Non-symbolic approximate arithmetic training improves math performance in preschoolers

https://doi.org/10.1016/j.jecp.2016.07.011Get rights and content

Highlights

  • Preschoolers underwent a pre- and posttest cognitive training experiment.

  • Experimental group children played a non-symbolic approximate arithmetic game.

  • Control group children played a picture memory game.

  • Symbolic math and other cognitive skills were assessed before and after the games.

  • Experimental, compared to control, group selectively improved in symbolic math.

Abstract

Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words.

Introduction

Mathematical competence during early school years is a powerful predictor of later academic success not only in math but also in other domains such as reading (Aubrey et al., 2006, Duncan et al., 2007, Geary et al., 2013, Jordan et al., 2010, Jordan et al., 2007, Jordan et al., 2009, Martin et al., 2014). Unfortunately, many children, especially from low-income families, start kindergarten with minimal competencies in math (Jordan et al., 2006, Jordan et al., 2007, Klibanoff et al., 2006, Starkey et al., 2004). Thus, enhancing mathematical competence during preschool years is an important societal challenge.

The traditional approach to enhancing mathematical achievement in young children is to target skills foundational to mathematics, including domain-specific abilities such as counting skills and domain-general abilities such as working memory (Baroody et al., 2009, Bryant et al., 2011, Chard et al., 2008, Clements and Sarama, 2007, Dyson et al., 2013, Fuchs et al., 2005, Ramani and Siegler, 2008, Siegler and Ramani, 2009, Starkey et al., 2004). Many of these programs are curriculum based and focus on enhancing specific foundational mathematical knowledge in everyday activities to improve children’s mathematical competence. In particular, nearly all of these programs focus on symbolic number concepts such as counting and number facts as well as arithmetic operations with numerical symbols. These intervention programs have started to show great successes in increasing children’s mathematical knowledge at young ages (Clements & Sarama, 2011). Nonetheless, there are some limitations to the approaches that currently dominate the landscape. First, many of these programs require a large investment of teacher training and must be implemented over a full academic year. Relatedly, because the teachers are given a great deal of additional training to implement the intervention curricula, it is often difficult to find a fair control group. Another limitation from the standpoint of cognitive science is that most interventions are very heterogeneous, often consisting of multiple different tasks or skills. Although such large-scale interventions may be a very effective strategy for improving mathematical ability, it is difficult to pinpoint which aspects of the curriculum are most effective.

Here we take an alternative approach and ask whether training aimed at children’s preverbal number sense could be an effective way to improve math readiness. Children come into the world with a preverbal number sense that allows an approximate sense of quantity (Dehaene, 1999, Gallistel and Gelman, 1992). This system has been termed the approximate number system (ANS) and has been shown to be present in newborn infants (Izard et al., 2009, Xu and Spelke, 2000), to operate in adults from cultures without symbolic counting systems (Gordon, 2004, Pica et al., 2004), and to be present in a wide range of nonhuman animals (Agrillo et al., 2014, Beran et al., 2015). Furthermore, the system increases in precision with age and is found across the lifespan (Halberda and Feigenson, 2008, Halberda et al., 2012).

