The New VCAA Study Design is Up

Well, sort of. The 2023-2027 SD is here (Word, VCAA, Idiots) and is linked on this page. Thanks to Red Five, whose detective skills are a hell of a lot stronger than VCAA’s announcing skills.

83 Replies to “The New VCAA Study Design is Up”

  1. The following dot points from Methods 3&4 have me quite concerned:

    · specify the similarities and differences between formal mathematical expressions and their representation by technology, in particular, equivalent forms of symbolic expressions

    · select an appropriate functionality of technology in a variety of mathematical contexts and provide a rationale for these selections

    · design and implement simulations and algorithms using appropriate functionalities of technology

    · apply suitable constraints and conditions, as applicable, to carry out required computations

    · relate the results from a particular technology application to the nature of a particular mathematical task (investigative, modelling, or problem-solving) and verify these results

    · specify the process used to develop a solution to a problem using technology and communicate the key stages of mathematical reasoning (formulation, solution, interpretation) used in this process

    Mostly because I don’t think they are clear at all and so I have no idea what the exam could look like (and exams have been bad enough recently…)

    I also have many, many concerns about Specialist but that is going to take me a few days to process (and a few beverages…) although, integration by parts making the final cut is a nice touch.

    1. That’s cute: strengthening calculus while eliminating one of the best sources of natural and beautiful applications. VCAA loves them their irony.

      1. I used to teach integration by parts anyway – maybe a lot of teachers did.

        So that may be a bit non-consequential.

        I need some time to digest the proof and logic vagueness in the Specialist dot points a bit. My first instinct is that 1&2 seems to have a lot more (Boolean, Logic Gates, Circuits) than 3&4 which raises quite a few questions, but mostly WILL THEY EXAMINE IT?

    2. All of these dot points were already in the old study design.

      Also, I am a student studying Methods 1/2 and doing Methods 3/4 next year, I was wondering if anybody had any resources for pseudocode – since that is getting introduced to Methods 3/4.

      1. I will disagree with all these dot points being in the old study design. Pseudocode was not in the old (technically, the current) study design for Mathematics.

        If you mean the draft study design, then yes, but even then there have been significant changes; thankfully most of them involve some level of “toning down” (opinion, not fact).

        “Specify the process” is a rather odd phrasing… seems to be more akin to Algorithmics than Mathematics, but again… what the study design says and what the exams actually contain can be quite different (anyone remember a 2016 draft saying “normals not required” and then seeing the 2016 paper 2 exam will know at least one example of this…)

        1. Maths Methods 3/4: Some observations.

          1) I don’t see any pseudo-code bullshit.

          2) The dot points that RF mentioned are in Outcome 3 – Bullshit *ahem* I mean ‘Use of Technology’. Nothing new, just different wording. I think there’s a subtle implied emphasises on programming in the ‘unique’ CAS calculator language. For those born post-2000 AD programming means coding. It would make more sense if a proper CAS such as Mathematica, Matlab or Maple was being used (maybe the person(s) who imposed their will on the rest of the committee (*) is unaware that the great Mathematica experiment was a disaster and VCAA pulled the plug).

          3) There was a missed opportunity for VCAA to be honest and re-name the subject to reflect what it actually is – Computational Mathematical Methods. VCAA is not interested in pure mathematics – time for it to be honest and declare this.

          4) Some good news – transformations using matrices is gone. That is one piece of gratuitous stand-alone shit I won’t miss.

          5) I see that the old fog notation has made a come-back. Not sure why …?

          6) Area of Study 4 now includes ‘Data Analysis’ in its title. This shows what VCAA truly thinks mathematics is.

          7) The new Stupid Design is still opaque and lacking clarity and detail.

          * There’s an interesting story here. I have it from a primary – and pissed off – source that some members of the committee were mere tokens. Representational boxes to be ticked. That there were one or two loud voices that imposed their decisions.

          1. Thanks, John. I have also heard, from an impeccable source, that members of the committees were treated as “mere tokens”.

