A teacher emailed me yesterday, asking for my opinion on which textbook his school should choose for Year 12 Specialist Mathematics. I answered as best I could, which was not very well, and it seemed worthwhile throwing the question on the blog, and for Methods as well. (And also for General and/or Foundation, if people care.) So, what do people think? Cambridge or Nelson or Jacaranda? Is there any fourth option, or a viable non-text approach?
Maybe this is all obvious. I assume the default option is Cambridge, and perhaps we’re done. But it’s not like Cambridge is actually good or anything, and I can see, and have heard, plausible arguments for not-Cambridge. I also have little sense of how you teacher guys, and student guys, out there think about it. I’ll be very interested in what people have to say.
I’ve only had the …. pleasure …. of using Cambridge, and the number of errors in the textbooks I’ve used (General 1/2 and Methods 3/4) is not only alarming, but unconscionable for the price.
Thanks, Ron. Errors in exercises/solutions, or in the text itself? And to what extent are these conceptual errors or more typo-ish.
All of the above. Some of them come from exercises being changed slightly but old values left in the solution. Mostly typos, but sometimes the solution is for another problem altogether, for instance finding probability of A when the question asked for the probability of A’. That sort of thing.
My real annoyance is the sheer number of them. Cambridge are regularly publishing new errata.
Given that large parts of the text are recycled from previous editions, I find the persistence of such errors has a real flavour of a cavalier “we’ve got your money” attitude.
Thanks, Ron. I’m less fussed by such errors than, for example, Cambridge not knowing what √(-4) is. But it’s not great, of course. I presume old errors get corrected but the updates produce new errors.
A long term alternative, not available immediately.
Our policy at Swinburne Tech (Years 11 and up to 15) was to never prescribe textbooks. We would prepare sets of exercises, with just brief description of the methods, which were sold to students at cost, about a dollar (AUD) for a one year course. There were textbooks in the library but I don’t recall students ever needing them; intensive classroom teaching was sufficient. The exercises we prepared were used by other techs around the state.
I’m reluctant to push this as there may be teachers relying on some feeble income from their contribution to the current texts?
These types of booklets would be great. Really help lock down expected / minimal work for students. And less effort to lug around than a textbook & less distracting than online resources!
I don’t mind Cambridge. I hate Nelson’s online platform. There’s also Edrolo which is ok but hasn’t really worked for me this year.
Thanks, Samantha. There’s Edrolo for Year 12?
Edrolo has the usual videos and assessments for all VCE maths, but only has a textbook for General Maths
Thanks, Simon.
The Haese books from SA are good , though not specific to VCE. Alternatively adapt from the excellent Pender et al books tailored for NSW HSC.
Thanks, Nordin. I was specifically thinking of Haese when pondering “fourth option”, since their IB books are very good. (I haven’t looked Haese’s SM, nor Pender’s EM.)
Do you think it is feasible to take a much better close-but-not-VCE text, such as (for argument’s sake) Haese or Pender, and then adapting it to use for your class?
Our school use Cambridge but I do not like some section of the book. For Methods, I found the trigonometric function and graphs sections are particularly chunky with too many examples on similar skills. Similarly, the transformation session is also not a good read for me. I do my own sequence when teaching those chapters. And for both 12 MM and SM, I found probability and statistics are poor, exercise wise. And the application question in differential equation for SM is lack of varieties.
Thanks, Victoria. Yes, Cambridge can really worry a topic to death. Are the other texts better on the topics you mention?
I’m not sure if the probability and statistics is all Cambridge’s fault: probability has been gutted by VCAA, and the stats is simply a garbage topic.
Cambridge definitely has the written-by-committee feel. But it’s a committee of people who hate each other and have long-standing disagreements about how important it is or isn’t for mathematical texts to be inscrutable. So they agree to divvy up the chapters and never talk again, and the end result is a book which is a mish-mash of the persnickety and the hand-wavey, the overwrought and the undercooked.
But maybe that’s uncharitable and I’m just feeling the end of term approaching.
I think there’s no question that Cambridge, and similarly any of these texts, is written by committee, albeit with Evans and some editor at least nominally overseeing it all. I don’t see that that is a critical problem for the flow or whatever: it’s simply that some chapters are significantly better than others. And I have no doubt that Cambridge is aware of the unevenness. But no one cares enough to do it right.
Why are there no open source textbooks? Does the syllabus change too often?
How would you imagine such open source texts being created?