Despite the profound differences between a symbolic representation of number, which allows the representation of number with extreme precision, and approximate non-symbolic representations, which are noisy and follow Weber’s law, recent studies have uncovered a correlation between individual ANS acuity and symbolic math ability (e.g., Gilmore et al., 2010, Halberda et al., 2008, Libertus et al., 2011, Mazzocco et al., 2011; but see Fuhs and McNeil, 2013, Gobel et al., 2014, Inglis et al., 2011, Kolkman et al., 2013, Nosworthy et al., 2013, Sasanguie et al., 2013, Tibber et al., 2013, Wei et al., 2012). We use the term symbolic math to refer to any learned mathematical concepts and knowledge, including identifying symbols, number words, using the count list, and solving arithmetic problems based on number words or numerals. This correlation between the ANS and symbolic math indicates that approximate numerical abilities may be foundational for learned math skills and, therefore, suggests an alternative approach to improving math readiness. However, given the correlational nature of the findings, alternative possibilities are plentiful (e.g., see Gilmore et al., 2013, Lyons and Beilock, 2011, Piazza et al., 2013). To investigate the causal nature of the relationship, our previous research asked whether repeated training on an approximate arithmetic task, which requires addition and subtraction of non-symbolic numerical quantities, would selectively improve mental arithmetic skills in college students (Park and Brannon, 2013, Park and Brannon, 2014). In these experiments, adult participants first received a set of pretests, which included a symbolic arithmetic test, among others. Participants were then randomly assigned into one of multiple cognitive training groups. In each study, the experimental training group spent 6 to 10 daily sessions engaged in approximate non-symbolic arithmetic, whereas control groups underwent other types of cognitive training such as visual short-term memory and numerosity comparison training. We found that participants who were engaged in the non-symbolic approximate arithmetic training—and only those participants—showed improvement in symbolic arithmetic skills. Given that numerosity comparison and short-term memory training did not yield significant benefit in symbolic arithmetic performance, we concluded that mental manipulation of nonverbal numerical quantity was the critical factor driving improvements in math skills. Consistent with our findings, another research group found that first graders briefly exposed to similar preverbal number sense tasks performed better than peers in a subsequent symbolic arithmetic test (Hyde, Khanum, & Spelke, 2014). Collectively, these recent findings suggest that engaging the preverbal number sense via approximate arithmetic may be an effective way to improve mathematical ability throughout the lifespan.

Here, we tested this possibility by asking whether approximate arithmetic training benefits preschoolers’ math abilities. Local preschoolers, largely from low-income families, first received a battery of pretests that assessed their math, vocabulary, verbal short-term memory, and executive function. Children were then pseudorandomly assigned to one of two groups; the first group played a tablet-based game that required adding and subtracting arrays of icons, and the second group played a tablet-based game that required remembering the location of pairs of pictures. Then, we assessed the effectiveness of the two cognitive training programs by comparing pretest and posttest scores for each of the test measures. From this study design, we aimed to evaluate how approximate arithmetic—presumably the process of mental manipulation of numerical quantity—could benefit very young children at the verge of the introduction to formal math education and often with minimal symbolic math knowledge. This study was meant as an important first step to test the effectiveness of approximate arithmetic training in preschool children with no formal math education and as a springboard for a larger scale math intervention study.

Section snippets

Participants

Participants were recruited from local preschools that were largely composed of children funded by a state-funded preschool program. This program provides assistance to children from families whose gross income is at or below 75% of the state median income level. We intentionally focused on children of low-income families because they represent the greatest need for improving early mathematical competence. A total of 109 preschoolers across four schools initially enrolled in the study.

Children

Results

We first report the performance progression in the two experimental games. Children who played the approximate arithmetic game showed a consistent decrease in the log difference level (Fig. 2A), as indicated by a negative slope of the linear fit for each individual child’s log difference level, t(50) = −20.391, p < .001. This monotonic decrease in the log difference level could reflect the progression of the threshold of the adaptive staircase procedure used in this game rather than children’s

Discussion

Although humans are uniquely capable of symbolic mathematics, we share with other animals an intuitive ability to estimate, compare, and manipulate large numbers of items without counting that is present during human infancy before symbolic math skills are acquired (Dehaene, 1999). A growing body of research suggests that the preverbal number sense that supports approximate non-symbolic number representations is fundamentally related to full-fledged math abilities, particularly in children (

Acknowledgments

We are grateful to the child participants, their families, and the preschool administrators and teachers for making this study possible. We thank our Duke University Bass Connections team of undergraduates for their assistance in data collection and analysis. We appreciate Mark Paris’s dedicated work in developing the two iPad games. This study was supported by NIH R01 HD079106 and a grant from the Initiative on Education and Human Development at Duke to E.M.B.

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