            Anybody who associates with the VCAA, as a committee member or as an exam writer or as an assessor or as a SAC thug, is an accomplice and/or a stooge. And, yes, if you think this comment is referring to you, you are almost certainly correct.

            1. *Ahem* A clarification for those who might get confused:
              Marty’s comment applies to any reader who thinks the comment might apply to them …. (The “you” is not me!).

                1. *Sigh* You got me. I admit it. I’m their mole. I’m a 5th columnist, a quisling. Hiding in plain sight. Collecting intel on this rotten anti-VCAA cell and reporting back to my VCAA handler.

                  OK, I need a distraction to fool you all and maintain my cover as a VCAA-hater …

                  I find it interesting that the publication of the Mathematics Stupid Design has not been mentioned in any of the School Notices …

                  BUT … I did see that the date when schools get told if a Unit 3 subject is being audited has been pushed back to April 26 (NOTICE 25 2022). There are so many reasons why this is idiotic and cruel (key VCAA attributes).

                  On the plus side, schools now have time to write not one but TWO SACs – the SAC given to VCAA and …

          2. Hi John,

            (1) All of the pseudocode references are now gone – not just methods!

            (2&3) The course is not rigorous enough to be a Computational Mathematical Methods. The use of CAS in Methods is mostly just handholding for algebra and calculus with the VCAA hoping for deeper thinking and exploration. Remove that handholding and the old graphing calculators still used elsewhere in the world would suffice for the graphs and stats in VCE.
            Using a proper CAS (one of the M’s listed above) would *maybe* improve things, but I’d still feel bad about the expensive and closed nature of them. Why was something like Sympy or Sage or Maxima not on the approved list?
            DLL always promised data on the Mathematica trial – but it never appeared (afaik)

            (4) The vestigial matrices in methods was always embarrassing – only one more year of teaching it!

            (5) The f∘g notation was always in methods, just optional in the old study design. Talking about composite functions is clunky without it. You don’t like the notation?

            (6) The corresponding area of study in all of the VCE maths units is now “Data analysis, probability and statistics” even in General maths where they do no probability (it used to be just “data anlysis”). I don’t think it implies much…

            (7) YES. As you and RF have pointed out – how and to what depth some of the content is to be assessed is not clear. But I’m glad at least the dot points are now fixed – makes teaching the new study design for spec 1 & 2 a bit easier.

            1. Hi Simon.

              1) Maybe even the stand-over men knew they couldn’t bludgeon that one through.

              2) Don’t get me started on the integrity and honesty of former Maths Manglers. I get into enough trouble from Marty already.

              3) The course is not rigorous enough to be a mathematics course, either. But it’s not about rigour, it’s about honesty and philosophical intent. The course is more honestly called Computational Mathematical Methods than Mathematical Methods.

              4) I wonder if the idiot that bullied it through on the current Stupid Design will ever confess.

              5) I think it’s fine. I don’t know why it ever got dropped. And I don’t know why it’s come back.

              6) ‘Data Analysis’ is a complete misnomer when applied to the content of Area of Study 4 of Methods and Specialist.

              7) Another missed opportunity. Deliberate, I think. I honestly think the VCAA wants the Stupid Design to lack clarity. Then VCAA has the flexibility to argue for any old bullshit it wants and defend its errors and those of its goon squad. Clarity means accountability.

              1. Pseudocode still exists in a few dot points unfortunately in Specialist. Not as much as it did, but enough to make me a bit unsteady.

                I’m relieved that Logic and Circuits (two totally separate ideas I reckon, but…) are only to be found in Units 1&2, although the line about any Unit 1&2 being assessable in Units 3&4 casts a LONG shadow…

                I think my main concern with this study design is that it is even more “bitsy” than the previous and so teaching the course with any sense of flow, with ideas knitting together just got a lot harder!

                1. Yeah, the only knitting to be seen is what the irrelevant tokens on the committee may as well have been doing. The whole pseudo-code is bullshit. Any appearance on an exam will be an outright declaration by VCAA that Specialist Mathematics is not a mathematics subject, it’s simply another algorithmics subject in a very flimsy disguise.

