or advice and/or opinion did the Publications Committee provide to the subcommittee, and why did Sai not also receive any such material? In particular, if the Publications Committee indicated substantive objections, after having failed for months to do so to Sai directly, why did the Publications Committee not then inform Sai of these objections?
Finally, in early June, the Publications Committee presented Sai with a fourth version of his article, presumably the work of the “subcommittee”. The Publications Committee indicated they had agreed to publish this fourth version in Vinculum. It was made clear that this version of the article, which still included Roger’s inserted paragraph as conclusion, was not open to any further discussion, and that Sai had to either accept or decline. It was also indicated that the “aim” was still to publish in Term 4. Given the changes from the third to the fourth version were few and very minor, and swallowing his annoyance with the demand to conclude with Roger’s paragraph, Sai quickly agreed to this fourth version of his article.
Sai was relieved when, presumably due to the wise counsel of the subcommittee, the reviewing ordeal finally ended with an agreement to publish. He is also very pleased to see his article appear in the Term 3 issue of Vinculum. The article as published is identical to the fourth version, except for a new title and the inclusion of a clarifying footnote, both agreed upon without dispute. Which raises the final questions.
Q13. Given that the changes from the third version of Sai’s article to the fourth version were very few in number and were all very minor, does the Publications Committee accept that the decision of the “subcommittee” repudiates the months of secretive stonewalling of the Publications Committee?
Q14. Given there are only minor differences between the second, March, version of Sai’s article and the final, July, published version of Sai’s article, and given Sai was never presented with a single substantive criticism of his article, will the Publications Committee now acknowledge that this whole review process could have been handled in a significantly more efficient, more thoughtful, more open and more respectful manner
Q15. Will the Publications Committee now extend a formal apology to Sai?
. Part (a) asks students to find 
and its domain, and part (b) then asks,
and 
.
for 
,
for 
, unless a specific argument is provided for the specific function. When valid, that can usually be done. Easily. 
and 
with 
equal to the indicated answer of 
.
with 
non-linear are not, or at least are not supposed to be, examinable.
is needlessly ugly and confusing. Part (c) is fundamentally independent of the boring nitpicking of parts (a) and (b). The writers still don’t appear to know what “hence” means.
.
are needlessly and confusingly excluded. The sole purpose of the question is to provide a painful, 
, which can be solved simply and directly.
![\[\boldsymbol{\color{blue}\frac{{\rm d}Q}{{\rm d}t\ } = e^{t-Q}}\,,\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-fb2a41dd03879170945f2458a03cc74a_l3.svg "Rendered by QuickLaTeX.com")
![\[\boldsymbol{\color{blue}Q(0) =1}\,.\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-ef47c12825205650a355b16c965bce3d_l3.svg "Rendered by QuickLaTeX.com")
![\[\boldsymbol{\color{blue}Q =\log_e\hspace{-1pt} \left(e^t + e -1\right)}\,.\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-c8de23f67eb44cdf2c494474a7426fd7_l3.svg "Rendered by QuickLaTeX.com")
![\[\boldsymbol{\color{red}\frac{{\rm d}t\ }{{\rm d}Q } = e^{Q-t}}\,,\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-ba19e5f34669916a558f0406f8658e0e_l3.svg "Rendered by QuickLaTeX.com")
![\[\boldsymbol{\color{magenta}Q'' = e^{t-Q}\left(1 - Q'\right)}\,.\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-c4a185d5168679bceb2e42e2c6f89b01_l3.svg "Rendered by QuickLaTeX.com")
![\[\boldsymbol{\color{magenta}Q' =\frac{e^t}{e^t + e -1}}\,.\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-9c28b2fdd232c34f3717d4b47ae2196d_l3.svg "Rendered by QuickLaTeX.com")
![\[\boldsymbol{\color{magenta}Q'' = e^{t-Q}\left(1 - e^{t-Q}\right)}\,.\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-a432d1ce661cc9a7b239a3c8088be5c6_l3.svg "Rendered by QuickLaTeX.com")
), and again we can conclude that Q has no inflection points. One might reasonably consider the details in the above proofs to be overly subtle for many or most VCE students. Nonetheless the approaches are natural, are typically more efficient (and are CAS-free), and any comprehensive solutions to the problem should at least mention the possibility. The MAV solutions make no mention of any such approach, simply making a CAS-driven beeline for Q” as an explicit function of t. Here are the contents of the MAV solution:
for all t,
for all t.
should be noted. In part (c), it is preferable to begin with the chain rule in the form 
, since no inverses are then required. Part (d) is one of those annoyingly vague VCE questions, where it is impossible to know how much computation is required for full marks; the solutions include a couple of simplifications after the definite integral is established, but God knows whether these extra steps are required.