What To Do When You Make A Mistake

Music isn't about being right. It's about being human.


Mistakes are a big fixation in the life of a piano teacher. Students come to piano lessons and play their pieces and sooner or later they play wrong notes, wrong rhythms, wrong articulations, wrong dynamic shapes, and so forth.

Once upon a not-so-long-time ago (let’s say 50 years ago) a particular breed of teacher would respond to a mistake with a physical action – a smack across the knuckles with a ruler, say – with the idea that this would focus the student’s mind on not making mistakes. (It’s more likely that this focussed the student’s mind on not being tortured, but, well, we’ll talk about that another time.)

Even though piano teachers don’t do that now, this idea of not making mistakes still looms large in the learning-to-play-the-piano scene. Students are taught to avoid them. When they do make a mistake the teacher puts a big circle around the note in the music, and a list of these mistakes is compiled for the student to go home and fix.

I’ve written before about the importance of not having lessons (or life) structured around correcting mistakes. But here I’d like to explore the idea from the point of view of the mistake-maker: what should we do when we make a mistake? Here’s where I always start:

1. Think about what makes this mistake a mistake. Did it sound bad? Did it fail to communicate what you wanted to express? Did it feel bad? Did your body get muddled? Did it prevent flow in your performance? (Or was it your worry about the mistake that prevented flow?!)

If you don’t know exactly what it is that you did that was The Mistake then you’ll struggle to not do it again! Just as true in life as it is as a musician.

Looking at it another way…

Most of the mistakes we worry about in piano lessons are mistakes of accuracy rather than mistakes of truth. In some ways it doesn’t matter which kind of mistake it is – we still need to locate the source of the error in order to prevent the mistake occurring again. But while an audience will ignore/forgive/fail to notice mistakes of accuracy, mistakes of truth will destroy a performance.

2. Explore the mistake. Can you repeat the mistake? (If you can repeat the mistake on purpose you are almost certainly not going to make that mistake again.) How does the mistake change the meaning of the music? (If you understand what meaning the mistake communicates you can choose to create a different meaning.) If you make this mistake at this point in the music, what else do you need to adjust to make the music make sense?

This kind of exploration can go on for a long time, and if exploration of this kind is new to you it can feel as if you are ‘mucking around’ or ‘not getting on with it’. Stick with this as long as you can – these explorations build a platform of deep understanding for your future performances. (Ignore that little voice that tells you you would be better off practicing scales. You would not.)

3. Ask yourself if your mistake really was a mistake. Maybe the ‘wrong’ thing you did was what you totally meant to do. When beginner students consistently play a tune with the wrong melodic contour I ask them to sing the tune – more than half the time they are playing the melodic contour to perfectly match the shape in their imagination, and they’re not making a mistake at all! They’re just not playing the same piece I’m looking at in the score. This is a question that is a “locating the source of the error” question, but it can also lead to some further introspection…

If you are committed to your changes to the original musical text you need to be aware of the implications in the cultural context of that work – are you performing in a context where variation, improvisation and recomposition are valued, or will this be seen as sloppiness? Are you committed to your ‘mistake’ because you aren’t all that interested in other people’s point of view?! Are you capable of giving a range of different performances of the same work? A commitment to a mistake can sometimes indicate a high level of rigidity in the thinking of the performer, and this will be more or less troubling/interesting/challenging-to-work-with depending on the age and developmental stage of the performer!

Often our ‘mistakes’ are a commitment to a muddle-headed conception of the work. This is when and where you need to trust your teachers and mentors – they’ve had loads more experience than you have.

So, now, what NOT to do….

1. Don’t stab and stab at different keys on the piano until you stab the right one. By the time you get the “right” note the whole piece will be wrong, you’ll have forgotten where you were and what your point was.

2. Don’t go back and start at the beginning. You can already play that part. Don’t waste your time. By the time you get to where the mistake was you’ll have forgotten what happened and you’ll make the same mistake again. Going back to the start means you are in a cul-de-sac of doom.