                  On the topic of Specialist, I have no idea why the Logistic Equation got its own special dot point. There’s a dot point for “formulation of differential equations from contexts in …” and a dot point that includes seperable DE’s. So why does the logistic get or need an explicit dot point? One of the stand-over men’s little pets …? Trying to be COVID-relevant?

                  And on the topic of flow, did you notice how the dot points in each Area of Study don’t. Look at the five dot points under Logic and Proof. Would anyone with a half a clue sequence things in that way. The natural order (numbering the dot points 1 to 5 in their current order) is surely 2, 4, 1, 3, 5.

                  There’s much more content to get through, it really will be a desperate sprint. Of course, idiot stand-over men don’t have to teach this subject. I know a man who has campaigned very hard for a number of years for “vector cross product, normal to a plane and vector, parametric and cartesian equations of a plane.” For what purpose or reason, I don’t know.

                  1. I’m quite used to the dot points not flowing, or being oddly… dotted. Some things get their own dot point, some dot points contain multiple ideas.

                    What gets annoying is certain “key ideas” either rarely (never?) being assessed or things that are decidedly NOT listed being examined.

                    Such experiences render study designs quite redundant.

                2. Yeah, I just noticed that – I think I had too many versions of the study design open…

                  And yes, I agree with your other two concerns. But I have enjoyed teaching more proof to the year 11s!

              2. Fair enough regards all of the points. Data analysis is mostly a misnomer for further maths too – maybe the data transformations they use can qualify, but the rest is just statistics.

              3. The phrase “data analysis” is used in many different ways. It used to mean applying statistical methods to analyse data. In universities in 2022, it is a broader term that includes many ideas from computer science. In my experience in industry it might mean using Excel.

                  1. “Data analysis” sounds impressive and 21st century but has so many different meanings that the phrase itself is totally meaningless without clarification.

                    When it comes to impressive sounding phrases and grandiose statements that are totally meaningless, VCAA is king. (And ACARA is the queen)

        2. I love how VCAA says at that page:

          “In 2022, schools must ensure they use the VCE Mathematics Study Design 2016-2022.”

          You must use the 2022 Stupid Design, except when you must not use it (for example, when designing your Unit 1/2 courses for 2022)

          1. So what does this mean for, eg. transformations with matrices in Methods Units 1&2?

            Should we teach it because it is in the current study design? Or ignore it because it’s irrelevant to Methods Units 3&4 in 2023?

              1. Indeed. And VCAA’s blunt implement advice is now an even more glorious example of its total stupidity!! Behold ….

                The Blunt Implement advice states that
                “first principles differentiation of polynomial functions”
                can be omitted.

                And yet the new Stupid Design includes:
                “the limit definition of the derivative of a function \displaystyle f'(x) = \lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}

                which is a very good thing (*) but shows that the Blunt Implement advice is untrustworthy (*). To paraphrase a popular advertising catchphrase: Ah McVCAA, you’ve done it again!” Idiots.

                * However, the current Stupid Design includes
                “first principles approach to differentiation of \displaystyle f(x) = x^n, \displaystyle n \in Z, and simple polynomial functions”
                but the new one does not. So maybe it’s not the good thing it initially appears to be. It’s just a formula without any requirement for application … So maybe the new Stupid Design doesn’t contradict the Blunt Implement advice. Which makes VCAA even bigger idiots in my book. And I think it confirms my theory that differentiation from first principles was missing in the Daft Stupid Design because VCAA decided the algebra was much too difficult for students to handle.

                1. Unfortunately, in my reading of the new SD, despite them adding back the limit definitions properly, they still left out first principles explicitly. I suspect it’s also related to the expansion of (x+a)^n being removed which is somewhat necessary.

                  Given that they couldn’t even correctly match an area of study with it’s outcome 1 correctly (General U1 AOS3&4), the bar is pretty low (not to mention other errors like missing brackets in specialist integration, inconsistent formatting of notation like vectors, dot points that were added but are actually the end of the previous one like SM U2 sampling distributions the (sample mean) is part of the previous dot point).

                  Ah the things you find when you reformat the document so you can actually read and compare it easier.

