What’s the Deal with Maths Fact Fluency?
With the re-release of Quick Math, I thought it might be an excellent time to talk about maths fact fluency. Obviously, the principle aim of Quick Math is continued practice to improve fluency across all operations, including switching between operations.
In all likelihood, rote learning of maths facts was a feature of your mathematics education. During my early schooling years, the memorisation of basic arithmetic facts, particularly times tables, was highly valued, and lessons consisted of the demonstration of a skill, followed by endless practice exercises (well, it certainly felt endless at the time!).
However, this emphasis on math fact fluency has come under some scrutiny over recent years. In many international curricula, the focus has shifted from from blind memorisation and passive instruction towards student involvement, mathematical thinking, and number sense. Just how much mathematics has changed is evidenced by the countless parents who have taken to the internet, baffled by the maths homework given to their children.
But the changes are important and necessary if we do, in fact, aim to teach our children mathematics — reciting times tables or plugging numbers into a formula do not equate to mathematical understanding. By way of example, being able to recite a phrase in French does not imply you either understand it or are able to speak the language.
Nevertheless, while fact fluency is certainly not the be all and end all, it still has a place in mathematics. In fact, it becomes particularly important as more difficult mathematical concepts increasingly rely on working memory. Essentially, humans have limits on how much we can hold in our working memory at any one time. Complex and novel tasks, such as encountering new concepts in mathematics, require a greater cognitive load. If math facts are fluent and automatic, the load is reduced, allowing a greater focus on the concept at hand, in turn, facilitating understanding.
I do not wish to imply that fluency is key to understanding higher order concepts. As discussed above, fact fluency alone is not enough. Understanding higher order concepts becomes possible when students have a solid number sense.
Quick Math provides students with a self-motivating way to practice with understanding in order to develop fluency in basic number facts, as well as number sense and problem solving. We cannot know every possible addition fact for numbers under 100, for example, and nor should we! When such a question arises during play, users must combine those practiced facts with problem solving to come up with the answer. In an example from Addition Extreme, the question 16 + ? = 45 is almost certainly not a memorised maths fact, but one can work it out by seeing that 16 + 30 = 46 and therefore 16 + (30–1) = 45 and so the answer must be 29. It is through repeated exposure to both learned facts and problem solving that students develop fluency and greater experience with mathematical thinking.
One thing we plan on reviewing in the future is the timed nature of Quick Math. We have received a number of requests over the app’s life requesting that the timer be removed. For many, adults and children alike, maths is a great source of anxiety. While racing the clock creates a sense of fun and challenge for some, it puts pressure on others, and that certainly isn’t something we want! Maths should be enjoyed, not feared! Given maths anxiety has a negative impact on performance and learning (see here also), and that speed is not related to mathematical ability, we hope to create a version in the future that allows practice without pressure, placing the focus squarely on the most important thing — the mathematics!