This is a continuation of a previous WitCH. To provide teachers with some guidance on the new VCE Specialist Mathematics curriculum (Word, idiots, and see comments here), VCAA had posted two webinars, on proof by contradiction and proof by induction; we WitCHed it. (31/01/24 Webinar link updated.) VCAA has now added four new webinars, which can be viewed here, and with companion documents as indicated below. (31/01/24 Webinar link updated.)
Get to work.
UPDATE: Calculus (14/02/23)
On we plough.
The calculus webinar is not nearly as bad as the proof webinars, but it is bad; some of the questions are very bad, and there are errors. And again, fundamentally, one must ask: what is the point? What is the purpose of a worse-than-a-million-other-videos “10 minute information bite”, which is actually 24 minutes, but still rushes through a bunch of poorly chosen examples?
The integration by parts section is kind of ok, but is very quick and not particularly clearly laid out. The single example worked through, Q11 of the sample exam 1 questions, requires two integration by parts, which a poor first choice.
The real problems begin with the discussion of surfaces of revolution. They begin with a “curve” y = f(x) rotated about the x-axis, and give the standard formula for the surface area, exactly as it appears on the exam formula sheet. Except the formula assumes that y ≥ 0. Now that wouldn’t be a problem, and we could accept the nonnegativity as understood, if it weren’t for the fact that VCAA examiners love to be nitpicking assholes, willing to dock students for the smallest, most meaningless infringement.
It immediately gets way worse. The first example discussed involves rotating such a “curve”, ,
to form a solid of revolution.
The question is then,
Find the total surface area of the closed volume of this solid [emphasis in the original]
This is so dumb, and so nasty. And so dumb.
To begin, they can emphasise “closed” all they want, but “closed volume of this solid” doesn’t mean anything. Try “region”, perhaps? But OK, we know what they were trying to say: they want to include the area of the end-circles as well. Fine. Except it’s not close to fine. And it’s not correct.
First of all, why clutter a first surface area question by worrying about other bits? Who does that? Well, they do that, because they’re preparing kids for the nasty exams. The question is adapted from Q11 of the sample exam 1 questions. But there is a notable difference in the wording:
Find the surface area of this solid of revolution.
Well, at least the wording isn’t wrong. But the question is pointlessly sneaky, made sneakier by the decision to exclude the word “total”. Exactly so that the examiners can be nitpicking assholes. But, anyway, the question is stuffed.
Remember how the question began? They rotated a “curve” to form a solid of revolution. Except, rotating a 1-D curve does not create a 3-D solid: it only creates a 2-D surface. Which means there is no region at all to have end-circles to be included. If you want a 3-D region, then rotate the 2-D area under the curve. Nitwits.
After this wrong, nasty question, the webinar continues with a very bad, and arguably wrong, question. This second question, which is Q7 of the sample exam 1 questions, concerns the curve rotated around the y-axis, again falsely suggested to have given a “solid of revolution”. The question then asks,
Find the surface area of the part of this solid of revolution where x ∈ [0, 8].
Does this surface area include or not the two end-circles? Are you sure? What does “the part of this solid of revolution” mean? What would the surface area of that “part” be? Have fun in November, kiddies.
It turns out, according to the webinar, that they didn’t want the two end-circles, just the surface of revolution. So why the hell talk about a solid at all? Why not simply stick to rotating a curve to give a surface, which is what has actually occurred? God works in wondrous ways, and VCAA works in wondrously idiotic ways.
After this, it’s on to rotating parametrised curves, going through Q9 of the sample exam 1 questions. This material is better, but/and a couple points should be noted. First, the surface area formula includes absolute values, although the exam formula sheet does not; God knows why. Secondly, the problem worked through only refers to “the surface area of revolution”, with no reference to any “solid”, and the same is true of the similar Q8 of the sample exam 1 questions; God knows why not.
It smells as if someone at VCAA imagines there is a difference between the function and parametric settings, the first creating a solid and the second not; which is false. Rotating a 1-D curve sweeps out a 2-D surface, however the curve is defined.