3. Don’t write in the names of all the notes. This doesn’t help. It distracts. And it makes you feel righteous when you’ve accomplished absolutely nothing at all. And you still don’t know why you made the mistake in the first place.

4. Don’t think you’ve sorted it out as soon as you’ve played the section correctly once. Tomorrow you’ll come back and make the same mistake, because all your practice has been practicing the mistake, and only 1.3 seconds of your practice was when you played it right.

Practice is fundamentally NOT about repetition and discipline – it’s fundamentally about listening and reflecting and noticing and exploring. Take your thinking away from an accuracy = perfection model. Music isn’t about being right, it’s about being human.

And remember, if you’re not making mistakes you’re not learning anything. Every single time you make a mistake you have the chance to become someone even more fabulous than you’ve ever been before – so celebrate your mistakes; they remind you you’re alive.

 

 

 

These ARE The Good Old Days

This last weekend I attended the Kennedy Awards, a New South Wales-based peer-awarded recognition of excellence in journalism, in the role of handbag to my journalist husband (who also happened to be nominated for, and go on to win, an award). Many stories were shared over the course of the night – events that had transpired behind the headlines, hair-raising exploits of reporters whose recklessness was matched by their journalistic brilliance. At some point in the evening, my husband noted that, for all the journalists in the room, these were ‘the good old days’ that would be recounted 20 years, 30 years, 50 years hence. From the premier undone by a bottle of wine through to disgraced former policemen being arrested for murder; from pervasively corrupt infrastructure deals involving Sydney’s water supply and regional mining leases through to politicians being handed paper bags of $10,000 cash just prior to elections; these are the good old days these journalists will look back on.

This last weekend also saw the passing away of iconic Australian composer Peter Sculthorpe, a man whose music and mentorship has defined much of what it means to express oneself as an Australian composer. Anyone whose lives were touched by his has found themselves complicit in communal remembering of various good old days and decades with Peter: former students, editors, performers, pop musicians who enjoyed drinking/collaborating with him, friends. Peter Sculthorpe’s death has suddenly rendered a whole suite of musical and human experience as part of the fondly remembered past.

The present becomes history so rapidly.

In my first year at university I was studying composition and the general music subjects one studies in one’s first year. But on the side I was taking a course in 20th century literature. This was 1984, and I was just 16 years old. The first term’s lectures were devoted to poetry, and the lecturer started with Gerard Manley Hopkins and took us the way through to boot-legged recordings of the then still (comparatively) nascent hip hop and rap that had been developing in New York. “This is your time,” the lecturer told us, “this is the time of your contemporaries. The art that will be talked about in 50 years time is the art being made around you right now. One day you will realise that you were here. Pay attention.”

I couldn’t believe how exciting it felt. I felt so privileged to be experiencing the living of history when I was still so young! Things that had already happened, that were already over, notated, documented, recorded – they weren’t the limit of what counted. Yesterday – this morning – this afternoon – mattered, too. It was all important. Suddenly, as I walked down the hill to catch the bus, the very atmosphere was heavy with all the creating that was possible, all the contemporaneousness that was.

In shaping learning experiences for my piano students I am always aware that as much as the past informs the present, so the present will soon be that past that informs future presents… How am I teaching my students about the past they are a part of? How am I helping them connect with contemporary experience as future memory? As future history?

I was gloriously fortunate in my teachers, both at university and at high school – teachers who understood that they were building the past even as they were building the future. I don’t just honour them by maintaining that tradition in my own teaching – I honour my students, present and yet to come, who are only just beginning to realise that these are their good old days.

Being Musical… Being a Music Teacher…

March was a month of conferences for me, the most recent of which was a conference where I had been asked to speak about (amongst some number of other things) the benefits to music education of utilising the opportunities social media affords.

This did not go well.

