Does this coven of bloodsuckers have any redeeming features whatsoever?
Tanya Plibersek, Australian Labor’s Shadow Minister for Education, has just been reaching out to the media. Plibersek has objected to the low ATAR sufficient for school leavers to gain entry to a teaching degree, and she has threatened that if universities don’t raise the entry standards then Labor may impose a cap on student numbers:
We [should] choose our teaching students from amongst the top 30 per cent …
This raises the obvious question: why the top 30 per cent of students? Why not the top 10 per cent? Or the top 1 per cent? If you’re going to dream an impossible dream, you may as well make it a really good one.
Plibersek is angry at the universities, claiming they are over-enrolling and dumbing down their teaching degrees, and of course she is correct. Universities don’t give a damn whether their students learn anything or whether the students have any hope of getting a job at the end, because for decades the Australian government has paid universities to not give a damn. The universities would enrol carrots if they could figure out a way for the carrots to fill in the paperwork.
The corruption of university teaching enrolment, however, has almost nothing to do with the poor quality of school teachers and school teaching. The true culprits are the neoliberal thugs and the left wing loons who, over decades, have destroyed the very notion of education and thus have reduced teaching to a meaningless, hateful and hated profession, so that with rare exceptions the only people who become teachers are those with either little choice or little sense or a masochistically high devotion to civic duty.
If Plibersek wants “teaching to be as well-respected as medicine” then perhaps Labor could stick their neck out and fight for a decent increase in teachers’ wages. Labor could fight for the proper academic control of educational disciplines so that there might be a coherent and deep Australian curriculum for teachers to teach. Labor could fight against teachers’ Sisyphean reporting requirements and against the swamping over-administration of public schools. Labor could promise to stop, entirely, the insane funding of poisonously wealthy private schools. Labor could admit that for decades they have been led by soulless beancounters and clueless education hacks, so as much as anyone they have lost sight of what education is and how a government can demand it.
But no. Plibersek and Labor choose an easy battle, and a stupid, pointless battle.
None of this is to imply that Labor’s opponents are better. Nothing could be worse for education, or anything, than the sadistic, truth-killing Liberal-National psychopaths currently in power.
But we expect better from Labor. Well, no we don’t. But once upon a time we did.
Tanya Plibersek has announced a new Labor policy, to offer $40,000 grants for “the best and the brightest” to do teaching degrees, and to go on to teach in public schools. Of course Plibersek’s suggestion that this will attract school duxes and university medal winners into teaching is pure fantasy, but it’s a nanostep in the right direction.
In this WitCH we will again pick on the Cambridge text Specialist Mathematics VCE Units 3 & 4 (2019): see the extract below. (We’d welcome any email or comment with suggestions of other generally WitCHful texts and/or specific WitCHes.) And, a reminder that there is still plenty left to discover in WitCH 2 , WitCH 3 and Tweel’s Mathematical Puzzle.
Below, we go through the passage line by line, but that fails to capture the passage’s intrinsic awfulness. The passage is, as John put it pithily below, a total fatberg. The passage is worse than wrong; it is clumsy, pompous, circuitous, barely comprehensible and utterly pointless.
Why do this? Why write like this? Sure, ideas, particularly mathematical ideas, can be tricky and difficult to convey; dependence/independence isn’t particularly easy to explain. And sure, we all write less clearly than we might wish on occasion. But, if you write/proofread/edit something that the intended “readers” will obviously struggle to understand, then all you’re doing is either showing off or engaging in a meaningless ritual.
An underlying problem is that the entire VCE topic is pointless. Yes, this is the fault of the idiotic VCAA, not the text, but it has to be said, if only as a partial defence of the text. No purpose is served by including in the curriculum a subtle definition that is not then reinforced in some meaningful manner. Consequently, it’s close to impossible to cover this aspect of the curriculum in an efficient, clear and motivated manner. The text could have been one hell of a lot better, but it probably never could have been good.
OK, to the details. Grab a whisky and let’s go.
- First, a clarification. The definition of “parallel vectors” appears in a slightly earlier part of the text. We included it because it is clearly relevant to the main excerpt. We didn’t intend, however, to suggest that the discussion of dependence began with the “parallel” definition.
- For the given definition of “parallel vectors” it is redundant and distracting to specify that the scalar k not be 0.
- As discussed by Number 8, the definition of “parallel vectors” should not exclude the zero vector. The exclusion may be natural in the context of geometric proofs, but here it is a needless source of fussiness, distraction and error. As an example of a blatant error, immediately following the above passage the text begins a proposition with “Let a and b be two linearly independent (i.e. not parallel) vectors.” A second and entirely predictable error occurs when the text later goes on to “resolve” an arbitrary vector a into components “parallel” and “perpendicular” to a second vector b.
- The definition of “linear combination” involves a clumsy and needless use of subscripts. Thankfully, though weirdly, subscripts aren’t used in the subsequent discussion. The letters used for the vector variables are changed, however, which is the kind of minor but needless, own-goal distraction that shouldn’t occur.
- No concrete example of linear combination is provided. (The more abstract the ideas, the more critical it is that they be anchored immediately with very specific illustration.)
- It is a bad choice to begin with “linear combination”. That idea is difficult enough, but it also leads to a poor and difficult definition of linear dependence, an unswallowable mouthful: “… at least one of its members [elements? vectors?] can be expressed as a linear combination of [the] other vectors [members? elements?] …” Ugh! What really kills this sentence is the “at least one”, which stems from the asymmetry hiccup in the definition. (The hiccup is illustrated, for example, by the three vectors a = 3 i + 2j + k, b = 9i + 6j + 3k, c = 2i + 4j + 3k. These vectors are dependent, since b = 3a + 0c is a combination of a and c. Note, however, that c cannot be written as a combination of a and b.)
- As was appropriately done for “linear combination”, the definition of linear dependence should be framed in terms of two or three vectors staring at the reader, not for “a set of vectors”.
- The language of sets is obscure and unnecessary.
- No concrete example of linear dependence is provided. There is not even the specialisation to the case of two and/or three vectors (which, again, is how they should have begun).
- If you’re going to begin with “linear combination” then don’t. But, if you are, then the definition of linear independence should precede linear dependence, since linear independence doesn’t have the asymmetry hiccup: no vector can be written as a combination of the other vectors. Then, “dependent” is defined as not independent.
- No concrete example of linear independence is provided.
- The properly symmetric “examples” are the much preferred definition(s) of dependence.
- The “For example” is weird. It is more accurate to label what follows as special cases. They are not just special cases, however, since they also incorporate non-obvious reworking of the definition of dependence.
- No proof or discussion is provided that the “example[s]” are equivalent to the definition.
- No genuine example is provided to illustrate the “example[s]”.
- The simple identification of two vectors being parallel/non-parallel if and only if they are dependent/independent is destroyed by the exclusion of the zero vector.
- There is no indication why any set of vectors including the zero vector must be dependent.
- The expression “two-dimensional vector” is lazy and wrong: spaces have dimension, not vectors. (Ditto “three-dimensional vectors”.)
- No proof or discussion is provided that any set of three “two dimensional vectors” is dependent. (Ditto “four three-dimensional vectors”.)
- The “method” for checking the dependence of three vectors is close to unreadable. They could have begun “Let a and b be linearly independent vectors”. (Or, with the correct definition, “Let a and b be non-parallel vectors”.)
- There is no indication of or clarification of or illustration of the subtle distinction between the original “definition” of linear dependence and the subsequent “method”.
What a TARDIS of bullshit.