Finally, the webinar works through a logistic equation question, Q10 of the sample exam 1 questions. The question is badly wrong: (b) is plain wrong, and the webinar indicates that (c) reads differently than intended. See this WitCH. Specifically, (c) asks for a “differential equation” to be solved, but what is intended is that an initial value problem be solved; these are not the same thing. Note also on (b), the webinar “solution” nowhere uses the initial population. But if the initial population is too high then the population will decay to the limiting value. It follows that the webinar “solution” is wrong, even on its own terms.
The webinar presentation of the logistic equation is also poor, which is minor compared to the problems indicated above, but is annoying. The lack of any graphs to illustrate the behaviour is silly, and may have helped lead VCAA into error. It is also gauche to solve of the DE by first flipping to give an equation for dt/dP. It is not wrong, but it is gauche.
That’s it. It is bad. Not as bad as the appalling proof webinars, but it is bad.
UPDATE: Vectors (15/02/23)
Once again, we have to ask what the point is to a “ten minute information bite”, which is 20 minutes, but still rushes way too fast, and with way too little care, through a bunch of new material? The main problem with the vectors webinar is that there is no purpose to it, but there are specific issues as well. So, once again, here we go.
The webinar begins with a discussion of the vector product,
also known as vector cross product
Well, no. It’s typically know as the vector product or the cross product. But no biggie. The biggie is that the fundamental properties of the vector product are stated without a single mention that any of these properties might be proved, much less how one might prove them; the right hand rule also receives not a single mention.
There is then an extraordinarily confused section on parallel, orthogonal and independent vectors:
This slide implies that the zero vector is permitted to be “parallel”, but suggests the zero vector cannot be “orthogonal”. (See posts on this issue, here and here and here.) But then there is the voiceover:
When vectors A cross B equal null vector implies parallelity is similar to vectors A dot B equal zero implies orthogonality. Note that parallel vectors could be the two vectors either have the same direction or have the exact opposite direction from each other, that is they are not linearly independent or if either one has a zero length.
We have tried, hard, to figure out what this is supposed to mean. We have failed.
It is then onto planes, with the fundamental equation introduced in the form . No clue is given to the origin of this equation. (UPDATE 16/02/23: We should have also noted that the webinar refers to this equation as “the vector equation of a plane”, which it kind of is, but which directly contradicts the formula sheet using the exact same phrase to refer to a parametrised equation for a plane.)
Having then gone on to give the standard Cartesian form, the webinar goes through the first example. Which is wrong. The question is a garbled version of Q12 of the sample exam 1 questions (or, more likely, Q12 is a corrected version the webinar question). The question asks for “the” cartesian equation of a plane perpendicular to two given vectors. Clearly what was intended was the two vectors be perpendicular to the normal of the plane. So, just a clunk, but a clunk that should not appear in such a webinar. The definite article is also wrong, since a cartesian equation for a plane can always be scaled, but this is a minor irritation in comparison to the webinar’s other flaws.
It is then on to lines, and the angles between planes and lines. The vector equation of a line is introduced without a hint of its origin, and with the no hint of the connection between the line and the parametrisation of a bug travelling along the line. The subsequent three examples, Q14 and Q15 of the sample exam 1 questions (and Q16 is also mentioned), are fine. There are some clumsy “given by”s, and some improperly definite articles, which we’ll address when we get around to hammering the sample questions (as an update, on this post).
Overall, the vector webinar is by far the most coherent and useful of the four content webinars. There is clunkiness, and the introduction of new concepts and properties as Commandments From God is shameful, but there is nothing nearly so painful or so wrong as exists in the other webinars.
UPDATE: Mathematical Investigations (27/02/23)
We learned three things:
(1) The “Mathematical Investigations” are going to be yet another mathematically trivial horror show;
(2) VCAA has mastered the art of the content-free webinar;
(3) VCAA is in desperate need of an audiovisual expert. Or a novice. Or a kid. Get a 10 year old kid. They would do a better job with the sound.
UPDATE: Pseudocode (27/02/23)
We really appreciated the minute of silence at the beginning of the webinar. It gave the listener a fair chance of changing their mind before wasting seven minutes of their life. Other than that, all we can think of, and all we can be bothered with, is to point out this (for slide 6), and this (for slide 8, and generally).