There are already a few avenues. There are CC licensed maths books (and OER open education resources) – some that are even remixable. But nothing organised to match VCE yet. However, the resources are all CC so can be remixed to match the VCE curricula.
OpenStax books (originally from Rice Uni) are remixable – and the base versions are fairly solid and come with online assessment tools: https://openstax.org/
Runestone academy started as just programming / computer science courses but now has maths text too: https://landing.runestone.academy/
Wikibooks are obviously an open collaboration, but not very complete last time I looked:
https://en.wikibooks.org/wiki/VCE_Mathematical_Methods
https://en.wikibooks.org/wiki/VCE_Specialist_Mathematics
Then there’s some larger collections that have a range of stuff – a lot of university material, but some high school too
https://open.umn.edu/opentextbooks/
https://math.libretexts.org/ – I used some discrete maths stuff from here to augment my year 11 specialist maths (eg https://discrete.openmathbooks.org/dmoi4.html)
https://oercommons.org/
Sorry about the link dump!
Very interesting; thanks
Like wikipedia with some form of downloadable PDF.
No, I mean who would you imagine creating it?
I would love to… if someone is willing to give me time/money!
The fact that so many resources get recreated over and over is insane. A proper remixable resource that can be used and modified widely is a bit of a day dream of mine.
Maybe once Ochre Education gets up to upper secondary content that will provide a path for this being created.
Yes, this ought to be doable, but I don’t think it would easy. There are plenty of guys, like yourself, working hard to write good notes and then at least some are happy to share them widely, like yourself. But you’d need someone in charge to be the administrator and the quality control officer, both of which would be very time consuming.
Yeah – the quality control / chief editor role needs to be there. Otherwise the quality of a single open resource / number of versions of a remixable resource would be hard to keep control of. I have thought about some reputation system (like stack overflow) to help manage it in an open way…
Naively I assumed there might be a taxonomy of maths (which after all doesn’t change much over time, especially at school levels). Then based upon a text section for each item in the taxonomy, you could select a group to form a textbook for a particular course. The libretexts appear to be pretty close to this model. At least they are free of a lot of the extraneous material that seems form part of modern textbooks.
Are the good old textbooks out of copyright yet? If yes, why not start with breaking one of them into sections, rather than from scratch and then doing a bit of open source?
I don’t believe so. I looked at trying to simply scan Fitzpatrick and Galbraith and making it freely available to people, but I think I looked enough to convince me that one could not simply do it (legally).
(I then asked Peter Galbraith and Bernie Fitzpatrick’s son for permission: Peter was flattered and agreed immediately, but Fitzpatrick Junior declined, for reasons that I still cannot understand.)
There are examples of open source software: LaTeX, R are two examples. Open source text books could be based on a similar model.
Jacaranda’s VCE Spec textbook is full of mistakes last time I checked (which was about half a year ago)
Their VCE Methods textbook seems to be okay though, apart from one nonsensical formula being repeatedly stated (see screenshot).
To put that formula into worded form:
If g'(x)=f(x), then antiderivative(g'(x))=f(x)+c
This could be shortened to antiderivative(f(x))=f(x)+c or “the antiderivative of f(x) is f(x) plus c”. This is obviously nonsense
(I think the mistake is that there shouldn’t be a ‘ after the second g)
PS: I’ll probably send Jacaranda an email about this, and then they can fix the online version at least
Geez. One has to accept that a few typos will always slip in, but that’s at least two big steps from reality.
Thanks, Jay. In general, how would you describe the nature of the mistakes in Jacaranda SM? Significant conceptual errors, or mostly wrong answers to exercises. If the latter, is it somehow decipherable what the cause of the error might have been? Whether faulty computation or faulty cut-and-paste or whatever.
They have worked solutions, so it’s always pretty easy to identify the cause. From memory (since I haven’t looked for a while), the cause was mostly simple mistakes. I assume they have a tighter budget for semi-rare subjects, such as Specialist Maths, which results in them rushing some of the chapters
PS: in case I wasn’t clear, the screenshot was Methods, but I think Methods textbook mistakes are much less common (although some of the questions attributed to VCAA got incorrectly copy-pasted by Jacaranda*)
*to clarify, I’m referring to Jacaranda incorrectly copy-pasting questions that VCAA wrote correctly. I’m not referring to VCAA’s mistakes
Thanks, Jay. Yes, it was clear.
I don’t get furious at “simple mistakes”. There’s a million exercises, so it’s not surprising if there are a thousand errors. But things like the FTC screenshot you attached, that’s insane.