Why You Should Welcome Times Tables Tests: Part 1January 30, 2016
I promised I’d write about this last weekend, and then ran out of time, so apologies for the delay.
I support the introduction of times tables tests at the end of Key Stage 2. The main reason is that I am a secondary maths teacher and I see so many students arrive at secondary school not knowing their times tables. The complacency of those who say “primary schools already do this” amazes me. There are some primary schools that are good at this, but to be honest, since the end of the original NNS I can’t think of any year 7 class (other than when covering at a top grammar school) I’ve had that turned up to secondary fluent in their times tables. And this includes top sets and classes at independent schools. Very often the only students who know their times tables were educated overseas, taught by their parents or had private tuition (particularly Kumon maths). Worse though, is how often students think they know their times tables properly but don’t. It’s common for me to ask a class who knows their times tables and get 50% of hands up, then to ask “What’s 7 times 8?” to a student with their hand up, only for them to start counting on their fingers. Often students arrive at secondary not only not knowing their times tables, but convinced that as they could work through a table by repeated addition, then they have mastered the skill. Often they know virtually nothing of the 12 times table. Some students are not even fluent in their 2 or 3 times table after 7 years of daily maths lessons.
The reason the lack of fluency makes a difference is something that should be obvious to anyone who has followed the debates about cognitive psychology and education in recent years. Our working memories are limited. The way we cope with more complicated calculations is to fluently recall helpful information from long term memory. We also learn better if we do not overload our working memories by thinking about too much at once. In practice, this means it is much easier to grasp the idea of simplifying fractions, and remember it in the future, if every time you think about simplifying fractions you do not have to think hard about times tables calculations at the same time. It takes a second to simplify 49/84 if you realise at a glance that both numbers are in the 7 times table, and know exactly how many times 7 goes into both numbers without thinking about it and the idea of simplification is easily remembered if you didn’t get distracted by the need to work out times tables. Every maths teacher has experienced the student who thinks all simplifying of fractions should involve division by 2, because those are the only questions on simplifying they have ever mastered. Also common is the student who loses track of what they are doing part way through simplifying a fraction, and writes down the common factor in the simplified fraction rather than dividing by it. These are failures that occur because of a lack of times tables knowledge. And all fraction calculations tend to involve similar considerations of times tables. As do the methods for dividing and multiplying larger numbers, negative numbers or decimals. Multiplication and division are also fundamental for accessing proportional reasoning and much of algebra. Even topics in geometry (eg. angles in regular polygon) and statistics (eg. pie charts), are often easier if you can divide fluently. If you don’t get how fundamental times tables are to learning maths, I am prepared to argue that you don’t understand how to learn maths. Maths is cumulative and fluency at one level leads to understanding (and more fluency) at the next.
Continued in part 2.