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.

VCAA’s Mathematical Flea Circus, Part One

To people not involved in Mathematical Methods it is difficult to convey the awfulness of the subject. Even regular readers of this blog, who will be somewhat aware of our million or so posts, cannot properly appreciate Methods’ unrelenting shallowness and pedantry and clunkiness and CASiness. The subject, to the extent there is one, is infested with fleas.

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My Previous Post on Julie Inman Grant

A (friendly)* lawyer advised me that I should delete my previous post on Censorship Commissar, Julie Inman Grant. I question the concerns, but he is a lawyer and I am not, so I have deleted the post. I believe it is safe to say I think Inman Grant is extraordinarily dangerous, and I am appalled by her heavy-handed and self-righteous censorship. My previous posts on Inman Grant are here, here and here. Continue reading “My Previous Post on Julie Inman Grant”

Can’t Do My Homework Anymore

It’s not a clever title but it leads into a great Fleetwood Mac song, guaranteeing one worthwhile feature of the post:

On with the post, which concerns a study conducted by academics at the University of South Australia and Nova Scotia’s St. Francis Xavier University, reported in their 2023 paper, Mathematics homework and the potential compounding of educational disadvantage. The study was announced a month ago in a UniSA media release, Numbers do not add up for maths homework, and was accompanied by the subsequent Educator report, Maths homework causing more harm than good – study. This all sounded like nonsense, so I took a quick look at the paper. I gagged, considered the work required to even skim the nonsense and decided to ignore it. Then frequent commenter Dr. Mike lobbed a Science Alert report at us, Math Homework Can End Up Doing More Harm Than Good, Study Shows. A third temptingly silly headline made me ponder further but I still decided to ignore it. Then then on the week-end Greg Ashman wrote a little about the study in his weekly curios. At which point I decided “to Hell with it”, and here we are. Continue reading “Can’t Do My Homework Anymore”

WitCH 138: Second Rate

Not counting the Witchfests on Nelson‘s Proof and Complex chapters, I don’t think we’ve had a textbook WitCH for quite a while. This one is hardly in the same league but it’s been on my to do list for a long time and it’s definitely a source of irritation. The topic came up in discussions with a colleague today, and I’m too busy and too tired to do the posts I should be doing, so this’ll do for now. It is an example from the differential equations chapter of Cambridge’s Specialist Mathematics 3 & 4, and it is related to this previous WitCH from the same text and chapter. As was the case with the previous WitCH, it is a representative, one of a type.

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TNDOT 5: The Party of the First Part

This multi-TNDOT is a little different, not as high a level or as old school as the previous ones, but the questions still seem pretty wild. We haven’t thought about the questions at any length, but conceivably they could also be used to challenge/tease younger students.

The TNDOT consists of two questions, each with two parts, from the 1911 Victorian Pass Algebra Matric exam. The exam paper instructed students to answer only one part from each question but we run a tough blog here and all readers are expected to answer all questions. As usual, commenters might refrain from posting answers too quickly, so that other readers have a chance to have a go. Have fun. Continue reading “TNDOT 5: The Party of the First Part”

AMT’s Trust Issue

Last year, I wrote about the Australian Maths Trust, on CEO Nathan Ford’s absurd censoring of an AIMO question, and on the aftermath. I later wrote a little about my maddening correspondence with Ford and Board Chair, Belinda Robinson. I then considered it done, at least for me.

A few weeks ago, however, I was contacted by a person who has worked with AMT. That person had some interesting things to say about the current state of AMT. The person has kindly permitted me to reproduce what they wrote, and it follows.

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