Perhaps people are done, but given the previous discussion, here and (weirdly) here, and a couple requests, it seems worth a shot.
Given VCAA’s pigheaded ramming through of their still-non-existent and now invisible new study design, some teachers have expressed concern about what and how to teach in Specialist Mathematics 1&2 in 2022. One teacher, we’ll call them Mr. Puzzled, emailed us:
I am a 11 & 12 specialist maths teacher and have been spending countless hours trying to prepare some sort of course outline for the upcoming year without clear advice from VCAA on what we need to cover.
I have been reading through “Discussion: VCAA’s Blunt Implement” to try to shed some light on the issue and found it very interesting reading to say the least!
I noticed a post mentioning the idea of some sharing of potential plans for SM12 courses for this year and I’m wondering if any of that came to fruition? I would be extremely grateful to be able to “check my work” so to speak as I have no one to collaborate with at my school.
Mr. Puzzled has sent us their draft outline for Specialist 1&2, and has kindly agreed to us posting it, hoping for comments and suggestions. We’ve posted the outline below. We’ve also reposted Red Five’s Boolean Logic Summary, and we’ve copied John Friend’s comment, indicating his general thoughts.
We’re happy to post other notes and outlines as we receive them, and of course people can and are encouraged to give their thoughts in the comments. For posting of notes, PDFs can be attached directly to comments, but it is preferable to contact or email us, so we link the documents directly to the post, as updates.
0. VCAA’s invisible study design for 2023 and, thus, 2022
VCAA’s nonsense is discussed here and here and here, and VCAA’s “advice” for teaching Specialist Mathematics 1&2 in 2022 is here (Word Doc because VCAA and thus idiots).
1. John Friend’s General Comments
Originally posted as a comment:
1) I strongly agree with most of what SRK says, particularly “that it’s better to make sure students are well practiced in skills / knowledge that will definitely be required in Units 3&4”.
a) I don’t think calculus should be a big deal (more to say below). It gets taught in MM2 and many schools teach the product, quotient and chain rules and their applications in end-of-year ‘Headstart’ programs for MM34. A lot of schools teach the chain rule in MM2. Focus on the algebra, do NOT drop partial fractions. See 3) for my further thoughts on calculus.
b) I think matrices should be taught. There’s a fair bit in SM34 in 2023 (based on the Daft Stupid Design) that uses matrices. You don’t want to be teaching matrices from scratch in 2023. I think the matrices topic lends itself to a bit of classwork and then a structured take-home assignment with references from the textbook.
I’d try to teach matrices vectors, to exploit using the dot product in the definition of matrix multiplication (introducing the representation of vectors as column and row matrices).
c) I think ‘Logic’ and ‘Graph Theory’ should be taught. In class. And then give students a structured take-home assignment.
2) Principles of counting is implied in SM34 (in the context of proof) but is NOT mentioned in the VCAA implementation advice. I’d be looking to add to what gets done in MM12 (so it needs to follow from this) or at least provide ‘extension work’ for students to work on outside of class – another structured take-home assignment with references from the textbook.
3) Calculus … I notice that VCAA do not mention ‘Kinematics’ in its Blunt Implementation. I think that kinematics MUST be taught in SM2. This is where you can BUILD on the calculus done in MM2. Do everything using calculus and the interpretation of x-t and v-t graphs. Forget about the straight-line motion formula for uniform acceleration.
NB: 2) and 3) greatly depend on SM12 sequencing ‘in harmony’ with MM12. It’s crazy teaching things that you ‘need’ in SM12 that get taught later in MM12. This is redundancy that wastes valuable time.
4) Statistics in SM12 is a joke. It is total rubbish. Mickey Mouse.
My advice – DON’T TEACH STATISTICS IN SM12.
All of the SM34 statistics can be taught in 2 weeks without the SM12 crap, PROVIDED that the co-requisite probability and statistics has already been taught in MM4. This is a tricky thing to juggle – another problem we can thank VCAA for (note that none of these VCAA idiots have to actually teach what they dump on us).
