Yeah, it’s the same joke, but it’s not our fault: if people keep screwing up trials, we’ll keep making “trial” jokes. In this case the trial is MAV‘s Trial Exam 1 for Mathematical Methods. The exam is, indeed, a trial.
Regular readers of this blog will be aware that we’re not exactly a fan of the MAV (and vice versa). The Association has, on occasion, been arrogant, inept, censorious, and demeaningly subservient to the VCAA. The MAV is also regularly extended red carpet invitations to VCAA committees and reviews, and they have somehow weaseled their way into being a member of AMSI. Acting thusly, and treated thusly, the MAV is a legitimate and important target. Nonetheless, we generally prefer to leave the MAV to their silly games and to focus upon the official screwer upperers. But, on occasion, someone throws some of MAV’s nonsense our way, and it is pretty much impossible to ignore; that is the situation here.
As we detail below, MAV’s Methods Trial Exam 1 is shoddy. Most of the questions are unimaginative, unmotivated and poorly written. The overwhelming emphasis is not on testing insight but, rather, on tedious computation towards a who-cares goal, with droning solutions to match. Still, we wouldn’t bother critiquing the exam, except for one question. This question simply must be slammed for the anti-mathematical crap that it is.
The final question, Question 10, of the trial exam concerns the function
on the domain . Part (a) asks students to find and its domain, and part (b) then asks,
Find the coordinates of the point(s) of intersection of the graphs of and .
Regular readers will know exactly the Hellhole to which this is heading. The solutions begin,
Solve for ,
which is suggested without a single accompanying comment, nor even a Magrittesque diagram. It is nonsense.
It was nonsense in 2010 when it appeared on the Methods exam and report, and it was nonsense again in 2011. It was nonsense in 2012 when we slammed it, and it was nonsense again when it reappeared in 2017 and we slammed it again. It is still nonsense, it will always be nonsense and, at this stage, the appearance of the nonsense is jaw-dropping and inexcusable.
It is simply not legitimate to swap the equation for , unless a specific argument is provided for the specific function. When valid, that can usually be done. Easily. We laid it all out, and if anybody in power gave a damn then this type of problem could be taught properly and tested properly. But, no.
What were the exam writers thinking? We can only see three possibilities:
a) The writers are too dumb or too ignorant to recognise the problem;
b) The writers recognise the problem but don’t give a damn;
c) The writers recognise the problem and give a damn, but presume that VCAA don’t give a damn.
We have no idea which it is, but we can see no fourth option. Whatever the reason, there is no longer any excuse for this crap. Even if one presumes or knows that VCAA will continue with the moronic, ritualistic testing of this type of problem, there is absolutely no excuse for not also including a clear and proper justification for the solution. None.
What of the rest of the MAV, what of the vetters and the reviewers? Did no one who checked the trial exam flag this nonsense? Or, were they simply overruled by others who were worse-informed but better-connected? What about the MAV Board? Is there anyone at all at the MAV who gives a damn?
Postscript: For the record, here, briefly, are other irritants from the exam:
Q2. There are infinitely many choices of integers and with equal to the indicated answer of .
Q3. This is not, or at least should not be, a Methods question. Integrals of the form with non-linear are not, or at least are not supposed to be, examinable.
Q4. The writers do not appear to know what “hence” means. There are, once again, infinitely many choices of and .
Q5. “Appropriate mathematical reasoning” is a pretty fancy title for the trivial application of a (stupid) definition. The choice of the subscripted 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.
Q6. An ugly question, guided by a poorly drawn graph. It is ridiculous to ask for “a rule” in part (a), since one can more directly ask for the coefficients , and .
Q7. A tedious question, which tests very little other than arithmetic. There are, once again, infinitely many forms of the answer.
Q8. The endpoints of the domain for are needlessly and confusingly excluded. The sole purpose of the question is to provide a painful, Magrittesque method of solving , which can be solved simply and directly.
Q9. A tedious question with little purpose. The factorisation of the cubic can easily be done without resorting to fractions.
Q10. Above. The waste of a precious opportunity to present and to teach mathematical thought.
John (no) Friend has located an excellent paper by two Singaporean maths ed guys, Ng Wee Leng and Ho Foo Him. Their paper investigates (and justifies) various aspects of solving .