              1. The new Study Design is officially implemented in 2023 but was unofficially officially implemented in 2022 at the Units 1/2 level by VCAA because VCAA is too pig-headed and wilfully stubborn to admit that implementing Units 1/2 in the same year (2023) as Units 3/4 is really dumb. The unofficial official implementation advice given by VCAA is attached.

                Note that matrices are prescribed in Specialist Maths Units 1/2 in 2022 to prepare students for Specialist 3/4 in 2023. In fact, Specialist Maths Units 1/2 is unofficially an officially prescribed course in 2022 (despite what the 2022 Study Design says).

                So much bullshit and confusion created by pure pig-headedness and wilful, derelict stubbornness.


                1. Hi John,

                  I can’t find the release of that information/document anywhere – VCAA bulletins etc. When & where was it communicated??

                  1. I downloaded it in the last week of December 2021. Two of VCAA’s (many) nasty habits are:
                    1) Prematurely removing important information, and
                    2) Making important information hard to find (certainly, publishing such information in a less than prominent way).

                    Your failure to find it will probably be due to one of the above. Anyway, it’s been published here so no need to let VCAA waste your time (something it also has a habit of doing to us all).

                    1. Then again, your failure to find it could be due to a very poor decision to try and navigate the VCAA website rather than doing an internet search … See attached.

                      See habit 2) above – VCAA’s website is typically user UNfriendly for navigating and finding information. Avoid making the mistake of assuming otherwise.

      2. Jesus H. Christ. Any school maths subject where you gotta ask about pseudocode is not a maths subject. This is insane.

        And, Charlie, sorry. It’s a fair enough question for you to ask, and perhaps one of the readers can help, but I can’t.

      3. i dont think pseudocode in methods is going to be much of an issue. honestly just dont stress about it at the moment at all, wait for the textbook to release next year and spend your 2 week holidays getting yourself well versed, the new methods stuff will be fairly easy in comparison to calc and trig functions. however if you’re taking spesh math then u should be scared lol. make sure start of next year u get on it right away if ur doing spesh.

        im also doing methods 3/4 next yr, (and spesh 3/4) so i feel you, its annoying how broad vcaa can be.

        1. Thanks, noah. There are two quite separate questions: (1) How easily will the students be able to manage the new material/emphasis; (2) What is maths educational value/devalue of the new material/emphasis? Naturally enough, your concern, or at least main concern, is (1). I’m not a good judge of that, although VCE maths seems so ritualistic, I don’t see that any change can have much effect. On (2), there is no question that VCAA has decided to get further away from mathematics and further into ritual.

          1. Noah is correct in some ways. Teachers stress because they know it’s new stuff (for them) and there is no clarity etc.

            On the other hand, from a student perspective everything is new (including the ‘old’ stuff). They don’t know that some stuff is newer than other stuff. If they’re worrying, they’re worrying about all the stuff!

      1. “appropriate functionalities of technology” just means using your CAS correctly. theres nothing inherently wrong with that statement.

  2. I hope we’re not place in the position where we look back fondly on the 2016-22 Study Design in comparison to the new one.
    What Red Five has highlighted leads me to think that, maybe, just maybe, that might end up being the case. I’m also concerned.

  3. Hey all,

    I don’t know if this is a place to ask questions (please let me know if it is not).

    I am a student studying Mathematical Methods 3/4 next year, I am currently studying Methods 1/2.
    I just was wondering for Pseudocode, how do you guys think that will be assessed in examinations and are there any resources that can be used to learn it?

    Also, I noticed that functional relations is gone in the methods study design – does this mean questions like the last MCQ in 2020 exam 2 paper will no longer make an appearance in exams? – I don’t know if its safe to assume so since the study design seems to be really vague, for example they included derivatives of inverse functions in one of their exams which was never actually explicitely in the methods study design (although can be derived from the content learnt within it).

    Thanks in advance,

    1. Hi, Charlie. From my point of view, anybody can ask anything. (Yes, the antibiotics did get rid of it, and thanks for asking.) In any case, your questions seem square in the middle of everyone’s puzzling about what VCAA has done, and what VCAA will expect. So, I expect some pretty knowledgable answers will be forthcoming.