Not teaching statistics will free up valuable time for teaching kinematics.
Finally, here’s the hard part – I strongly urge all VCE teachers to maintain regular correspondence with VCAA via telephone and email. Give VCAA plenty of feedback on a regular basis. Let it know how swimmingly well things are going with teaching what it has dumped on us. Make sure you cc the Executive Director of Curriculum and the Mathematics Mangler (assuming an appointment is made and VCAA don’t have to re-re-advertise …) Suggest to your students that they also give feedback.
2. Mr. Puzzled’s Draft Outline
Mr. Puzzled also had some comments on his draft:
3. Red Five’s Boolean Logic Summary SheetBoolean Logic Summary Sheet 2
50 Replies to “Specialist Mathematics 1&2 Note-Sharing and Idea-Sharing”
Marty calling it SM 12 might be confused initially with SM 3/4 (“year 12 SM”). Maybe SM 1/2 or 1&2 would be easier to read.
Thanks, Anonymous. I’ve switched to 1&2. I *always* struggle with the 12-34 and 11-12 ambiguity, and am never sure of the best labelling. The monumental idiocy of VCAA, to not even be able to choose automatically clear names, is astonishing. Why is each year two things? What is wrong with Specialist A for one year and Specialist B for the next? Why are these people so, so stupid?
(Of course is this spreads into sharing 3&4 notes and ideas as well, that’s also fine.)
When I was trying to plan the Logic unit for Specialist 1&2, I made extensive use of the following two pages for initial ideas and double-checking my own (very limited) understanding:
I actually found the second more useful from a VCE perspective.
I’ve since made an attempt (not sure how good or useful it will prove to be) to write some review questions that are a bit more logical (pun accidental, unlike a previous attempt that mostly failed) and more difficult than those found in any recent textbook I have seen.
Along the lines of, “here is a complex operation (definition in terms of the three Boolean operators).” Is it commutative, associative etc…?
Asking students to simplify complex operations with AND without using truth tables (without is a really good way to learn the subtleties of Boolean logic as a teacher, I found) is another idea I was playing around with.
As with all things, until we see SOME idea of how VCAA is/is not planning to assess this topic, I have no idea if this was time well spent or not.
Thanks, RF. Totally up to you, but if you want me to update the post with any draft (or polished) notes, I’ll do so.
I am using a topic sequence that includes the following subsequences (I’ll give my rationale below):
Principles of Counting
Rationale for the sequence includes:
1) A large part of proof is induction and having Principles of Counting and Matrices before Proof allows for more interesting proof by induction examples and questions.
2) Doing Logic before proof enables ‘proof by the contrapositive’ to be very easily justified and understood.
3) Graph theory includes the adjacency matrix.
4) Logic sets up the ‘structure’ for Proof.
5) A lot of complex numbers involves trigonometry (I actually teach the Euler identity as part of complex numbers).
6) There are some nice trig formula that can be proved using proof by induction.
7) I like to use the dot product to teach matrix multiplication (dot product of row of first matrix with column of second matrix).
I advise against teaching SM1/2 statistics. It’s rubbish, a complete waste of valuable time. Use the time to teach kinematics.
I recommend the topic sequence starting with Counting Methods be taught later in the year.
Plan closely with Methods1/2 teachers so that the teaching sequences are in as much harmony as possible. Work closely with Yr 10 teachers to try and get some of this stuff introduced in Yr 10 (eg. matrices, counting methods).
The big BUT … none of use know for sure how well our best laid plans will work until their execution. Expect to learn from 2023 and make necessary changes for 2024.
Something I’ve found – none of the ‘big three’ textbooks cover Logic or Graph Theory to my satisfaction. There are gaps in content and types of questions. I’ve spent a lot of time thinking about what content to include in both Logic and Graph Theory and how to best sequence this content. I would suggest writing up your own set of teaching notes by consulting from a number of textbooks and websites. Think about the sequencing of content that you think works best, the types of examples and questions you want etc. You might find that you don’t ‘follow the textbook’, and you will certainly need to supplement your examples and the questions you set with additional material. This will also help you understand the content a lot better.
