A blog about maths, just like old times.
Over the past couple of years, I’ve had educators who are also parents approach me to ask for advice about their child and how he or she can catch up. There is a common theme among these requests: their children tend to be around 7 or 8 years old, they’ve become aware that their child is on the ‘low table’ and then they try a few things out with their child at home and are horrified to see their child struggle with even the most basic of calculations because they’re still stuck using their fingers to count up and down all the time. Thinking about my own experience of various primary schools, primary educators and children whom I’ve taught, I would say these requests are not isolated incidents, rather indicative of a widespread problem: young children do not have their basic maths facts off by heart. What are the contributing factors and what can be done about it?
- A skills-based approach in the early years assumes that the objective ‘being able to do simple addition or subtraction’ can be ticked off if the children can do it via counting up and down with fingers, beads, toys, whatever, but no expectation that they would be fluent (speedy and accurate)
- The incredibly high amount of visual and aural distractions in the reception classroom that regularly interrupt children’s counting such that they often arrive at the wrong answer (no one’s there to check it because there are only 2 adults in a class of 30 with many different activities going on) and never get to really know for sure that, for example, 2 and 5 make 7. This is more of a problem for children who haven’t got the habit of concentration (see my other posts on learning to concentrate being as important as learning knowledge) in an environment that actively discourages it
- A teaching approach that confuses ‘showing understanding’ with ‘learning’, leading to children being moved on to something else, usually problem solving, before they’ve had a chance to do enough practice and commit what has been taught to long term memory
- Some early years and KS1 educators have a subconscious bias against maths, seeing it as inherently boring or hard, and seek to mitigate against this by making maths ‘fun’, thus obscuring and distracting from the core knowledge that children need to have
- Awareness of the reasons why children need to know, for example, their times tables, but an inability to draw parallels with what must be known off by heart in early mathematics
- Calculation policies mandating the use of inefficient methods of calculation in order to ‘show understanding’ before children are allowed to proceed onto the formal methods holds many children back
- The need to evidence differentiation which means that over the years, the LAPs not only do fewer calculations per any unit of time, but they’re always being given manipulatives which removes the requirement for them to learn maths facts off by heart
- Sometimes the differentiation is by calculation method, with LAPs expected to remain on those number lines while the HAPs get to use their column addition and subtraction to do many more calculations and learn so much more about number facts and relationships (place value, for example) through this practice
- Teachers of mathematics in the earlier years (Year R, 1), while being aware of cognitive load theory, do not (or cannot) necessarily apply these concepts to teaching and learning of maths
- Ideological opposition to SLOP and ‘knowing things off by heart’ in maths
For me, I cannot help but see parallels with the teaching of reading. We now know that systematic synthetic phonics is so much more effective than the old Look & Say methods that encourage various forms of guesswork; children need to learn the little parts of words and how to sound them out and blend them, but we don’t stop there because we expect the requisite amount of practice to take place such that children become fluent at segmenting and blending and this means knowing the graphemes off by heart. However, in mathematics, it’s like we teach the equivalent of the phonics (actually, sometimes we don’t even do that), and then give the children some Shakespeare to read while also playing experimental Jazz in the background.
So, the children get to practice some simple recall on the reading table within continuous provision, or will have opportunities for recall in extra phonics sessions at various points of the day, but the maths retrieval practice will be lots and lots of counting up and down, or perhaps recall of shapes, time, the weather, days of the week – anything but knowing off by heart, through teaching and lots of practice in reception year and year 1, that if we pop a 2 and a 5 together, they always make 7. They may or may not twig this fact, and even if they do, it is a fleeting moment that is not emblazoned in their long term memory because they’re swiftly moved to the ‘shopping task’ and suddenly their heads are filled with apples and pears. As these children progress onto working with larger numbers in year 1, 2 and 3, the constant counting up and down leads to errors: sometimes 9 and 5 make 14, sometimes 9 and 5 make 15 – so these children don’t then start to learn the patterns (that you also need to know off by heart) for, say, adding 9. They cannot see the mathematical tree for the leaves, never mind the woods for the trees! Some children go up into year 2 not being able to look at 6 objects and instantly know that there are 6 objects – you’ll put 6 counters down in a typical 2 by 3 array and they’ll bloody start counting one by one.
To many who read this, these little parts of number knowledge seem insignificant and therefore nothing to really worry or bother about. The common sentiment is that children will arrive, when they’re ready, at all this knowledge and then we can just focus more intensely on maths knowledge and SLOP in KS2 (quite often the maths lead will be in year 6). But that surely is the equivalent of expecting children to learn to read by immersion and magical osmosis?
If I were to change things, I’d shift the focus to a knowledge-based approach in early mathematics and really systematically teach, assess and expect lots of practise of specific, small bits of number knowledge – just like we’re expected to with phonics. Children who haven’t learned the little parts off by heart would then be expected to discretely practise more until they’ve got it. This is kind of the opposite of what the EYFS mandates, so we’re a little stuck at the moment, and I’m finding a focus on fluency in year 1 and 2 is really difficult as a result.
Until then, when teacher-parents approach me for advice, I usually recommend counting at home (without distractions) to 5 and then recognition of what 1, 2, 3, 4, 5 and 6 look like in a really systematic way, as well as the use of games such as dominoes, snakes and ladders where turn taking and slight increase in adrenalin induce more concentration (which is associated with enhanced memory formation and is an oft-forgotten reason why summative testing and competition are so useful). I also then recommend plenty of systematic practice such as through attending Kumon classes or just buying Kumon practice books off Amazon and doing them at home – the practice is really repetitive, but this is exactly what the child who is behind in their learning needs in order to commit maths facts to long term memory. It doesn’t take much, and with daily practice they can catch up, feel successful and move on to that top table in class. If you’ve got sons who are starting to be more consistently accurate with their calculations, I recommending making your own maths ‘league’ with ‘levels’ that are based on particular sets of maths knowledge, tell them a complete myth about a legendary boy who could do any level in under a certain time (make the target SMART), then whip a stopwatch out and see their faces light up with joy and ambition.
Who’s with me?