I began by talking about the ways in which high school students use music rather expertly without the assistance of teachers, for:

  • identity formation;
  • communication (especially in regard to emotion);
  • making sense of, or organising emotional experience;
  • organising executive function;

and I went on to assert that these four uses of music are more fundamental to human musical experience than are the ‘performance’ / ‘composition’ / ‘analysis’ modes of musical experience dictated by the curriculum; that it is a kind of concert hall-think that permits us to structure music education in the 21st century primarily in regard to such a narrow set of musical experiences (performing, composing, analysing) and to blithely ignore the rest.

In retrospect I think this, long before a mention of facebook (which was poorly received, needless to say), was where I lost most of my audience.

Once upon a time school music education was assessed by theory exams, harmony exercises and essays about music history; it was a triumph of some considerable magnitude when music educators succeeded in prioritising the performance of music in school music marking systems, a triumph that many still feel great pride in having helped to achieve.

So it was completely naive for me to waltz in and start talking about the function of music in the formation of identity or in the organisation of executive function and to fail to attempt to connect the dots from what is still perceived in classroom music education as a recent breakthrough of transformational proportions, let alone to acknowledge the history that was/is within the professional lifetimes of half the members of my audience.

I very much suspect that this first section of my presentation was apprehended as a babbling prologue to the real business of my presentation (talking about social media). This was a terrible pity, because the value social media might have for you and your students will change, vastly, depending on what you think your job as a music educator might be.

Surely we all believe that we are training musicians? And if we all think we are training musicians then surely the main game is teaching students to play musical instruments, no?

Well, no.

Before the instrument comes musical thinking. And musical thinking is exactly what is going on when kids choose one style of music to listen to, and to share with their friends, rather than another style; any act of selecting music to accompany life is an act of musical thinking. In fact, in the 21st century musical thinking is what we use to make it through the day: from choosing a ringtone to understanding the plot cues a soundtrack signals in a film or a piece of TV pseudo-journalism or advertising.

Everyone is musical these days in ways we could not have imagined in the 80s when teachers were fighting for instrumental performance to be included in the curriculum.

And if you, as a music educator, don’t acknowledge how musical the world has become, how underscored our lived experience is, how imbued with musical fragment, rhythmic motif, decontextualised timbres and insistent tone colours our days now are, you have no idea what you are doing.

You know what you were doing, back in the day. Back when intervals were learned with reference to song openings and modes were taught via medieval folk tunes. Back when a backbeat was still quietly considered to lead to promiscuity and chromaticism was widely believed to be to blame for political upheaval.

But in the age of YouTube, GarageBand, SoundCloud, Spotify, facebook shares and twitter retweets, you haven’t got a clue. Not if you think that being musical can be measured by how well someone plays an orchestral instrument. Or how well they write an 8-bar tune.

So…. if everyone is already engaging in musical thinking, what is the music teacher for?, I imagine you’re asking (possibly with a disapproving facial gesture and a bit of an eyeroll).

The music teacher is there to structure experiences that lead to more nuanced musical thinking, more informed musical thinking, more conscious musical thinking, more creative musical thinking. (Feel free to keep adding to this list – it is by no means intended to be comprehensive!). The music teacher is there to help students develop critical thinking skills in relation to their musical experiences; to build a vocabulary for the many experiences that students have no words to describe; to build a fluency in musical reasoning and an understanding of the musical narratives that have built the range of musical experiences the 21st century has to offer.

But we can’t even begin to be that kind of music teacher if we think that music education is about delivering performances, compositions and analyses. These are just not appropriate means of assessing what it is to have a good musical education anymore.

And I wish I’d spent the whole session exploring that. The first mention of facebook brought outbursts and outrage (it’s the end of PRIVACY, don’t you know?!), and there’s no purpose to exploring the opportunities social media brings as long as educators believe that their job is about cultivating and assessing 19th century ways of being musical (performance, composition, analysis).