Mastering the new content is going to require significant time and effort. It takes a lot more than reading the textbook or attending a PD. It requires working through questions and thinking carefully. I do not exaggerate in suggesting it will take at least 120 hours, so the sooner people start the better. (Another advantage for teaching the new content later in the year than earlier).
I expect Graph Theory in SM3/4 to be a lot more theoretical and proof based than it is in FM3/4. I am teaching the SM3/4 Graph Theory (see Daft Stupid Design) in SM1/2 – the content appears identical to what the current Stupid Design has for SM1/2. The Daft is a lazy copy and paste job.
Finally, I see this blog as less of a resource sharing service and more a forum where we can ask questions about the new content in SM1/2 and SM3/4, including textbook questions and questions from elsewhere!
Thanks, John. Can you suggest what your plan implies for Mr. Puzzled’s tentative plan?
Of course, I also don’t think of the blog as a resource-sharing site. But, I’m happy for the blog to be however it is useful. This situation is pretty crazy, and if people wish to share, I’m happy to facilitate that. Especially given Cambridge are being dicks.
My plan suggests a re-ordering of the topic sequence in Puzzled’s plan. But everyone is entitled to their own plan. I have mine and provided a rationale. But individual circumstances will dictate individual plans, and there will be differences between plans.
Greater detail for why I have Vectors before Matrices is given here: https://mathematicalcrap.com/2021/11/15/discussion-vcaas-blunt-implement/#comment-13475
FWIW it’s repeated below:
My main reason for teaching matrices vectors is that it makes matrix multiplication a lot easier to teach and understand (and provides a certain rationale for the rule). So I’d be teaching the cross-product of vectors as an application of the determinant of a matrix. But of course:
a) Using the determinant is simply an efficient heuristic for calculating the cross product, and
b) The cross-product can and should be taught in vectors by defining it and then using , and for calculations (until the heuristic can be taught).
Complex Numbers is not going to be a great early topic in schools where most students study Methods 1&2 at the same time as Specialist 1&2 AND have not had a lot of exposure to polynomial algebra in Year 10.
I am always hesitant about the timing of such a key topic.
Leaving the new material until terms 3&4 does have some clear advantages though, so will ponder further.
In support of your comment about the need to “do” the work – I find writing assessment tasks (and worked solutions) can really tell you a lot about what you do and really do not understand about a topic.
Another possibility with the Proof topic is to do a small (5 lessons maybe) version at the start of the year and then work it into all other topics. Maybe that way there is a constant reminder of the role proof plays in proper mathematics…?
RF, maybe I should clarify. The sequence I posted is a part of my entire topic sequence. I do not teach Complex numbers first. I’m simply showing what order within the entire course sequence I think those topics should be done in.
In fact, I taught sequences and Series first. Complex Numbers is topic 9 in my overall topic sequence.
While I’m clarifying, I will state my complete opposition to teaching Complex Numbers first in SM3/4. I know many schools that do this and I have never heard a good reason given for why.
And agreed. De Moivre’s theorem can be left until 3&4, but I would hope solving and factorising over C was done at 1&2 level.
But then as a Methods 1&2 teacher, I hope lots of things would be done at Year 10 that seem to be missing.
As a Year 7 teacher I could say the same about primary schools…
With each successive kick of the proverbial can down the road, there is one set of teachers who will be audited (internally or externally).
FWIW, I think the draft outline Mr Puzzled has suggested work.
If time was an issue (it always is), maybe the circle geometry could be quietly retired.
It is a nice topic, one of my favourites actually, and involves lots of really nice geometric proof, but it is one of those topics that if a student struggles, so be it. In its place, perhaps with partial fractions, could go a bit of calculus work, implicit differentiation is a nice one, or derivatives of the inverse trig functions.
Overall though, it looks like a well planned course.
