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Shoes and partition numbers: a developing mathematical mind wanders

Does this picture make you think of Srinvasa Ramanujan? I’m always fascinated by the pace and range of little conversations with my seven-year-old son that wander in and out of maths. Let me tell you how we got there during a five minute chat while leaving the house and walking to school this morning.

Two shoes, one slightly larger than the other

Mathematical Objects: Plate of biscuits with Alison Kiddle

Mathematical Objects

A conversation about mathematics inspired by a plate of biscuits. Presented by Katie Steckles and Peter Rowlett, with special guest Alison Kiddle. What do you notice? What do you wonder?

Alison’s Noticing and wondering page.

We also mentioned A Problem Squared Episode 014 = Final Cheese Drama and Quick-Fire-O-Rama.

You can see Peter’s kitchen floor in this tweet.

Plate of biscuits described in the episode in two configurations.
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Mathematical Objects: Hundred square with Susan Okereke

Mathematical Objects

A conversation about mathematics and education inspired by a hundred square. Presented by Katie Steckles and Peter Rowlett, with special guest Susan Okereke.

In the episode, we mentioned the original Prime Climb colouring sheet and Peter’s Prime Climb colouring sheet on GitHub as drawing-primes.

Grid of numbers 1 to 100
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Square wheels in an Italian maths exam

There have been various stories in the Italian press and discussion on a Physics teaching mailing list I’m accidentally on about a question in the maths exam for science high schools in Italy last week.

The paper appears to be online.

(Ed. – Here’s a copy of the first part of this four-part question, reproduced for the purposes of criticism and comment)

The question asks students to confirm that a given formula is the shape of the surface needed for a comfortable ride on a bike with square wheels. (Asking what the formula was with no hints would clearly have been harder.) It then asks what shape of polygon would work on another given surface.

What do people think? Would this be a surprising question at A-level in the UK or in the final year of high school in the US or elsewhere? Of course, I don’t know how similar this question might be to anything in the syllabus in licei scientifici.

The following links give a flavour of the reaction to the question:

6 hours, 1 question out of 2 in section 1, 5 out of 10 in section 2. My own initial reaction is that if I had to do this exam right now I’d do question 2 in section 1 but I’ve not actually attempted question 1 yet.

Education bits: new PBS maths series, National Numeracy game, etc.

I’m not normally interested in education stuff, but we’ve had a flurry of emails from various people telling us about their projects, and I’ve got nothing else to do today, so I thought I’d round them up.

Exam timing

When I have been involved with running exams (I wasn’t, really, this year), special care seems to be made to spread these out so that where possible students don’t get exams bunched together. Still, I’ve heard students complain “we only have one day off between the Monday and Wednesday exams, that isn’t enough time to revise for the second topic”. I have a lot of sympathy for this; assessing a module (or proportion thereof) by how you perform in a one-, two- or three-hour window is quite a problematic arrangement, and if you haven’t had sufficient time to get up to speed on the topic, even more so. But I have had in mind that, essentially, “when I were a lad, we had it much worse”. Clearing out some boxes to move house, I found exam timetables from five of the six semesters I spent as an undergraduate, so now I can confirm or refute my feeling on this, in the latest of my series of posts that are surely only of interest to me.

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