12 of 12, March 2020

This is a 12 of 12 in two parts: the first from my class for future maths teachers this morning, and the second from tonight’s TSO Chorus rehearsal.

So, to my class. One focus for this semester’s unit is to look at different types of activity that get school maths students reasoning about conceptual ideas, instead of just doing routine procedural tasks that don’t get at deep understanding. I set the scene by providing my future teachers with four sets of numbers, and asked them which data set was different from the others (in fact it was possible to find reasons for each one to be judged different from the other three (for example, three of the data sets had the same mean/average, while the fourth didn’t; and then one of the other sets had its mode different from the remaining three, and so on*)).

I then took the teachers to our maths equipment storeroom, and allowed them to grab whatever they liked, and challenged them to come up with their own “one of these things is not like the others” collections. Here’s what they came up with (in many of the cases we could find reasons to make each one of the items the odd one out, but not always (or only by saying “it’s the odd one out because it’s the only one we can’t find a reason for it being the odd one out!” … but perhaps you can come up with reasons)).

1. Set of cubes (small, no hole, exception-because-it-isn’t-an-exception, different colour (assuming the first three are the same colour).

2. Mostly rectangular-shaped objects (not rectangular, no plastic involved, exception-because-it-isn’t-an-exception, multicoloured)

3. Sets of square tiles (not even, not a square number, exception-because-it-isn’t-an-exception, not a power of 2). (We tried hard to find a reason to exclude 4, but couldn’t come up with something that wasn’t too contrived).

4. Triangles (different colour, different size, exception-because-it-isn’t-an-exception, decomposed into smaller shapes)

5. Representations of 10 (different colour/shows 10 as a single unit; 10 as both single unit but with individual ones visible, 10 as 10 individual ones, 10 written symbolically)

6. Some prisms (triangular rather than quadrilateral, exception-because-it-isn’t-an-exception, decomposable prism, red not blue)

7. More prisms (exception-because-it-isn’t-an-exception, quadrilateral not triangular, not an RGB colour (!), large in comparison to others)

8. Random number generators where I had to do drawings because I didn’t have some of the objects I wanted (spinner not dice, has dot markings instead of numerals, has 12 equally likely outcomes instead of 6 (the bottom left picture was meant to be a standard dodecahedral die), there are two ways that each of the 6 outcomes can occur)

So, to part two: tonight’s TSO Chorus rehearsal. Mostly we rehearse on Tuesday nights but in performance week we have additional rehearsals, and tonight it was time to get together with the orchestra for a run through of Brahms’ Ein Deutsches Requiem (A German Requiem), which we are performing on Saturday night.** I was nurturing my voice this week: I limited my encouraging cheers of “Go La Per-oooouse” at regatta to two per race (and admit that even that probably overdid things!) and have been dosing up on butter menthols.

We gathered together for a warm up before going on stage.

Here is a couple of pages of the score. We’re getting better at singing in German, but sometimes it is really hard work getting the consonants out at the required force, especially when the tenor range already demands so much energy from me on the low notes.

Here’s the stage starting to fill up with musicians and choristers.

Finally, here is Maestro Eivind Aadland in action (the chorus wasn’t singing at this point, so I could sneak a photo).

* Well, that was what was supposed to happen, but I’d had to construct the sets in a screaming hurry, and didn’t get them quite as well designed as I’d intended. Fortunately my students got the idea.

** In fact the public performance was cancelled, due to coronavirus/COVID-19 precautions, but we still performed on Saturday night to an empty hall and a set of cameras and microphones, so that it can be broadcast at a later date. It was rather weird having no audience, and we missed some of the adrenaline that is generated by having spectators, but we managed to focus and generate a bit of atmosphere for ourselves.

[This is  “12 of 12” post number 127; are we bored yet?!]