      Regarding functional equations, that’s interesting if they’ve disappeared from the study design. One would presume that means they’re no longer examinable, but others here will have a better guess.

      Regarding the derivative of inverses, this was definitely not in the previous study design (even if, as you note, the technique is used in (an invalid manner) to get the inverse trig and logarithm derivatives.) Nonetheless, and as you note, such questions have appeared, in 2018 and 2019: I hammered that here, and see also here.

      Would VCAA be stupid enough to examine derivatives of inverses again? That would be pretty damn stupid. So, let’s say it’s a 50-50 bet.

      1. Greetings Charlie – good luck in advance with studying across the great switch over of study designs, hope it all goes well…

        I have an idea of what pseudocode means, but what really matters (and why I’m not rushing out to write class notes just yet) is what the VCAA examiners think it means.

        As JF has pointed out, correctly, there is already confusion about Boolean Logic/Algebra, so there is ample reason to suspect pseudocode will, for 2023 at least, be examined quite gently.

        That said… a quick internet search for “pseudocode” provides a plethora of (mostly US, UK) tertiary-level study notes which I plan to use as background reading in the near future.

        1. They do pseudocode in VCE Software Development, and there is one examiners’ report here where they outline students’ “common errors”:
          I don’t know if it would help much – I imagine VCAA would have things one way in maths and another way in another subject anyway.

          I’ve heard this website is used by some computing teachers as well: The slides down the bottom have conventions for pseudocode. But I don’t know how conventional they are, and whether the same rules would apply in maths. But they are local, so I just thought I’d share that.

          1. Unlike most other curriculum bodies (NESA, IB, GCSE/A-levels, AP,…) the pseudocode used in the VCE Software Development has never had a clear standards on keywords or syntax. The VCE SD exams often have issues with their pseudocode…

            For someone with experience programming (stronger VCE students), picking up pseudocode is fairly easy. But less experienced programmers – including maths students – can struggle. Though tracing code by hand does help students build their internal model of how a computer runs code.

            Here are my notes on pseudocode in the VCE and pseudocode in the IGCSE

            To be honest, I can’t see myself teaching any pseudocode in specialist unless we get clear direction about it being examined. Algorithms, such as the Euclidean algorithm, Bisection, Newton’s, etc are candidates for structured English descriptions of the algorithm…

            1. Thanks, Simon. Great post. Your first paragraph articulates exactly what I attempted to say earlier about Algorithmics. This is exactly the problem with all of VCAA’s Stupid Designs – a total failure to be clear. I think a large part of this problem is either:
              1) VCAA does not understand the content it’s trying to enact (very likely with the pseudocode bullshit), or
              2) You have someone very smart with no talent to communicate or understand the needs of those less smart. Its an Evans money bet either way, I think.

              You can see VCAA’s attempt to be clear in parts of Specialist 3/4, but unfortunately the parts where they tried to do this are exactly the parts where it WASN’T needed! VCAA has no understanding of when and how to be clear.

              And I unreservedly agree with your last paragraph sentiments. It will be interesting to see if and how VCAA respond to this.

        2. Pseudocode is included in the Stupid Design because it’s a buzz word that VCAA \displaystyle thinks makes it sound smart and relevant to the 21st century. It’s also included because VCAA don’t want ‘old fashioned’ mathematics subjects that focus on *ahem* mathematics. VCAA’s understanding of what is mathematics is very different to a mathematician’s understanding.

          Pseudocode doesn’t appear in Methods, so Charlie is safe.
          In Specialist I’m assuming it could be examined indirectly via a students ability to write CAS-calculator programs (or Mathematica code) to answer questions whose solution requires a coded algorithm. An understanding of pseudo code is a basis for efficient and effective writing of code. Or more directly, I can – unfortunately – imagine questions asking a student to write pseudocode that finds the first 40 prime numbers.

          It will be a cold day in hell before VCAA actually defines what it means by pseudocode and how, or if, it will be assessed. It probably doesn’t even know itself.

