VCAA’s Mathematical Flea Circus, Part Two

Yesterday’s post was on the 2023 Methods Exam 1 report (Word, idiots), its foggy focus on trivia and also on the ludicrous non-solution of one particular question. Now, it’s on to Exam 2 Report (Word, idiots), which is what prompted these posts.

Here are the Exam 2 General Comments in their entirety. I have commented elsewhere on a couple aspects (here on Q3(a), here on Q3(e) and here on Q5(b)). I won’t comment further now, except to note that it seems to me to be nothing but fleas. I can detect no sign whatsoever of any underlying host.

This is the first year of the new study design and most students were able to respond effectively to the questions involving the introduced concepts, such as Newton’s method in Questions 3f. and 3g. and the point of inflection in Question 3d.

As the examination papers were scanned, students needed to use a HB or darker pencil or a dark blue or black pen.

Some students had difficulty understanding some of the concepts, such as the difference between average value of a function and average rate of change (Questions 2b. and 2c.). This year two questions involved strictly increasing and strictly decreasing functions. In Question 3e. many students used round brackets instead of square brackets. In Question 5b. either bracket type was appropriate as the maximal domain was not required. Some students did not attempt Question 3a. They appeared to be confused by the limit notation \color{OliveGreen}\boldsymbol{\lim\limits_{x\to -\infty}g(x)}.

Students need to ensure that they show adequate working where a question is worth more than one mark, as communication is important in mathematics. A number of questions could be answered using trial and error in this year’s paper, especially in relation to probability, Questions 4f. and 4g. Drawing a diagram can often be helpful to show the output for some of the trials. Students are allowed to use their technology to find the area between two curves using the bounded area function, but they must show some relevant working if the question is worth more than one mark. Often, questions require that a definite integral is written down, such as in Question 1cii. In Question 4d. students were expected to identify and write down the n and p values for the binomial distribution, not just the answer.

There were a number of transcription errors, and incorrect use of brackets and vinculums, in Questions 1b., 1ci., 1d. and 3ci. Students needed to take more care when reading the output from their technology. For example, some students wrote \color{OliveGreen}\boldsymbol{-\frac{\sqrt7 + 1}{3}} instead of  \color{OliveGreen}\boldsymbol{\frac{-\sqrt7 + 1}{3}} in Question 1b. Others wrote \color{OliveGreen}\boldsymbol{\pm\frac{\sqrt5 - 1}{2}} instead of  \color{OliveGreen}\boldsymbol{\frac{\pm\sqrt5 - 1}{2}} in Question 1ci.

Students need to make sure they give their answers to the required accuracy. In most of Question 1, Questions 3b. and 3h., and Question 4i., exact values were required. In all questions where a numerical answer is required, an exact value must be given unless otherwise specified. A number of students gave approximate answers as their final response to these questions. In Question 3f. some students gave their answers correct to two decimal places when the response required three decimal places.

There were a number of rounding errors, especially in Questions 1ciii., Questions 3d. and 3f., Questions 4a. and 4h., and Question 5ci. Students must make sure they have their technology set to the correct float or take more care when reading and transcribing the output.

Students need to improve their communication with ‘show that’ and transformation questions. There was only one ‘show that’ question this year, Question 2a. Sufficient working out, presented as a set of logical steps with a conclusion, needed to be shown. In Question 5a., the transformation question, the correct wording needed to be used, such as ‘reflect in the y-axis’.

In general, students appeared to have made good use of their technology, for example in finding the equations of tangent lines, finding bounded areas and using graph sliders to get approximate answers to complicated questions. Some students, however, need more practice at interpreting the output from their technology, especially when the technology uses numerical methods to find solutions. In Question 3cii., the tangent line passes through the origin, but some students gave y = 4.255x + 8.14E-10 as their final answer, not appearing to recognise that 8.14E-10 should be zero.

Most students made a good attempt at the probability questions. Some students, however, still misinterpreted the wording. Errors occurred in Questions 4a., b., c. and d.

Students are reminded to read questions carefully before responding and then to reread questions after they have answered them to ensure that they have given the required response. Question 1a. required the answers to be in coordinate form. Question 3ci. required an equation. In Question 3cii. many students only found the value of a and did not continue to find the equation of the tangent.

21 Replies to “VCAA’s Mathematical Flea Circus, Part Two”

  1. Some random observations (there are plenty more that could be made):

    “This is the first year of the new study design and most students were able to respond effectively to the questions involving the introduced concepts, such as Newton’s method in Questions 3f. and 3g. ….”

    No, Newton’s Method is not an “introduced concept”. It was in the previous Study Design (attached for those who are interested).