To be continued…

A small rant about diagrammatic illiteracy in the Arts Curriculum draft document

This has been my longest ever break in blogging since I began nearly three years ago. Family matters have been very pressing, and I ended up shutting down all my projects until things were on a more even keel.

During this time, however, I’ve either tried or wanted to blog about any number of things: the Steve Reich retrospective held at the Sydney Opera House at the end of April, the value of learning the melodic minor scale, background information on my piece Vendetta which is currently on the Trinity Guildhall Grade 5 piano syllabus, a post on how I’ve let a student down by not teaching her to read chord charts before now, a review of the Nico Muhly/Sufjan Stevens/Bryce Dressner collaboration “Planetarium” as performed here in Sydney at the end of May, a Top 5 Things Parents Need to Know Once Their Child Starts Taking Piano Lessons list, as well as a discussion of the value and challenge of playing on the black keys in the very first lessons, a discussion of the new-look and hopelessly fuddy-duddy Limelight magazine, and looking at piano lessons through the lens of gifted education.

But I have a new topic to add to the blog-post-wish-list: the latest Arts Curriculum draft document from ACARA. About 18 months ago I blogged (relentlessly) about the buried misconceptions about music education in the previous draft document, and I’ve taken a quick look at this new draft and felt my spirits sink as I see a whole new batch of blind spots, insufficiencies and outmoded assumptions.

For now, however, let me simply draw your attention to Figure 1 on page 5. This is a diagram of such woeful conception that it calls into question the general literacy of the authors of the draft. I know it’s a tad old-fashioned of me, but I do expect that educators understand basic concepts as what a Venn diagram is for and when not to use one. The most generous interpretation I can put on the inclusion of this poorly conceived figure is that the writers of the curriculum have just discovered the possibilities of SmartArt in their Word program. Which begs many questions about their capacity to author the Media Arts section of the curriculum document.

But, you know, if it’s good enough for a US presidential candidate, right?

Is the Study of Piano Declining in the United States of America?

This topic in the Tuesday afternoon line-up of MTNA Conference presentations seemed almost arcane on the page of the conference booklet, especially by way of comparison to other topics with immediate practical application in the 30 minute piano lesson. And the question seemed one of those asked-and-answered types: is the study of piano in decline? Hell, yeah. Who doesn’t know that, right?

But I’m an arcane-topic kind of chick, so I bounded with enthusiasm into this panel presentation-discussion. It was already impressive just checking out who was in the panel: Peter Jutras, who is the editor of the wonderful Clavier Companion; E.L. Lancaster, who is both Vice President and Keyboard-Editor-in-Chief of Alfred Publishing; Brian Chung, Vice President of the Kawai Corporation; Gary Ingle, CEO of MTNA; Mike Bates, Senior Member of the Institutional Solutions Group, Keyboard Division, Yamaha Corporation of America; and Sharon Girard, NCTM, a private piano teacher since 1976 in Connecticut.

To begin: college-level study (and beyond). The raw number of students taking piano as their major for the undergraduate degrees in the United States has increased significantly over the past twenty years (roughly a 25% increase), numbers for masters have increased slightly (currently around the 1000 mark)  and numbers of students enrolled in doctoral programs with a piano major have increased astronomically (currently around 1000, up from only about 400 less than ten years ago). But these raw figures don’t tell the complete story. More and more piano majors (all levels) are international students (so these figures don’t reflect piano learning activity in the US in any case); there are more options for students to choose from when selecting their music major (so students who might previously have taken piano are now specialising in some other aspect of music); there are more students studying music (so the proportion of students piano majors  in comparison to the entire student population cannot be inferred from the raw data).

