How is developing fluency in maths like learning a musical instrument?

    Published: 07 September 2021

    Many primary schools have time set aside within their timetable for helping children recall, rehearse and secure mathematics learning. These might be called maths fluency sessions, maths meetings, daily fluency, or other similar titles. And, although the name and style may differ slightly, the general purpose is the same; to give time and space for the rehearsal of knowledge and skills, so that pupils become ‘fluent’ with the mathematics required for their age.

    There is support within the national curriculum in England (KS1 and KS2) for this.

    The very first aim states:

    The national curriculum for mathematics aims to ensure that all pupils:

    • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

    In primary maths, clear, well-modelled curriculum teaching is often necessary, followed by appropriate rehearsal and exploration time. But we know that after the initial learning, further opportunities are also needed in order for learning to be recalled and retained in a useable way, hence the suggestion of ‘varied and frequent practice’ above.

    To note here, my aim is not to define being ‘fluent’ in maths. This is about considering and supporting time spent on the recall, rehearsal and securing of mathematics learning, drawing out the potential similarities to learning (and practising) a musical instrument. This blog has been a personal journey of noticing, wondering and writing (to clarify my own wonderings).

    This originally started as a series of observations, watching my son (aged 6) practising the piano. He’s at the early stages; learning the names of notes, where they sit on the stave and where they are on the piano. Also, observing how his piano teacher supports him; how routine rehearsal tasks such as flash cards of the notes are woven together with practicing pieces of music and these are interspersed with some ‘improvisation time’. They also listen to the work of composers, commenting on how the music makes him feel. On a personal note, I think his piano teacher does a wonderful job of weaving together aspects of learning the piano into a short 30 minute weekly session. My role is to support him between piano lessons, providing encouragement to practise.

    I will pause for a moment to reflect that I do not have the skill to read and play music beyond the very basic entry level, and my son in 18 months of lessons has already surpassed what I am currently capable of. However, because of his young age, I often sit with him whilst he practices between lessons. I am a parent who supports his home learning through offering time and encouragement but without necessarily a deep subject knowledge. But, as a primary school teacher, I cannot help but notice the learning naturally happening, which is a joy to watch.

    Over time, I’ve also noticed strong parallels with how we learn in mathematics, particularly how we support and encourage pupils to ‘become fluent in the fundamentals of mathematics’ and the similarities to becoming fluent when learning to read and play music. And, how to support pupils to ‘recall and apply knowledge rapidly and accurately’, whether this is solving increasingly complex problems or playing longer and more challenging pieces of music.

    Fluency in mathematics might include being able to recall and use concepts, knowledge and skills, so that these can be drawn upon and applied as needed, such as the relationships between numbers (including number bonds and multiplication tables for example). Fluency in the early stages of learning to play the piano might similarly involve being able to confidently read notes on the stave and find these on the piano keyboard, and piecing the information together to form short pieces of music.

    In the same way children need time to rehearse and secure knowledge such as number bonds or multiplication tables, they also need rehearsal time for the names of the notes (both the ‘type’ of note; crochet, minim or semibreve for example, and where they sit on the stave and keyboard, for example, middle C). In a music lesson, part of the time might be given to a flashcards or a similar music theory activity to promote this recall until it is so secure, it can be recalled with automaticity (and so does not require much working memory space). In a school timetable, this might be where maths fluency sessions come in.

    It is very important to say, I am not suggesting automaticity without understanding. On the contrary, both in music and in maths, we should advocate that automaticity needs to be with, and because of, a depth of understanding, including making connections and seeing patterns. However, once the recall is secure, it means that working memory is not spent on figuring out basic information, but focusing on the overall piece and how to play with it with the tone and style intended by the composer, or being able to see the steps required to solve a complex maths problem.

    If we suggest that a bigger maths problem is like a longer piece of music; the problem may require factual knowledge (such as properties of regular 2D shapes and how to calculate perimeter), operational knowledge and calculation methods. It may also require multiplication facts. When you tackle unfamiliar complex problems, you draw on your bank of knowledge and skills, selecting what you need in order to be successful. This could be similar to when you approach a new piece of music; you bring your knowledge of the reading of music (the note types, the stave, the time signature and key), drawing on the knowledge you have in order to piece together how the music should sound.

    And, thinking about ‘how the music should sound’, alongside tackling these longer or more challenging pieces, we also need to encourage children to spot their own errors. Whether this is hearing when a note doesn’t sound right within a musical piece, or spotting a calculation error because the answer doesn’t feel right, being able to identify and correct your own errors is also important.

    When you observe children in maths, you can see those who have the knowledge and skills required to tackle a question or problem and those children where this is less secure. This is where I would argue a need to continually interweave the ‘basic’ routine rehearsal, to develop a level of automaticity of recall, until this is deeply rooted in memory and strong neural pathways, so that when tackling something new, longer or more complex, we can draw upon the knowledge we already have easily, rather than our lack of fluency hampering working memory.

    These ramblings are not designed to be an academic piece, but more observational and anecdotal. However, it has helped me to again rationalise why we weave opportunities for developing fluency in maths into our timetable at primary school. My recent reading seems to support the same thinking:

    Mary Myatt puts this much more succinctly in the chapter on Mathematics in her book The Curriculum: Gallimaufry to coherence;

    ‘…children need to have a firm grasp of number bonds, times tables and place value. These are the fundamentals and it is important that pupils know these inside out, back to front and in any combination. Why? Because when these are secure, the working memory is not overloaded, trying to figure out what eight threes are.’

    I’ve also been reading a book; Make it stick: The Science of Successful Learning by Brown et al. 

    ‘Whilst the brain is not a muscle that gets stronger with exercise, the neural pathways that make up a body of learning do get stronger, when the memory is retrieved and the learning is practiced. Periodic practice arrests forgetting, strengthens retrieval routes, and is essential for hanging onto the knowledge you want to gain.’

    So, to bring this to a close, what are the possible conclusions you could draw; to ensure that we develop fluency in mathematics (or when learning a musical instrument):

    • frequent rehearsal of the basics, striving for the automaticity (but based on an understanding of relationships) that means the learning can be called upon with quick recall and applied to a variety of situations. In maths, this might include age appropriate knowledge such as multiplication tables, number bonds, calculation strategies and methods
    • noticing when these ‘basics’ are not secure / automatic, and so can be seen to hamper the longer or more complex work. Then giving time to return to focus on developing automaticity with those core skills. Whether with individuals, groups or the class
    • retrieval practice of previous learning, not assuming that because something was learnt that it remains accessible, but checking though retrieval periodically. This might include some of the learning less frequently used or some of the more subject specific vocabulary. I often think of geometry within this; in year 3 we teach the language of horizontal, vertical, parallel and perpendicular
    • bringing together the knowledge and skills to tackle new, longer, more complex problems/pieces, which deliberately utilise the learning that has been mastered

    Find out more about our complete suite of resources for primary schools to support effective maths fluency sessions:

     Maths Fluency sessions materials

    References

    Department for Education (2014) The national curriculum in England: mathematics programmes of study: key stages 1 and 2. Available at: Gov.UK: National curriculum in England: mathematics programmes of study (Accessed: 31 August 2021)

    Myatt, M 2018, The Curriculum: Gallimaufry to coherence, John Catt Educational Ltd, Woodbridge

    Brown, P, Roediger, H & McDaniel, M 2014, Make It Stick, The Science of Successful Learning, The Belknap Press of Harvard University Press, London

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