Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies

ABSTRACT

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition problems using a min-counting strategy and were accurate using it. We investigated if these children were adaptive when it came to using retrieval for simple addition and if they were disadvantaged when it came to demonstrating mental computational flexibility with multi-digit addition. We found accurate-min-counters represented over 30% of participants. These children were often incorrect when they were required to use retrieval for simple addition and were less flexible than most peers with mental computation strategies. The findings indicate that educators should be concerned about the prevalence of accurate-min-counting and call into question the widely held view that it is mostly children with a mathematics learning disability (or persistent low achievement) who display the protracted use of counting-based strategies for simple addition. Further research is needed to investigate if, and how, current teaching approaches are encouraging children to rely on counting beyond a time when it is advantageous to do so.

KEYWORDS:

• Counting
• retrieval
• mental computation
• flexibility
• addition

Notes

1. Thevenot et al. (2016) challenged the common assumption that children’s strategies generally evolve from counting to retrieval. They argued that reaction times (generally under 1.7 seconds) recorded for single-digit addition problems with small sums (involving operands from 2 to 4) do not necessarily reflect direct retrieval, even when children report just knowing the answer, but instead represent very fast, compacted counting strategies.

2. As well as the Arithmetic Scratch-Paper Test, Blöte et al. (2001) administered an assessment that required children to solve a set of problems using two different strategies for each problem; however, this test was considered an assessment of conceptual understanding and not strategy flexibility. As noted by Star and Rittle-Johnson (2008), students’ ability to generate multiple strategies is not a good assessment of flexibility since children tend to come up with strategies that are novel but inefficient.

Additional information

Notes on contributors

Sarah Hopkins

Sarah Hopkins is a senior lecturer in the Faculty of Education at Monash University. Her current research is focused on understanding and addressing students' difficulties learning mathematics and preparing teachers for inclusive classrooms.

James Russo

James Russo is a lecturer in the Faculty of Education at Monash University. His current research interests are in task design, mental computation and estimation in the elementary years, and on examining the teaching and learning of mathematics through an affective lens.

Robert Siegler

Robert S. Siegler is Schiff Foundations Professor of Psychology and Education at Columbia University. He is a recipient of the American Psychological Association's Distinguished Scientific Contribution Award, as well as having been chosen to be a member of the National Academy of Education and of the Society of Experimental Psychologists. His current research focuses on the development of mathematical thinking, particularly children's understanding of rational numbers; ways of improving children’s mathematical thinking; and educational applications of cognitive-developmental theory.