What are piano teachers in the suburbs, cities and small towns noticing? An increase in adult students and in very young beginners (4 and 5 year olds) and a sharp decline in beginners aged 9 and 10. The GFC seems to have had a pronounced (negative) impact on enrollments, but further to this there seems to be a decline in the value parents in 2012 ascribe to piano lessons in the broad education of their children. From my Australian perspective I was also fascinated to learn that school teachers are drivers of enrollments in piano lessons! In Australia school teachers have absolutely no impact on the propensity of a child to begin lessons – and if anything, their neutral impact skews slightly negative. But in the US many children learn band instruments through the school, and so children can still have an instrumental education without taking private piano lessons. Apparently it’s the band teachers who promote piano to some large degree, and when those teachers don’t encourage piano lesson enrollment a sharp decline can be seen.

Next: sales of educational and classical print music. These sales have declined since 2006, but only slightly (4%), and it’s hard to see that as anything other than a ripple-on effect of the GFC. The breakdown of print music sales in the US works out at something like 19% Classical Music, 19% Christian Music and 13% piano methods, with the bulk of the remainder being taken up by pop titles. This proportion appears to have held steady. In any case, print music sales are a poor indicator of piano study, because younger siblings often use the print music older siblings used before them, and it’s entirely possible that in a climate of financial restraint parents are more likely to seek these kinds of economies.

We move on to sales of instruments: grand pianos, uprights, digital pianos and keyboards. There has been a massive decline in sales of grand pianos since 2005 – down from 35,000 then to around 12,000 now. Seeing as most new grand pianos are purchased by institutions and very rich people it’s possible to infer that the rich people are being careful and the institutions have had their budgets slashed – neither of which reflects on the current number of piano students in the US. It’s when we get to the other categories that we see some interesting trends. Upright acoustic piano sales are also consistently down, as are sales of digital pianos. The category that is doing just fine (although not increasing, particularly) is the under $200 keyboard. These instruments are purchased by parents who want to invest the bare minimum to afford their children access to music education, with the intention to trade up if their child demonstrates prolonged interest and/or aptitude. In the US roughly 1,000,000 units of this kind of keyboard has been sold every year for the past decade. Do the instruments live in the back of cupboards? Who knows! This statistic is as enigmatic as the numbers on grand piano sales in terms of establishing a trend of piano study decline in the United States (although it potentially reflects an opportunity).

Meantime, the percentage of MTNA members who teach the piano has been increasing. Again, this fact doesn’t really tell us anything: are memberships of MTNA in decline or are they increasing? Has there been a recent trend of the teachers of particular instrument families to not sign up to the Music Teachers Associations? Has the MTNA been catering very well for piano teachers of late, and dropping the ball as regards the other instruments?

One comment was made by a panelist that I found very interesting: “we live in a culture of deflection and distraction”, a comment intended to speak to a broad trend away from educational practice that engaged students in critical thinking and practical skill acquisition. I tend to take the view that gaming cultures are educationally preferable (in so very many ways) to traditional classroom practices, and I further take the view that learning the piano is much more like a game than it is like a traditional school classroom learning experience. But I suspect this comment reflects some things that are particularly true not of Western culture but of American culture.

Comments were opened to the audience, and one emerging theme (reflecting comments also made by panellists) was the tension between sport and piano in the broad culture of childhood in the US – this idea that you either play soccer or you learn the piano, the idea that promising students find themselves pressured into team sport participation that then compromises their musical education, and so forth. Implicit in this theme was the notion that parents these days just don’t get what piano lessons are for (as touched on above), that soccer and team sports are widely seen to provide benefits for children while piano lessons do not.

Another theme (again, reflecting comments already made by panelists) was that piano teachers are not very marketing savvy, and that they are not very technology savvy. Sometimes these two lacks merge into one big piano teacher fail, with piano teachers not taking advantage of the internet to reinforce community awareness of their services and not taking advantage of social media to communicate with current and prospective students. There was an implicit sense that piano teachers do not look at their teaching as being a business (much in this theme was not unpacked, but, I think, broadly understood by the audience).

A third theme was that piano teachers are often quite rigid in their idea about what they do; instead of looking at their available skill set and thinking about a range of services they can provide to the community, teachers imagine that their real job is to provide the same kind of piano lessons as those they received, last century. Some comments from the floor detailed the wide ranging activities some exception-to-the-rule teachers engage in in order to have a solid business model.

