Building number fluency

What can teachers do to target children’s individual difficulties in developing basic number fluency?

When building basic number fluency in children, strategy choice is the key to effective practice, according to Monash University academic Sarah Hopkins.

A Senior Lecturer in the Faculty of Education, Hopkins has been working with individual case studies of children in Years 2-8, monitoring the strategies that they use as they practise solving simple addition problems every day for extended periods of time.

‘The approach I use allows me to investigate what factors actually lead to the discovery and use of more efficient strategies, including retrieval-based strategies – by that I mean direct retrieval, just knowing the answer and stating it – or using decomposition strategies, where students partition numbers to make use of the facts that they do know,’ Hopkins says.

‘What I found is that this kind of research has highlighted just how much practice children need to become confident and accurate in using retrieval strategies.’

Hopkins says her research has also uncovered the many, varied reasons why children have difficulty learning from practice and the different types of sticking points that they experience. ‘For example, some children get stuck using an inefficient counting strategy like counting all, or they make the transition to min-counting where they count on from the larger addend but they forget which addend they start at, or they over count, or they forget to stop counting, or they under count so they make errors using miscounting strategies. Other children actually construct a faulty rule or a faulty decomposition strategy that they then practice. Or they can confuse double facts, so they might say 7+7 is 16 and 8+8 is 14, for example.’

Drawing together findings from the literature and the case studies she’s monitored and analysed, Hopkins has found that strategy choice is an essential element of all children’s mathematical experiences. ‘What I’ve found is the key to effective practice is allowing students to use whatever strategies they want to use and then encouraging them to know more than one strategy for solving a particular problem.’

Hopkins presented her research in greater detail at the Mathematical Association of Victoria’s 54th Annual Conference (MAV17).

For educators looking to help students move away from inefficient counting strategies, Hopkins says some children will discover new strategies by themselves, while others will benefit from being exposed to new strategies through whole class discussion, where students share how they solve a problem and the teacher follows the explanation and models it to the rest of the class.

‘I hope that more teachers will experiment with different ways to increase a child’s confidence to try different strategies when solving problems. Confidence using a new strategy builds with experience and is reinforced using a trusted back-up strategy when children are allowed to choose the strategy they use during practice.’

Hopkins, S., & Bayliss, D. (2017). The prevalence and disadvantage of min-counting in seventh grade: problems with confidence and accuracy. Journal for Mathematical Thinking and Learning, 19(1), 19-32. doi: 10.1080/10986065.2017.1258613.

This is an edited version of an article that first appeared in Teacher magazine and has been reproduced with the permission of the Australian Council for Educational Research. To read the full article and to read more articles like this visit