If time were an issue …
Thanks very much, RF. Hopefully Mr. Puzzled finds your, and JF’s, comments, helpful.
This is now grammatical crap as well as mathematical I see… (actually, in fairness you have always corrected my grammar, so fair play).
As with all things VCE Units 1&2, the assessment (how, when and at what depth) is often more difficult than planning the lessons.
I don’t have anything sharable on this front as yet, but will see if the SM1&2 teacher(s) of 2022 that I know are willing and able to share some examples for the benefit of all.
Just a tease, and very much appreciate you responding to Mr. Puzzled.
I can’t help but notice the subjunctive, ever since this song:
I like to start SM1&2 with Proof, although not as an assessed topic and I like to make sure to include:
– Direct Proof
– Proof by contradiction
– Proof by induction
I then like to teach Sequences and Series, including proof in each lesson (where relevant) and will often do some type of investigation late in term 1 which also has an assessed Proof component.
I’ve found a lot of inspiration for investigation tasks from IB HL exam papers (you can buy them direct from the IB Organisation for about $3USD per paper – money well spent I reckon, but you can get the old papers in bundles at a discount).
Marty – I’ll find an example investigation and send it to you “soon”.
How do you find teaching ‘proof using the contrapositive’ so early in the year? For me, that’s a big reason for doing Logic before Proof.
I find it all a bit of a steep learning curve for the students – I use heavily contrived examples for pretty much everything so that the proof is no more than a few lines.
Because sequences and series immediately follows, I put most of the emphasis on Proof by Induction (divisibility tests and the like) and refer back to things like Proof by Contrapositive when it arises in other topics.
My logic (pun accidental) is that if students are not hearing the phrase for the first time they are less likely to be worried by it.
The plan has worked for me in the past.
Unfortunately, I feel the Geometry topics may not get as much time under the new study design as I enjoyed in the past; a lot of direct proof and proof by contradiction (radius-tangent theorem is probably the most common) in there (and so many different ideas for investigation work as well that will now, quite possibly go the way of kinematics…)
I was never formally taught logic. I remember “discovering” the contrapositive for myself and using it in a proof in a real analysis subject I was taking. I struggled to know how to justify that the statement I had proven was equivalent to the original and ended up drawing venn diagrams in such an attempt.
When I went to university I enrolled in a BA. My father advised me that, whatever I do, I should do Philosophy 1 because it contained logic. I followed his advice – as I always did; we used Copi “Introduction to logic”. It was good advice. Up until that point, I was not good at writing essays. But logic taught me how to construct an argument, and then I could apply this to structuring my essays. I passed on the same advice to my son when he went off to university and he majored in phil with lots of logic. Still, eventually the family tires of our dinners when we are asked “Would you like red wine or white wine?” and my son and I both say “Yes please”. Sadly, I gather you can now major in philosophy at some universities without ever doing logic.
That would be insane. Do you have an example of such a university?
There’s no logic in that!
a few IA ideas are here for both SL and HL including one on proof and paradoxes 37)
Maths IA – Maths Exploration Topics
I’ve attached the document below here rather than https://mathematicalcrap.com/2021/11/15/discussion-vcaas-blunt-implement/ (where it more naturally belongs) because I think it will be more useful here. It’s the last part of the 1988 Course Description Booklet for Mathematics, written by VCAB (the very distant predecessor of VCAA *). VCAA’s Stupid Design is not fit to lick the boots of this Booklet.
My main point is that this is this sort of clarity and detail that we should be DEMANDING of VCAA and its Stupid Design.
* VUSEB –> VCAB –> VBOS –> BOS –> VCAA
VCAB Mathematics A and B – Accrediation 1986-190 – Part 3
Thanks very much, John. I agree it’s useful here, but I might also attach to the Blunt post in some manner.
Recently I picked up a copy of “The Sorting Process: A study in mathematical structure” by Room T. G. & Mack J. M. (both of whom taught me at university). This deals with sets, proof, binary arithmetic, Boolean algebra and related matters, and grew out of some lectures given to teachers in Sydney. About 230 pages, a good read.