In short, I felt as if this session were the first two pages of an introduction to a 350 page book on the topic; we just began to frame the conversation when it came to an end. And as fascinating as what was said was what was not. What about socio-economics? Are there some parts of the United States where piano study is thriving? Some cities that are doing significantly better than others? [I can't imagine piano lessons are as common as they used to be in Detroit, for example.] Are language issues an impediment to piano study? [The paucity of Spanish-language piano methods, for instance, as compared to Spanish-speaking population in the US surely indicates a swathe of the population disengaged from piano study.] How about the decline of the use of the acoustic piano in churches and other worship settings? [Once upon a time many not-wealthy churches would have a good, mid-range grand piano in addition to an organ.]

The panel mentioned the rise of online, do-it-yourself-by-watching-videos-and-buying-the-book piano study, and this touches on another aspect of this topic. It could be that piano/keyboard study by volume has seen no significant decline, but there’s every chance that the national pianistic skill set is in decline.

It’s a fascinating time in the United States, a time of substantial cultural reframing and contention. The study of the piano could well be a case study for this rethinking of what it means to be an American with an education (even if you never did make it to college)….

Teaching v Learning in the Piano Lesson [Part I]

One of the biggest privileges of being a piano teacher is the opportunity to become a consistent part of a student’s life. Each school week for maybe even a decade or longer the piano teacher and the piano student have time one-on-one (more or less) to explore musical puzzles, pianistic tricks, and challenges both physical and imaginative.

This is not a relationship in the knowledge-transmission model (where the teacher pours knowledge into student until student is all full up) but rather a relationship that is built on the teacher tweaking the learning experience to match the interests and accomplishments of the student. This teacher-student relationship is usually nurturing and supportive, in the sense of helping the student achieve their musical/pianistic goals and ambitions and substantially beyond. Piano teachers get to notice things about their students that can be missed in the hurly-burly of classroom activity, and piano teachers participate in building a sense of achievement in students who might otherwise never feel as if they shine….

So piano teachers are in a tremendous position to work with students who fall outside the bell curve; teaching can be modified to fit the precise needs of the student and without a class of other students to manage the teacher can organise the learning process to be perfectly timed for the individual student.

That’s the theory.

In real life, as always, it’s more complicated. And the number one thing that gets in the way of this perfectly customised learning experience is the idea (held by both parents and teachers) that the job of the teacher is to teach.

The job of the teacher is in fact not to teach but to help the student learn. And there is a massive difference between the role of ‘teaching’ and the role of ‘facilitating learning’.

When you think your job is to teach you begin with a list of all the things you want to ‘teach’ to your student, a catalogue of the things they should know or be able to do by the time you are done with them. Piano teachers who work in exam cultures (half the planet, at least) even have this big list of all the things you want to teach broken down into examinable chunks (“Last year you learned D Major? OK, this year we’ll work on E flat…”, etc.). Things that aren’t on that list are deemed either of secondary or of no importance (particularly once students start taking annual exams).

But when you begin with the idea of facilitating learning you begin with a desire to discover what makes your student tick, what intrigues them, what doesn’t, what they yearn to master, what they hanker to understand. You also, over time, begin to understand how the student sees themselves in relation to their family, their school and classmates, in relation to their future (and their past), and in relation to their culture (and this might be simple through to extremely complicated). These understandings then feed into your understanding of what drives their learning, and you can better facilitate learning.

You still have a checklist in relation to skills, vocabulary, literacy, experience, recognition, and so forth, but this list is always at the service of maximising learning, rather than the learning experience of the student serving you as you, the teacher, work your way through that checklist.

Let’s make up some examples: a very intelligent but not very socially mature 8 year old who has been learning for about a year suddenly decides to figure out how to play every single major and harmonic minor scale – all 24 of them. If you are tied to your piano teacher checklists you’ll be thinking to yourself ‘You don’t need all these scales for years yet!! Why don’t we just keep learning the pieces in your method book and we’ll come back to these scales when you’re ready?!’.