          If you look at the Stupid Design for Algorithmics, you’ll see statements like:
          “specification and uses of the following ADTs:
          – list, array, dictionary (associative array)
          – stack, queue, priority queue”

          Impressive and clear, eh? But it’s not. It’s unclear. Because these words have a number of different meanings. VCAA does not define these words. So it’s a mystery to everyone what VCAA actually means if you drill down to details. You have to join the dots from exam questions when a simple glossary would solve this issue.

          But clarity is not VCAA’s strong suit. Secrecy, opaqueness, fogging are VCAA’s tools.

          1. Algorithms are also in the Victorian Curriculum mathematics content descriptions.
            Level 10: Implement algorithms using data structures in a general-purpose programming language (VCMNA334) [an interesting “elaboration” in this one is “using pointers in algorithms”… just that. no further details.]
            Level 10A: Devise and use algorithms and simulations to solve mathematical problems (VCMNA358)

            It was only tonight that I realised these are not in the Australian Curriculum. I thought that apart from the capabilities etc, the VC content descriptors were mostly a reorganisation of the AC.

            Appropriately, the Digital Technologies VC and AC require structured English and flowchart descriptions of algorithms.

            1. *Sigh* Yep, there it is:

              “key elements of algorithm design, including sequencing, decision-making and repetition, and representations of the ordered steps for an algorithm including through the use of pseudocode”

              I have no idea what this chicken vomit means. And I’ll bet neither does VCAA.

              Charlie, you sure know how to ruin a guy’s day. But I’m not going to lose any sleep over it. It’s VCAA’s responsibility to explain what it means and how it will be assessed.

              1. Hey John, (apologies haha)

                Do you think the new study design will affect scaling? And if you were a student would you prefer to do Methods under this study design or the previous?

                1. I don’t think it will affect scaling.

                  As for which piece of shit is better …. *Ahem* I mean which Stupid Design is better for Maths Methods …
                  On balance, I think the new Stupid Design is better than the old one for Maths Methods 3/4 (but NOT for Specialist 3/4). Why?

                  1) The moronic ‘transformations using matrices’ (when matrices themselves are not even on the course) has been deleted. This is a very big plus.

                  2) The moronic stand-alone functional equations stuff has been deleted.

                  But depending on what VCAA says about
                  “key elements of algorithm design, including sequencing, decision-making and repetition, and representations of the ordered steps for an algorithm including through the use of pseudocode”
                  I might change my mind.
                  Which choice of death do you prefer? Eaten alive by a tiger or starvation. Either choice is pretty crap.

  4. I collated what differences I found between the draft and the new version on my twitter @vmn_alex

    Glad they made the recurrence relation notation consistent throughout General now (all u_0) and removed matrices from Methods.

    If you need a laugh, check General unit 1 AOS3 and 4 and the corresponding Outcome 1 section. Someone clearly wasn’t paying enough attention when they put the sequences back together and moved Matrices.

  5. Can anyone clarify what VCAA means by “solution of first order linear recurrence relations of the form t_(n+1)=at_n+b, a≠0, with constant coefficients and their application to financial problems and population modelling.” in unit 1 specialist or is it as nonsense as I think it is?

    1. Look at any Further Mathematics textbook from 2000 to 2005ish (perhaps other years as well), specifically Module 1.

      A lot of this new Specialist content seems eerily like old (or current) Further content, now with added proof (perhaps).

      1. Yeah, I know the application questions of the recurrence relations from Further (before they decided to focus purely on finance), was more confused on the “solution” part as (from my understanding) a recurrence relation by itself doesn’t have a single solution but John pointed out the nth term rule as a solution.

        Seems like VCAA is trying to salvage some of the old General content that Specialist used to borrow from.

        1. IMHO, the emphasis on finance in studying recurrence relations in Further Mathematics is not a bad idea. So many different financial models can be expressed this way. Students can see that one mathematical model represents many different financial situations.

          The teacher can mention other contexts along the way to show that the idea has applications beyond finance.

          1. The issue with your opinion is not that it is humble, but that it is wrong. The emphasis on finance is a very bad idea.

