Implicit Suggestions

One of the unexpected and rewarding aspects of having started this blog is being contacted out of the blue by students. This included an extended correspondence with one particular VCE student, whom we have never met and of whom we know very little, other than that this year they undertook UMEP mathematics (Melbourne University extension). The student emailed again recently, about the final question on this year’s (calculator-free) Specialist Mathematics Exam 1 (not online). Though perhaps not (but also perhaps yes) a WitCH, the exam question (below), and the student’s comments (belower), seemed worth sharing.

Hi Marty,

Have a peek at Question 10 of Specialist 2019 Exam 1 when you get a chance. It was a 5 mark question, only roughly 2 of which actually assessed relevant Specialist knowledge – the rest was mechanical manipulation of ugly fractions and surds. Whilst I happened to get the right answer, I know of talented others who didn’t.

I saw a comment you made on the blog regarding timing sometime recently, and I couldn’t agree more. I made more stupid mistakes than I would’ve liked on the Specialist exam 2, being under pressure to race against the clock. It seems honestly pathetic to me that VCAA can only seem to differentiate students by time. (Especially when giving 2 1/2 hours for science subjects, with no reason why they can’t do the same for Maths.) It truly seems a pathetic way to assess or distinguish between proper mathematical talent and button-pushing speed writing.

I definitely appreciate the UMEP exams. We have 3 hrs and no CAS! That, coupled with the assignments that expect justification and insight, certainly makes me appreciate maths significantly more than from VCE. My only regret on that note was that I couldn’t do two UMEP subjects 🙂

 

See the Evil Mathologer and the Evil Marty, December 3

On Tuesday December 3, the Australian Mathematics Society will hold a free education afternoon at Monash University, Clayton, as part of their annual conference. The talk details are below, and full details (except for the lecture theatre, TBD) are here. You aren’t required to register, but you can do so here (and it is appreciated if you do).

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1:30 Joanna Sikora: Advancing Women in Australian Mathematics: context, challenges and achievements

This talk reviews recent research undertaken by social scientists on women in mathematics. First, adopting a life-course perspective it summarises findings on the persisting gap in vocational interest in mathematics among adolescent boys and girls, including its potential to widen over time. Systematic differences between boys and girls in the choice of basic and advanced mathematics for ATAR (Australian Tertiary Admissions Rank) are discussed. Next, the consequences of these choices for tertiary education specialisations and availability of suitably qualified male and female graduates are considered.

Following this introduction, the talk summarizes research on underrepresentation of women in mathematics departments in Australia and across the world. The focus is on structural and institutional process which, over the course of individual careers, can amount to significant disadvantage even in the absence of overt discrimination. Topics discussed include cultural stereotypes that link perceptions of brilliance and academic talent with masculinity, gender differences in professional capital, i.e. peer esteem, accorded to male and female mathematicians, the gender gap in rates of publications and impact, documented bias in student evaluations and factors that enable success in establishing international collaborations. The talk concludes by summarizing the literature on practical steps that we can take to improve gender equity.

2:20 Julia Collins and Katherine Seaton: Knitting and Folding Mathematics

Mathematical thinking is not confined to mathematicians, but one place you may not expect to find it is in the world of crafts. Even the most maths-anxious knitters will display an astonishing familiarity with concepts from geometry, topology, number theory and coding, while modern origami artists are turning to mathematical algorithms to create models previously thought to be unfoldable. This talk will highlight a number of surprising connections between maths and craft, and will be followed by a hands-on session facilitated by Maths Craft Australia where people can create some mathematical craft for themselves. (Knitting/crochet needles and origami paper will be provided, but participants are also encouraged to bring their own! Knitting in the audience is strictly encouraged.)

2:45 Afternoon Tea

3:10 Marty Ross: How I teach, why the Mathologer is evil, and other indiscrete thoughts

In this shamelessly narcissistic talk I will reveal the One True Secret to teaching mathematics. Along the way I will explain why you can and should ignore STEM, calculators, Mathematica, iPads, the evil Mathologer, constructivism, growth mindset, SOLO, Bloom, flipping classrooms, centering children, lesson plans, skeleton notes, professional standards and professional development and many other modern absurdities.

3:35 David Treeby: How to Instil Mathematical Culture in Secondary Education

Over the past few decades, mathematicians have ceded the educational space to two groups: mathematics educators and technology companies. This has had a dire effect on what mathematics is taught and how it is taught. The result is a commodified brand of distorted mathematics. This talk will focus on how some well-resourced schools have resisted these changes, and how broad and equitable change will require the support of working mathematicians and their professional bodies.

4:00 Burkard Polster: Mathologer: explaining tricky maths on YouTube

In this session I’ll talk about my experience running the YouTube channel Mathologer and I’ll give you a sneak peek of the video that I am currently working on.

WitCH 29: Bad Roots

This one is double-barrelled. A strange multiple choice question appeared in the 2019 NHT Mathematical Methods Exam 2 (CAS). We had thought to let it pass, but a similar question appeared in last’s weeks Methods exam (no link yet, but the Study Design is here). So, here we go.

First, the NHT question:

The examination report indicates the correct answer, C, and provides a suggested solution:

\Large\color{blue} \boldsymbol{ g(x)=f^{-1}(x)=\frac{x^{\frac15}-b}{a},\ g'(x) = \frac{x^{-\frac45}}{5a},\ g'(1) = \frac1{5a}}

And, here’s last week’s question (with no examination report yet available):

WitCH 27: Uncomposed

Ah, so much crap …

Tons of nonsense to post on, and the Evil Mathologer is breathing down our neck. We’ll have (at least) three posts on last week’s Mathematical Methods exams. This one is by no means the worst to come, but it fits in with our previous WitCH, so let’s quickly get it going. It is from Exam 1. (No link yet, but the Study Design is here.)