You can see the problem here plain as day: the student is ready to learn how to play all these scales – in fact, they’ve basically mastered them all just for fun while you weren’t watching! It’s not that they are not ready to learn – it’s that you are not ready to teach. Yep, this is the moment where you can choose to make the piano lesson all about you, or all about your student. Your call.

Another example: you have a 12-year-old student with a sunny disposition, learning for 4 years already, they’ve done a Preliminary exam at the end of the previous year, just started high school (Australia), they have no particular academic gifts, but they love playing the piano, and they’ve just returned after the school holidays with nine piano pieces they’ve composed since the last lesson 8 weeks ago. They begin to show you their (not-so-well notated) compositions as the minutes of the lesson begin to click over. You know how hard it was to get through that Preliminary exam at the end of last year, and you don’t want to waste a term working on ‘composing’ (which truth be told you don’t feel that comfortable dealing with) because you’d like them to do well in their Grade One exam at the end of the school year.

This is the moment where you can make the lesson all about your checklist (getting the student ready for Grade One) or you can make the lesson all about the student’s musical experiences (and learning) over the holidays. Is it going to be about them? Or about you?

Of course, there’s always that 5-15% of students who appear to have no interest in learning whatsoever, the kind who ask “Do we have to do this?”. The challenge here for teachers is how to tempt students into having a more robust appetite for learning without falling into the trap of creating new kinds of checklists (what kinds of learning the student should want to engage in). I really do regard these children (adults just don’t have this problem, in my experience) as being ‘learning anorexic’ – for some reason they feel it’s a Good Thing to restrict their learning experiences and opportunities, and it’s really, really hard to convince them otherwise.

I’ve been becoming more and more hardline on this issue the more experienced I’ve become in my teaching: once upon a time I really would have insisted on students struggling through a piece for some number of weeks rather than ‘give in’ to the student and just move on to a new piece of repertoire; once upon a time I would have politely listened to a student enthuse about this great new piece they’d discovered that they’d been trying to learn to play, and then after no more than 10 minutes (probably 4) I’d have steered the lesson back to the repertoire I had assigned; once upon a time I’d have left activities generally deemed to be ‘creative’ til the end of the lesson because we had to get the ‘real’ work done first. But all these once-upon-a-times represent woeful educational practice, and I’m ashamed of every single example of this in my teaching history.

Then we have the rare 1-4% who love to learn things in the order we plan to teach things, who practice regularly and consistently for their entire learning lives, who explore new kinds of learning in their own time, but prepare for lessons so well that we can fit nearly everything into 45 minute lessons each week, and whose parents are keen for them to have extra lessons as their learning requires. And I think (deep down in  a little part of our hearts) we piano teachers think that in an ideal world the other 96-99% of our students would just morph into this kind of  a student.

But we only think that because we (deep down in our hearts) believe our focus should be on our teaching, not on the student’s learning.

As soon as we shift into a learning-centric focus the fun of the piano lesson becomes all about connecting with our students, with their unique gifts, challenges, contexts and needs.

And all those lists of requirements, prerequisites and checklists begin to gather a little more dust each week as we work to meet the evolving and unfolding learning needs of our students.

Music and Mathematics Part 1

The past year or so seems to have hosted a steady trickle of articles, blog posts and public debates about the connection (or, more usually, the lack thereof) between music and maths.

Discussions involving mathematics bring on a sense of alienation/torpor to many in the general public, but I’m one of those who find mathematical thinking exciting, exacting, exhilarating. And as music is (really quite literally) on my mind all the time, I am deeply interested in the assertions of others regarding the links (or lack thereof) between these two (musical and mathematical) aspects of organisational thought and expression.