From my read of the draft study design, plane geometry (ie Chapters 9&10 from the Cambridge text) is no longer included, so there should be some flexibility here for finding more time for other topics.
I guess one could argue that some important ideas from plane geometry (which are in the year 9 / 10 curriculum) like similarity, tangents to circles, etc. are prerequisite knowledge, so if they weren’t taught earlier, perhaps they should be taught in Year 11. And perhaps also students should be familiar with a range of facts about “special quadrilaterals” since they are often useful when doing geometry with vectors.
Sudoku and KenKen puzzles provide enjoyable exercises in applying ideas from logic. They are simply applications of “and”, “or”, “not”, “if…then”.
I don’t think that VCAA knows which sequence they think things should be taught in – they have mixed up unit 1 and unit 2 topics (has this been noticed on this blog before?).
Mostly “Graphs of nonlinear relations” with “Graph theory” are in the wrong unit. Do you think they were confused by the two meanings of “Graph”? (Or maybe they are using as-of-yet unpublished version of the study design instead of the draft…)
Here I’ve annotated their suggested sequence with the Unit and Area of Study that the topic occurs
Number Systems (U1 AOS1.1 *) and Recursion (U1 AOS2.1)
Graphs of non-linear relations (U2 AOS4)
Logic (U1 AOS1.3) and Algebra († if they mean Boolean algebra then U1 AOS1.3)
Geometry in the plane ( ‡ ) and proof (U1 AOS1.1)
Simulation, sampling and sampling distributions (U2 AOS1 **)
Graph Theory (U1 AOS1.2)
Vectors (U2 AOS1.3)
Transformations (U2AOS2.1), trigonometry (U2AOS3.1), matrices (U1 AOS2.3)
* Number systems might include Complex Numbers (U2 AOS3.1) as there is no other place in their sequence for it…
† In the Study Design it’s titled “Logic and Algorithms” not “Algebra”, and it includes pseudocode. Do you think they really mean that? Could students really be expected to “perform” (trace) a computation defined given pseudocode in an exam?
‡ Apparently “Geometry in the plane” is not in the study design anymore (but some standard results are suggested as vector proofs.) How many teachers will follow the VCAA advised sequence and teach this old but good topic here?
** I guess this includes combinatorics (U1 AOS2), or maybe that is better near the proof unit…
Simon, some VCAA apparatchic with a pseudo-brain put ‘pseudocode’ in the Daft Stupid Design. I won’t be teaching it. In fact, some schools already teach it anyway during Yr 10 as part of a general coding topic.
Area of Study 1 (Proof and Number) clearly includes complex numbers, but only as part of number systems in general. Complex numbers should be taught as a separate topic (which I have previously stated) and Area of Study 3 makes this clear. Actually, given that the writers of the VCE Specialist Maths Exam 2 don’t know that real numbers are a subset of complex numbers, I find the statement in the Stupid Design hilarious.
“Number systems for the natural numbers, N, integers, Z, rational numbers, Q, real numbers, R, and complex numbers” is naturally taught at the start of the Proof topic (this is what I’m doing, anyway).
“Simulation, sampling and sampling distributions” is total rubbish. It’s Mickey Mouse crap. My advice is Do Not Teach it. Teach kinematics instead.
“Geometry in the Plane”, as well as all the “circle theorem stuff” is something that should be getting taught in Yr 10. I don’t know what gets taught in Yr 10 these days – not much given what Yr 11 students bring to the table. Less Mickey Mouse in Yr 10 and more mathematics would be a big help.
I would NOT teach Combinatorics as part of that Simulation, Sampling etc. bullshit. It is clearly stated as part of Area of Study 2. I’m teaching it as part of a separate topic – Principles of Counting.
There are 11 sorts of people that would follow the VCAA sequencing:
VCAA couldn’t be trusted to organise a meat plate at an abbatoir. I’ve provided a suggested structure for the sequencing of topics earlier in this blog. Every teacher needs to think very carefully and collaborate closely with their methods 1/2 colleagues so that both subjects have a chance of efficiently supporting and consolidating each other.
