In 2020, the UK government will introduce a multiplication tables check for primary school children aged 8–9 in England. ‘Times tables’ are a contentious issue because they represent a lot of our ideas about what learning mathematics is. We need to understand whether the focus of the test will develop children’s mathematical fluency or corrupt their experiences of maths learning in the classroom.
While fluency in multiplication is a key mathematical competence (Kling & Bay-Williams, 2015), it is not one that the check will assess. The test more narrowly aims at measuring ‘recall’ (DfE, 2018), giving value to accuracyin calculation, but potentially undermining its necessary complements of flexibilityand efficiency (Russell, 2000).
With six seconds to answer, children will be asked to find products of multiplication equations up to 12 x 12 (for example, 6 x 4=?). Does knowing these facts equate with being grounded in the ‘basics’ of multiplication? In fact, in part as a means to such factual knowledge, children need to develop an awareness of multiplicative structures and relationships: knowing multiplication as, for example, repeated addition, the inverse relation of division, the associative, commutative and distributive laws, Cartesian products, scaling and making connections from these ideas to other mathematical strands. Baroody (2006) asserts that fluency in multiplication develops through three phases.
- Counting strategies (for example, being able to count in the 7-times tables through a basic understanding of repeated addition).
- Reasoning-derived facts (for example, if I know 7 x 5 is equal to 35, I can know 7 x 6 is equal to 7 more).
- Mastery: fast and accurate computational fluency.
Where children are encouraged only in phase one and then expected to reach phase three (‘you just have to learn them’), it is unsurprising that at least some learners find it difficult to remember such a large set of disconnected facts. It is questionable, though, whether the multiplication check will always be measuring such recall at all. Will some children not simply count up quickly in their multiples?
‘When strategic thinking, reasoning and meaning are separated from learning maths, so too is the spirit of mathematics.’
When strategic thinking, reasoning and meaning are separated from learning maths, so too is the spirit of mathematics (Ball, 2003). As a well-regarded district maths specialist in Tokyo put it to me a few years ago, when I asked how much emphasis the school put on recall, ‘children must know their facts, but we say that mathematical thinking is most important’. In a lesson I then observed, children spent around three minutes quickly filling out a multiplication grid at the beginning of the lesson, and the rest of the 45-minute lesson making impressive connections between different patterns in the products on the grid. At points in the lesson, even the class teacher appeared surprised with their ingenuity and originality of thought. By the age of 8, they certainly knew all their multiplication facts with ease, but their fluency was a means to deeper thinking rather than an end in itself.
The lack of nuance and potential pitfalls of the test highlight how problematic education policy can be when unrooted in an understanding of subject-specific content and progression. The multiplication check may have been envisaged as a means to knowledge-entitlement for all children. Its unintended consequences, however, could be to inhibit the types of learning experiences that help young mathematicians to flourish and develop a real interest and curiosity in maths. As there is little sign of policy change, the mathematics education community needs to come together to support educators with practicable knowledge for mathematics teaching. We need to ensure that children do not receive an impoverished maths diet in among pressured schools’ efforts to prepare for another accountability measure.
Ball, D. L. (2003). What mathematical knowledge is needed for teaching mathematics? Speech delivered at Secretary’s Summit on Mathematics, US Department of Education, 6 February 2003. Retrieved from https://www2.ed.gov/rschstat/research/progs/mathscience/ball.html
Baroody, A. (2006). Mastering the basic number combinations. Teaching children mathematics, 23, 22–31. Retrieved from https://pdfs.semanticscholar.org/dd26/0bdf77064f703916ffdbeff4b3b61bf74aef.pdf
Department for Education [DfE] (2018). Multiplication tables check: development update. [online]. Retrieved from https://www.gov.uk/guidance/multiplication-tables-check-development-process
Kling, G. & Bay-Williams, J. (2015). Three steps to mastering multiplication facts. Teaching Children Mathematics, 21(9), 548–559. Retrieved from https://www.usd379.org/view/12129.pdf
Russell, S. J. (2000). Developing computational fluency with whole numbers. Teaching Children Mathematics, 7(3), 154. Retrieved from https://investigations.terc.edu/inv2/wp-content/uploads/2017/10/Developing-Computational-Fluency-with-Whole-Numbers-in-the-Elementary-Grades.pdf