Supporting fluency when solving problems
Fluency helps children spot patterns, make conjectures, test them out, create generalisations, and make connections between different areas of their learning — the true skills of working mathematically. When learners can work mathematically, they’re better equipped to solve problems.
But what if learners are not totally fluent? Can they still solve problems? With the right support, problem solving helps learners develop their fluency, which makes them better at problem solving, which develops fluency…
Here are ways you can support your learners’ fluency journey.
Don’t worry about rapid recall
What does it mean to be fluent? Fluency means that learners are able to recall and use facts in a way that is accurate, efficient, reliable, flexible and fluid. But that doesn’t mean that good mathematicians need to have super-speedy recall of facts either.
Putting pressure on learners to recall facts in timed tests can negatively affect their ability to solve problems. Research shows that for about one-third of students, the onset of timed testing is the beginning of maths anxiety. Not only is maths anxiety upsetting for learners, it robs them of working memory and makes maths even harder.
Just because it takes a learner a little longer to recall or work out a fact, doesn’t mean the way they’re working isn’t becoming accurate, efficient, reliable, flexible and fluid. Fluent doesn’t always mean fast, and every time a learner gets to the answer (even if it takes a while), they embed the learning a little more.
Give learners time to think and reason
Psychologist Daniel Willingham describes memory as “the residue of thought”. If you want your learners to become fluent, you need to give them opportunities to think and reason. You can do this by looking for ways to extend problems so that learners have more to think about.
Here’s an example: what is 6 × 7? You could ask your learners for the answer and move on, but why stop there? If learners know that 6 × 7 = 42, how many other related facts can they work out from this? Or if they don’t know 6 × 7, ask them to work it out using facts they do know, like (5 × 7) + (1 × 7), or (6 × 6) + (1 × 6)?
Spending time exploring problems helps learners to build fluency in number sense, recognise patterns and see connections, and visualise — the three key components of problem solving.