Here’s hoping pseudocode does not appear in the final document. It appeared more than once in the draft, so I’m left to think it was deliberate.
There are two types of FM teachers in this world: those who can extrapolate from incomplete data.
I have taught Further Mathematics, and it is possible to extrapolate from incomplete data. One often encounters time series with missing data. The data may be missing for all sorts of reasons, but they are missing. There are methods for estimating (“imputing” is the technical word) the missing data and one goes from there. For further reading, I recommend:
It’s also possible to miss the joke.
The danger of extrapolation …
I’m sure it was deliberate. But hopefully it will not survive past the draft. It feels like it is contrary to the move back to the more “pure maths” type of subject – unless we’re going towards computability / incompleteness 😁 Then we can talk about noncomputable real numbers as part of the number systems dot point!
If it does survive, it will be interesting to see how they plan to examine pseudocode…
VCAA wouldn’t recognise a pure maths subject if you hit them in the head with one.
Marty, I’m a big believer in the scientific method. Your hypothesis requires collecting data – a lot of data involving all of the relevant heads … I’m sure there would be no shortage of volunteers to conduct the experiments.
I second the motion, and would applaud the subsequent motions.
RF, a vain hope. The pseudocode poison has infiltrated all parts of the final Study Design.
What VCAA clearly does not understand is that pseudocode means ‘plain English’ but there are many different interpretations of what this plain English looks like. I claim that VCAA does not understand this because if it did, by now it would have provided clarity – a definitive glossary with examples of exactly what it means by pseudocode. Instead we are all left guessing what this crap might look like in the VCAA reality. I intensely dislike what I see in the new textbooks (I assume the writers were guessing just like the rest of us *) and I intensely dislike what I saw in the MAV PD presentations (I assume the presenters were guessing just like the rest of us *). It is not mathematics. It is mathematical poison. Most of the MAV pseudocode output was copied straight from textbooks (which weren’t available at that point in time). And the very small example given in the VCAA presentation by MacNeill was trivially nominal.
* I would be extremely angry if it turned out that the MAV and textbook writers were given some special, secret briefing by the VCAA on what to write about pseudocode … (It will not surprise me if it turns out that a sweetheart arrangement was done with them regarding the pseudocode. VCAA’s silence on all this is deafening).
So much for the resources on all this crap that VCAA promised.
My comment was more about exploring what the VCAA advice was, than saying I wanted to teach it that way. Before I started planning I was thinking of using their sequence, but no longer – I still haven’t figured out what sequence I think is best – especially working with the methods sequence. I agree with you about teaching complex numbers, combinatorics, etc as separate units.
Who knows about the what’s and whys of pseudocode in SM… From my experience teaching computing, it requires more time than a couple of dot points would allow. (It also has “binary number systems”, note the plural, in the draft study design…). I’m not going to try to teach pseudocode in y11 spec.
Does the school you’re thinking of teach it as part of maths (a la VCMNA334 and VCMNA358) or as part of digi tech? Digi tech is not a required in the VC for students in years 9 and 10, so can’t be a requirement for y11 maths.
Circle theorems are part of 10A – but it’s not very explicit and now that it’s not in specialist, I’m guessing it will be skipped by most schools… It’s a shame.
A couple of questions:
1) Do you think Kinematics could/should be taught in y11 methods instead? It is a good application at the end of their calculus sequence. Then in y12 specialist more advanced cases can be considered as applications of DEs.
2) Why do you say “Simulation, sampling and sampling distributions” is not worth teaching in y11? The draft study design is a bit more explicit about introducing samples as the sum of n identical random variables etc. I imagine that then gaining an understanding for how samples work by actually simulating sampling before diving into CIs and p-values could be useful. It also echoes the bootstrap approach to statistics.
An analogy is making sure that students have a good understanding of kinematics before supplying SUVAT equations so they don’t misuse SUVAT.
