What’s 17 x 24? Fantastic thinking!

This week I have been asking my piano pupils (to their initial surprise – ‘this is a piano lesson!’) to work out the answer to 17 x 24, in their heads, talking me through their calculations as they go. Most go for something along the lines of:

10 x 24 = 240
5 x 24 = half of 10 x 24, which is 120
add the 240 to the 120, that’s 360
2 x 24 = 48
Finally add the 48 to the 360, and the answer is 408.

This system 2 thinking requires us to be able to hold pieces of information in our head whilst we manipulate other information, and then to recall them when needed. In fact, our heads are crammed full of facts and figures which have been stored there, and mental arithmetic is a good way of demonstrating how this works (or doesn’t!) Problems arise when we get to the end of the sum, and realise that we can’t recall one of the components; then we have to work it out again, and hope that in the meantime we don’t lose a hold of anything else which we are going to need to complete the task.

When we are learning a new piece of music, we are essentially doing just the same thing as detailed above. Each melodic shape, chord or rhythm is a small piece of information which can be stored in our head, with the specific aim of also being able to recall it. Unlike numbers, these elements have numerous other qualities – for instance sound and pitch, visual appearance (both on the page and on the instrument), feel – which can be an additional help in storing them reliably.

Having started each lesson this week with a maths problem, I have then given each pupil a new passage of music to play. Rather than just wading through it in blissful ignorance we have looked in detail at those melodic shapes, chords and rhythms, with a view not just to playing them, but also to remembering them. Having just come from a task in which they know that they are required to store information carefully, each student has been remarkably attentive in memorising each detail.


A brief example (for a pupil working at approximately Grade 7 standard)

  • In the left hand, after an initial middle C, the first minim chord is E flat minor (all black notes.) The physical sensation of playing and lifting the chords whilst holding the bass note is very memorable.
  • The bass note in the bar 2 is a fifth lower than middle C (basic theory, fifths apart are either both on lines or both in spaces).
  • In bar three the chord looks like a triad of D flat major, with the colourful sound of an added C. (The chord shape is white / black / white / black)
  • Bar 4 looks like a G major chord (the dominant, which will inevitably lead back to C) – but the D# makes it into an augmented triad – good opportunity to learn/revise this.
  • In the right hand, the melodic shapes in bars 1-2 have all sorts of elements which will aid memory. The first two pairs rise, the second two fall; the finger patterns are the same for each pair (1-2, 1-2, 4-3, 4-3); the first pair are white notes, the second pair black etc,
  • Choice of fingering helps not only in playing the notes, but to instil a strong feel for the shapes.
  • Bar 3 is the same chord shape as the LH (my pupil has already noticed!) and just leaps an octave. Again, a swift roll of the wrist makes it instantly memorable, and after one more glance the pupil is no longer looking at the music.
  • Bringing finger 2 over to land on the B in bar 4 is actually fun! And of course it’s a B, because that’s the leading note of C which is where the music is going to return to.

Most significantly perhaps, having worked with each hand separately (and it really didn’t take that long) I then took the music away and my pupil pieced together all 8 bars, hands together; not fluently, but entirely accurately, and with all the LH syncopated chords in the right place (which we had not even discussed). Teacher impressed + pupil empowered = success!

It’s gone off the top of the screen by now, but can you still remember the sum in the title, and the subtotals which you stored to get you to the final answer? It’s not a difficult sum, but it does require us to summon up what Daniel Kahneman calls ‘effortful mental activity.’ In short, it’s hard work but we know we can do it.

Our memories are amazing, and if they can store a few numbers – 240, 120, 360, 48 – then why can’t they store E flat minor, perfect fifth, LH ‘pivot’ feel, roll of the wrist, leading note? Fact: they can. This can be introduced at the most elementary level, and indeed it should be – even just covering the music and asking the pupil what the first note was will begin the process of encouraging them to use their brain to store and recall, which is developing an enquiring mind. Minus this recall, they will have to be resigned to working it all out again, every time, which is arguably even harder work, and not in the least bit empowering. In my experience children love to be challenged, and we should do some of that every lesson!

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