“Oh calculator… How do I love thee? Let me count the ways…”
Said no secretary of state for education. Ever.
For decades now, there has been increasing wariness and suspicion of the role of calculators in the primary classroom, being viewed more as a hindrance than a help.
Perhaps the final nail in the coffin was Elizabeth Truss’ announcement in 2012 that calculators would be banned from Key Stage 2 SATs in order to emphasise children’s mental and written mathematical understanding.
The legacy of this decision lives on. In a culture where teachers and schools feel increasingly pressurised by a results-driven system, it is no surprise that calculators are being used far less frequently in English primary schools, given pupils are no longer tested on their use.
Rethinking calculator use
But why so? It is hard to think of another scenario where children are denied access to something perfectly safe that they will certainly use in everyday life. Schools exist to equip children with the skills they will need in the future, yet these rules do not seem to apply to the calculator.
As mentioned earlier, it is thought that children’s mathematical understanding could be hampered by overuse of a calculator.
To be clear, I would certainly not advocate a curriculum where children use a calculator instead of calculating mentally. After all, developing a feel for numbers is crucial to checking the answers to calculations, among many other important things.
But the use of resources in the maths classroom has long been seen as effective pedagogy and this has been accentuated by the move towards a mastery curriculum where children are encouraged to deepen their knowledge in order to embed it, as opposed to gaining only a superficial understanding.
Notwithstanding the benefits of other resources, the calculator possesses unique characteristics that can enhance such understanding.
Calculators as learning tool
Children as young as five are expected to count in 2s, 5s and 10s up to 100 from any number. Initially, children would begin with smaller numbers, e.g. 3 + 5 = 8 and this could be modelled easily using cubes, Numicon etc.
However, pressing ‘=’ will continue the sequence (in this instance, 13, 18, 23…) and quickly enable children to spot patterns in a far more efficient way than using any of the aforementioned resources (imagine the amount of Numicon needed to represent 98).
And children’s ability to interpret the numerals on the display is not only an opportunity to develop mathematical vocabulary, but also an opportunity for a practitioner to assess and then outline next steps.
At the risk of sounding obvious, it is impossible to use a calculator correctly without fully understanding the four operations. Children can calculate mentally without this understanding, but, as highlighted earlier, a greater depth of understanding is acquired before mastery can be attained. For example: “Charlie has 10 toys. How many more does he need to make 12?”
The answer is not difficult but what is difficult is that ‘counting on’ from 10 to 12 (a strategy also associated with addition) is actually abstractly represented by 12 - 10 = 2.
Asking a child to enter the correct calculation into the calculator is therefore an effective way of assessing children’s understanding of operations.
As identified by Conrad Wolfram, renowned mathematician and technologist, a surprisingly large amount of curriculum time worldwide is dedicated to written methods for the four operations, given how infrequently they are now used by adults. English 11-year olds are expected to perform calculations such as 3416 ÷ 24 and 17 × 5918. Why? It is hard to envisage a set of circumstances where such calculations are required and wouldn’t one use a calculator to check when the numbers are that big anyway? The need for written speed has diminished, but maths curricula have not adapted accordingly.
Making room for necessary maths
Interestingly, one thing that calculators cannot do actually makes them a most valuable tool. They cannot think (yet). Posing a question, deciding how best to solve it and then assessing whether the original question has actually been answered are all roles that are performed by humans. And thus it would be logical for pupils to spend more time in school honing such skills.
Using a calculator can create significant time savings, leaving more time for pupils to predict, to reason, to “think” - all of which are skills that pupils will one day required in the workplace, no matter what their chosen career.
In a similar manner to the Computing curriculum, the maths curriculum needs a major overhaul in order to equip children with the skills that they actually need rather than supporting a return to a supposed “Golden Age” of maths education. Rows of bank clerks calculating ledgers by hand are a thing of the past, yet the content of the maths curriculum is weighted towards preparing pupils for such imaginary roles.
Of course, teachers have little control over the prescribed content of the curriculum. However, I would implore teachers to look closely at the curriculum aims. As I have hopefully shown, the calculator can support these three aims: the fundamental of mathematics, reasoning and problem-solving. And thus calculators should be dusted off and, just like other resources, be used by pupils to promote mathematical understanding. This will help to reaffirm their status in the mathematics classroom and help them be viewed more as a white knight rather than the black sheep of the mathematics family.
David Boorman is senior lecturer in primary education (mathematics) at Edge Hill University
Want to keep up with the latest education news and opinion? Follow TES on Twitter and like TES on Facebook