I have not taught y11 spec much over the last few years and am not a statistics expert – so I’m interested in the opinions of the readers of this blog!
Q1: No. MM 1/2 is already full enough, and kinematics is not something that should be added. It should be done in SM 1/2, where the idea of a differential equation can be introduced and x-t and v-t graphs can be introduced and explored. If there’s room enough in MM 1/2 for kinematics, I’d much rather see that time used to teach the chain rule. As well as differentiation from first principles, which has moronically been removed from VCE maths altogether. ‘SUVAT’ is no longer on the course, I won’t be teaching those formulae, but I will show how they emerge as special cases.
Q2: The “Simulation, sampling and sampling distributions” is Mickey Mouse. It can all be done, alongside a decent understanding of random variables and the normal distribution, in SM 3/4. And the theoretical underpinning can be introduced. It is a total waste of space in SM 1/2.
I agree with all you say about the pseudocode. And the binary number system*S* was not lost on me. That was written by an idiot:
a) If VCAA was simply trying to imply contexts for THE binary number system (and I think it was), then this should have been clearly said.
b) Otherwise, if VCAA really thinks there is more than one binary number system, then …
On the plus side, VCAA seems to understand there is more than one Boolean algebra – I’d have bet they thought that the two-element Boolean algebra was THE Boolean algebra, so that was a pleasant surprise. But this should have been emphasised, in my opinion. Be that as it may, it’s only the two-element Boolean that they’re interested in rather than a Boolean algebra as a mathematical object.
By the way, I heard that the reason mechanics got the chop was that females didn’t like it … So the changes to the Stupid Design are gender-motivated in part. I’m sure there’s a logic joke somewhere in all this.
Re Kinematics: There are a couple of sections in the Cambridge MM textbook that introduce Kinematics, which the MM teachers at my school taught last year and meant there wasn’t too much I needed to add – which was good considering the amount of lost time last year. But you are right that if time is tight in MM then “first principles” derivatives is more important. Chain rule can maybe wait for units 3&4…
Re First Principles: the Draft Study Design does say students should know the limit definition, just doesn’t require they can use it… which is strange. And there is a dot point about the central difference approximation (incl its equation) which doesn’t have a corresponding key knowledge or key skill dot point in any of the MM units.
Re: “Simulation, sampling and sampling distributions” – I’m not sure. I have taught y12s that did not do the stats in y11 and it was ok, but there are concepts in there that students find hard to disentangle and a more prolonged exposure might help…
I am unsure about what VCAA want re Boolean algebra. Teaching it connected to both propositional logic and logic circuits in the one course feels like it could get confusing. There seems to be so many bits and pieces crammed in with no details of what is actually expected. I’ve attached the webpages I made for Boolean Algebra and Logic Circuits that are in the HSC Software course. Do you think simplifying Boolean algebra expressions like that is expected? Boolean algebra and logic gates are not explicit in Units 3&4 – so students probably only need what is required for proofs…
Overall, I’m feeling uncomfortable about teaching the new SM course – VCAA need to release the final study design, advice to teachers and sample exams (plural is wishful thinking) to help clarify some of the issues.
Declining numbers of specialist students is concerning, but chopping mechanics and thus removing all calculus based physics from high schools is not great, nor necessarily a fix. Maybe a FOI request could see if the rumor you mention is true?
Yr 12’s should see some statistics in Yr 11 Methods but they don’t because, contrary to what Area of Study 4 is called, there is NO statistics, only probability. The dot point
“set up probability simulations, and describe the notion of randomness, variability and its relation to events”
is vague and ridiculous. There is no mention anywhere of the magic words ‘random variable’.
And, has been discussed elsewhere, many teachers have a poor understanding of probability, let alone random variables. My advice about statistics in SM 1/2, to anyone wanting to teach it, is to teach the idea of a random variable and then focus on the normal distribution. It would then also be possible to incorporate the Hypergeometric Distribution (very useful for the bogus sampling stuff in MM 3/4) and the Binomial Distribution within the context of Principles of Counting. I would NOT be teaching the Mickey Mouse bullshit written in the Stupid Design.