          2. I’ve seen the opposite impact though, schools focus almost purely on the financial models in units 1&2 to the exclusion of all else despite the SD saying to look at multiple contexts.

            Also, the financial models in General don’t work well as an example to work from if these students were to later consider the series.

    2. Hi Alex.

      It’s reasonable to expect nonsense from VCAA, but in this isolated case it’s not quite the nonsense you might expect (but it comes close).

      I would imagine that VCAA wants students to solve recurrence relations of the form
      \displaystyle t_{n+1} = at_n + b
      ‘by hand’ and using CAS technology in the context of financial problems and population modelling.

      Using CAS technology: Trivial and therefore very VCAA-esque. VCAA’s focus is technology, not mathematics.

      ‘By hand’ 1: Use a formula with no understanding of where the formula comes from. Which is trivial and pointless and therefore very VCAA-esque.

      ‘By hand’ 2: The standard approach is to re-write it as \displaystyle t_{n+1} - at_n = b.
      Then you solve the homogenous recurrence relation \displaystyle t_{n+1} - at_n = 0 by assuming a solution of the form \displaystyle t_n = c \lambda^n where \displaystyle c is an arbitrary constant:
      \displaystyle c \lambda^{n+1} - a c \lambda^n = 0
      \displaystyle \Rightarrow \lambda - a = 0
      \displaystyle \Rightarrow \lambda = a.

      Then you look for a particular solution to \displaystyle t_{n+1} - at_n = b of the form \displaystyle t_n = \alpha where \displaystyle \alpha is a constant (the method of undetermined coefficients):
      \displaystyle \alpha - a \alpha = b
      \displaystyle \Rightarrow \alpha = \frac{b}{1 - a}.

      Then \displaystyle t_n = c a^n + \frac{b}{1 - a} which is the formula students will probably just be expected to memorise. The value of \displaystyle c is calculated from any given initial condition, that is, from \displaystyle t_1 = whatever.

      The difficulty most students will have is constructing an appropriate recurrence relation for the given context, the actual mathematics itself will be trivialised (which is just the way VCAA likes it).

      1. So, the solution is finding the rule for the nth term given the recurrence relation? They could have just said that instead of being a tad cryptic🙄. I’ll be looking into that method more, thanks John.

        1. The method generalises to higher order recurrence relations with constant coefficients (and is analogous to solving differential equations with constant coefficients).

  6. I noted that in the examination of Foundation Mathematics, “student access to a scientific calculator will be assumed” (p. 82). This suggests to me that CAS calculators would be not allowed, but the Study Design does not make this clear.

    1. Foundation used to have the same line as the other subjects for that in the draft and has been changed to scientific, so I would presume scientific only. How powerful a scientific calculator they’ll allow will be another story, but I would presume the same as what they are allowed in some of the sciences.

      1. Excel would be a suitable calculator of Foundation Mathematics. I have found that many VCE students have little idea about using Excel. Foundation Mathematics would provide a context for students to improve their skills in using this ubiquitous software.

        1. Perhaps SACs will be written with this in mind, but given the circus that was Methods CBE, I can’t see Excel being permitted in a VCAA exam for now.

          But who really knows.

          Excel is not the only skill to suffer, of course. You would not, but others may be surprised how even word-processing skills are quite lacking in the era of “computing” being taken to mean “coding”. Although, I also notice English teachers not being blamed for this…

            1. Terry, I don’t think that’s what RF is saying.

              But you raise an interesting point: Is something that can’t be examined ‘worth’ including in a syllabus …?
              (I suppose it depends on your definition of ‘worth’).

              Personally, I don’t see how letting students use Excel is any different to letting them use Mathematica.

              1. The difference is that Excel is widely available on nearly all computers in nearly every environment. Given the general philosophy behind Foundation Mathematics, I thought that Excel would be ideal for that subject. If the examining authorities cannot figure out how to assess students on Excel, they could ask Microsoft for advice.

                PS I was not intending to mis-represent the views of RF. I sincerely apologise if my post gave that impression.