    “A number of questions could be answered using trial and error in this year’s paper, especially in relation to probability, Questions 4f. and 4g. ”

    True, but this misrepresents the reality of the technique and makes it sound like blind guess-work.

    “but some students gave y = 4.255x + 8.14E-10 as their final answer, not appearing to recognise that 8.14E-10 should be zero.”

    We understand the intent of the statement, but it’s poorly worded. In particular, it does not explain why.

    And sorry Marty (your typo, not their’s) …

    “They appeared to be confused by the limit notation \color{OliveGreen}\boldsymbol{\lim\limits_{x\to\infty}g(x)}.

    The limit is \displaystyle {x \to -\infty}. But in fairness, it’s very hard to read the minus sign in their comment.

    2016-2022 Mathematics SD

    1. Thanks, John. The limit mistake was my error (in converting the Word crap), not VCAA’s. (VCAA’s error was to not tell anybody that such limits are fair game.) Corrected now.

      But the point is not to nitpick the exam report. The point is that the exam report itself is nothing but nitpicking, and mostly technological nitpicking.

  2. “Students need to ensure that they show adequate working where a question is worth more than one mark, as communication is important in mathematics.”

    Communication is important everywhere. So is clarity, transparency, accuracy, honesty, integrity, …

    Pots and Kettles.

      1. I know I’m a sucker for punishment who is too lazy to move to NSW, but why does everyone else put up with this from VCAA?

        1. Assuming your question is not rhetorical:

          Fear. Apathy. Lack of knowledge, experience, confidence or time. Sense of futility. Misguided reverence.

          There are any number of reasons. The better question might be why do some people not put up with this.

        2. There’s no choice I’m afraid RF. And no one really politically important noticed until Marty and mates did their thing.

          1. I’m the noisy one, but it wasn’t me. It was Kermond willing to go kamikaze and Burkard having the stature and the standing with his colleagues that resulted in VCAA being forced to take notice.

            Nonetheless, whether or not there is any likelihood of complaining making any difference, I can only think of one good reason for the dearth of loud complaint: the majority of mathematics teachers are too ignorant and/or too stupid to realise how bad things are.

            I cannot understand how any teacher who is aware of the awfulness can shut up about it. I started this blog not out of hope of changing anything but simply out of disgust.

        3. If we did all move to NSW, I suppose it could be called a Mathematical Flee Circus.

          (And I encourage any recent graduate teacher to flee the circus if they can. Although I suppose the VCAA should be given a chance to show it can make meaningful and permanent structural and cultural changes for the better. But for me, I think this takes more than just one or two good people inside the VCAA but we’ll see).

          1. The point of this post is not really to nitpick VCAA’s administration of the maths exams, but rather what the MM2 exam report indicates of the utter poverty of Methods. Of course that poverty is also due to VCAA, but it is a separate issue and a much more difficult issue to address.

            Still, nonsense also needs to be called out. I’ve honestly been trying to ease up on VCAA, while they attempt to get their act in order. But the utter bullshit in the exam reports, particularly on MM1 Q9 and on MM2 Q3, has to be flagged. Whoever wrote this stuff simply does not get it, and perhaps cannot get it.

              1. Hope also springs eternal, RF. I am quietly optimistic that the person(s) who wrote those Reports will not be writing future reports (or VCAA exams), and that future reports will be proof-read by real mathematicians.

                I consider both these reports and the 2024 NHT exams the vestigials of a broken process, and that future exams and reports will be written under a much improved process.

                  1. Well, we have an acting CEO, who has been pretty good. The question is, will Gniel return, and if not then does the acting CEO become permanent?

                    1. She had an interview that I thought was good, seemed honestly accepting of the Bennett report. There are also some non-public signs, which I won’t go into.

                    2. Given Gniel’s tear-jerking opening statement here:

                      Estimating Stephen Gniel


                      and the acute shortage of teachers, particularly Primary School teachers, it’s very reasonable that he would return to his roots as a Primary School PE teacher, allowing a competent CEO to continue leading the VCAA.

                    3. But what if his tear jerking statement was insincere? Maybe Mr Gniel was only acting to try and get a sympathetic hearing and he actually thinks he’s far too good to return to primary school teaching.

                    4. Bravo! I love a good spoonerism! Particularly when it’s deliciously appropriate.

Leave a Reply

Your email address will not be published. Required fields are marked *

The maximum upload file size: 128 MB. You can upload: image, audio, video, document, spreadsheet, interactive, text, archive, code, other. Links to YouTube, Facebook, Twitter and other services inserted in the comment text will be automatically embedded. Drop file here