The vestigal of differentiation from first principles in the Daft Stupid Design is absurd. The decision to get rid of this content was made by an idiot. And probably made because of the ‘onerous’ algebraic demands it places on students. Every single person on that panel has mathematical blood on their hands.
You’re right about waiting for the final Stupid Design to appear. As has been said several times, it beggars belief that the VRQA approved it nearly 3 months ago and yet there is STILL no sighting of it. It will appear some time in term 1, when it’s too late to be of more than trivial use in informing how Units 1-2 should be taught (the blunt implement advice VCAA released for Units 1-2 was a farcical substitution for implementing the new Stupid Design over 2 years). The cynic in me likes to think that VCAA are embarrassed by what’s been said about it, and are ‘tweaking’ it before making it public.
Regarding your attachment – I think there’s too much on digital circuits and not enough on propositional logic. I’ve attached a couple of questions from old exams that I think might be what VCAA have in mind – it would be good if VCAA provided a lot of sample questions on the new material, not just a couple of moronic sample exams that might have only one question on the new stuff. My advice would be to get an old Checkpoints from the early 90’s and look at the Logic and Boolean Algebra questions (back in the 80’s and early 90’s that stuff was part of one of the optional modules in Specialist 3/4 – most teachers choose the Mechanics module instead).
We need to make VCAA accountable for its Stupid Design. If most teachers sent feedback, I think VCAA might listen. Particularly since the old Maths Mangler is gone (unfortunately to ACARA, apparently not content with limiting their damage to VCE).
Sample questions from old exams
That first question requires some careful interpretation…
Part of me wants to argue that as it is written none of the answers are perfect because the second statement does not preclude non-islands from having the property “surrounded by water” and therefore…
…although MAYBE the question is saved by the qualifier A conclusion instead of THE conclusion.
Argh! Just put B (the best, non perfect answer in my opinion) and move on…
Attached is the answer given in Checkpoints – good call on B, RF.
“B makes sense”. Yes and no.
I’ve studied logic outside the realm of Mathematics and using that viewpoint B is the least bad answer.
I would not call it a good answer.
Nor would I call the explanation a good explanation.
However the other options are either wrong or useless.
Euclid uses proof by contradiction (Elements, 1:6)
For an Australian resource; see
and the video
Thanks for sharing the Proofs in Mathematics textbook – it looks like a really good resource; lots of good examples and explanations, including how to think when trying to find proofs.
The papers available at the following links may be of interest:
Simulation of the Sampling Distribution of the Mean Can Mislead:
Click to access watkins.pdf
Simulations of the Sampling Distribution of the Mean Do Not Necessarily Mislead:
Click to access lane.pdf
Effects of teaching the Sampling Distribution of the Means Using Simulation With and Without Stating the Central Limit Theorem:
The Cambridge textbook gives no warning of what these papers discuss (and therefore the number of samples that should be ‘used’ for the simulation), the Cambridge textbook writers are probably not even aware of the potential for constructing misconceptions. Particularly when the samples are being drawn from a NON-normal population. So if you’re planning to do all the ‘dot plot’ crap in the textbook, be sure to understand the potential consequences.
Wow, y’all do a lot of different stuff. And then you have to do it the way they want since there are national examinations. I would think American high school is easier where you just teach stuff with hackneyed labels like algebra 1 and 2 and geometry and trig and analytic geometry and calculus, for course names.
And I didn’t see Boolean algebra and the like until a survey class in EE (for general engineers) in college. I mean, they are totally understandable at much younger age. And maybe make sense in a CS class. But it didn’t hurt me to get them a bit later.
I donno. I think I am kind of torn on this mixing in a lot of different stuff approach. It is kind of nice to be getting the truth tables and the baby stats earlier. But then it does kind of muddle and mess up what would be a traditional course. Not really sure which is better/worse in the end for the kids.