                1. Terry, I think you have misunderstood \displaystyle me this time …

                  “Personally, I don’t see how letting students use Excel is any different to letting them use Mathematica.”

                  means that since VCAA lets students use Mathematica in the exams, I don’t see how that is any different to letting students use Excel in the exams.

                  PS – To assess students on Excel, you simply ask some questions that require Excel to be used. It’s that simple. I think even VCAA could figure that out.

            2. Not because we can’t examine it – more because the attempt at using computers in Methods exams was… not successful.

              1. Regarding Methods CBE…
                I have heard from various sources that “sketching the graph” type questions are now limited to exam 1 *not on exam 2*…, because Mathematica students will do it all on computer.
                Honestly I partly understood why…simply put, if the graph sketching questions were on MM2 paper, then it isn’t a fair play with other TI, CASIO and HP CAS users etc (though the other CAS brands are merely countable across the state).
                Excel operations and applications *were* nice…good old days when the CAS calculators were not as powerful as today’s machines – i.e.: using spreadsheets and iterative formulae to carry out Newton’s method, bisection method, Euler’s method and so on… I feel that now, not only the students, but also a large amount of maths educators have got to used to shortcut with only shallow understanding to the basic principles…The exams set the trends…so that teachers and students only focus on shortcuts like “euler(dy/dx, x, y, {x_0,x_n},y_0,h)” or similar stuff. Consequently, when the exam questions were set in a different manner, such as providing pronumerals instead of numbers, most students tend to stuff it up, because they haven’t exposed themselves sufficiently to these founding principles or had relevant practice sufficiently…
                I quote from a very experienced and retired teacher – she said: “we will do everything, [it] can be everywhere…”

                1. Above I was suggesting that Excel would be suitable for Foundation Mathematics. Excel is useful in all sorts of situations. It is on almost all computers. Yet I have met students, and professionals, who have little idea of how to use Excel.

                  In health care I helped a colleague with spreadsheets; she had a Masters degree in health; but she did not know that you could add up numbers on a spreadsheet; she would punch the numbers into her calculator, and then write the answer in the appropriate cell.

                  I recall the reaction of an academic when the university insisted that staff put their results into a spreadsheet. Having never used a spreadsheet, this lecturer had no idea of how to do this.

                  Foundation Mathematics would be a good place for assisting students to develop their skills in Excel.

                  1. Terry, I agree with your post. I have no issue with spreadsheets being used in Foundation Maths. I have a particular view of what the philosophy behind Foundation Maths should be. I see the use of software such as Excel as essential for the students enrolled in this subject.

                2. Not withstanding the fact that CAS poisons everything (so Marty, don’t jump on me), Exam 2 is too long and Exam 1 is too short.

                  VCAA got an albatross/noose around its neck 20 years ago with CAS and doesn’t have the guts to admit it. And who was the idiot who weaponised this albatross with Mathematica?

                  (As an aside, if you’re going to have a CAS, at least make it authentic – Mathematica, Matlab, Maple … Get rid of the stupid hand-held CAS that is NOT used beyond secondary school).

                  Exam 2 should be a couple of questions where the CAS is useless unless a student has used his/her mathematical understanding to know what to get the CAS to do. These sorts of questions are very difficult to write, which is why Exam 2 is bloated with triviality.

                  Take graphing … If you were to examine if a student can draw a graph, there are several types of graphs that should appear. Suddenly 10/40 marks on Exam 1 have been used. Take equation solving … If you were to examine if a student can solve equations (and inequations), there are several types of equations that should be appear. Suddenly another 15/40 marks on Exam 1 have been used. So we’re down to 15 remaining marks and we haven’t started on calculus, vectors etc.

                  I’ve said it before and I’ll say it again, IF CAS is here to stay (Marty, don’t jump on me) then the 1 hour Exam 1 should be the CAS exam (with NO multiple choice) and the 2 hour Exam 2 should be the CAS-Free exam (with NO multiple choice).

                  The current examination arrangements make it very clear (as if clarity was ever required) that VCAA sees mathematics as nothing more than button pushing and code writing.

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