It turns out that many of those who spend time disputing the existence of links between music and mathematics go on to reveal that they were never that good at maths. In fact, they confess that they’ve failed key mathematical assessments throughout their schooling. What they don’t acknowledge is that they have a vested interest in denying connections between mathematical and musical thinking, and no one seems to think it worth mentioning that someone who is no good at maths probably won’t have a very nuanced idea as to what mathematics actually is [and therefore is probably not best equipped to detail how unconnected music and maths might be].

Along these lines, if you think that mathematics is just a fancy word for “counting” the argument will go something like this: maths and music are linked because in music you do counting (of beats and intervals). That’s it. As soon as we notice that music is more than counting (either beats or intervals) it’s no great stretch to be convinced the hoopla about maths and music having all that much in common must be based on a trite understanding of what music is.

The problem is that the trite understanding isn’t of music so much as it is of mathematics. Mathematical thinking does involve quantity (which concept does involve, amongst many other things, “counting”), but it also necessarily involves spatial thinking/awareness as well as pattern recognition, two substantial non-counting aspects of how to think in and about the world.

But even within the confines of “quantity” we find ourselves in a world of relationship: “this is bigger than that” might not sound particularly profound, but a lot about our experience of music can be described within this single concept of quantity. No matter which way we hear it, louder, longer, faster, further, more (and their corresponding softer, shorter, slower, closer, less) describe nearly everything that can happen in music.

Stephen Hough makes a quite convincing case that it is the ambiguities of music that make it wildly different to mathematics, that mathematics is about stasis and containment while music is about flow and escape. But this argument only convincing as long as you buy into its proposed divide before you debate the possible connections; if you see pattern as being the apparatus through which emotion/heart is experienced (and expressed) in music, then a head/heart divide doesn’t make much sense, for example. And where Stephen Hough’s sees the experience of rhythmic ‘irregularity’ as taking music away from any connection or analogy with mathematics, I suspect a mathematician might immediately think of prime numbers, and other ‘irregular’ or singular mathematical entities.  And the notion of ‘unexpected’ reflects pattern-spotting competencies and experientially or culturally based perceptual expectations rather than anything intrinsically structural. Saying that music is nothing like maths because it includes unexpected developments is like saying a list of numbers is not mathematical simply because you can’t figure out (or predict) the next number in the sequence.

Say we were to ask ourselves what links between music and mathematics we could find, rather than the ways in which we could refute possible links, I think we would quickly establish that playing a musical instrument involves an exceptional degree of mathematical thinking. From spatial thinking (up, down, high, low, near, far, close, beside, under, above, and all manner of prepositional variations of ways we map and describe spatial relationships) through to fractional thinking (subdividing) through to symbolic representation of relationship, shape and direction and garden-variety counting: even when a musician is completely focussed on an emotional journey or an artistic truth, the expression of that journey and truth can take place without the aid of mathematical thinking.

So how do a significant number of musicians manage to persuade themselves that their music has no relationship to mathematics (if we accept that the two are deeply linked)? My first instinct and considered judgment is to blame it on poor mathematics education in primary and early secondary schools; if you don’t understand what maths is then you are unlikely to credit it as being much use or relevance to the things that define your identity.

I’ve been fascinated to learn this week that the mathematical knowledge that a preschooler brings to their first year of primary schooling is by far the strongest “predictor of a host of social-emotional skills” (see Early Childhood Mathematics Education Research: learning trajectories for young children, p.6).

I mean, wow.

I’ve not explored the research or analysis of that finding (what is it about early acquisition of mathematical skills and concepts that facilitates enhanced social and emotional skills?, is this a causal or a casual link?, etc.), but the idea that mathematical skillfulness has emotional and social benefits surely challenges every cliché that exists in the western educational model about maths and the limits of its purpose in education.

So far I am deeply persuaded that music and mathematics have complex connections, overlaps, correspondences and links, and the fact that we debate the existence of those links is mostly a sign of how little western culture understands what mathematics is.

To be continued….