Improving arithmetic performance with number sense training: An investigation of underlying mechanism

Abstract

A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should explore implications from this finding that training young children on approximate arithmetic tasks even before they solidify the symbolic number understanding may be fruitful for improving readiness for math education.

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

“…This certainly suggests that there are instances where nonsymbolic numerical processing can influence SNS processing, though the results above do not appear to extend to training on nonsymbolic comparison (Park & Brannon, 2014). Regardless, it is certainly possible that approximate arithmetic performance at the outset of Kindergarten might predict growth in symbolic number skills.…”

Changing the precision of preschoolers’ approximate number system representations changes their symbolic math performance

“…Three recent studies provide some evidence that ANS-based training can improve arithmetic performance. In two of these, Park and Brannon (2013; 2014) trained adults to add or subtract two non-symbolic dot arrays and compare the estimated answer to a third dot array. After ten training sessions, adults’ accuracy had significantly improved.…”

Úvod do aproximálního numerického systému

“…Bližší charakteristika ANS bývá, jak jsme již uvedli, nejčastěji popisována jako hrubá vnitřní reprezentace čísla (Gallistel & Gelman, 2000;Feigenson et al, 2004), která není závis-lá na jazyku nebo symbolické matematice (Xu & Spelke, 2000;Gordon, 2004;McCrink & Wynn, 2007;Spaepen et al, 2011). Existují přesvědčivé důkazy (Feigenson et al, 2004;Gilmore, McCarthy & Spelke, 2007;Mazzocco, Feigenson & Halberda, 2011b;Piazza et al, 2010;Park & Brannon, 2014) o tom, že jde o klíčový systém tvořící základy symbolických matematických dovedností u dospělých lidí. K vysvětlení tohoto tvrzení je potřeba blíže rozebrat samotnou podstatu ANS.…”

“…Někteří autoři (např. Sasanguie, Defever et al, 2013;Sasanguie, Gobel et al, 2013;Tibber et al, 2013;Park & Brannon, 2014) toto tvrzení popí-rají a argumentují tím, že na každou studii, která logaritmický vztah potvrzuje (např. Gilmore et al, 2010;Piazza et al, 2010, Mazzocco et al, 2011a, 2011bLibertus, Odic & Halberda, 2012), existuje podobný počet studií (např.…”

“…V předchozím textu jsme uvedli studie, které tuto možnost experimentálně ověřily (např. Park & Brannon, 2014;Wang et al, 2016;Park et al, 2016). Je však potřeba upřesnit, jak by takový trénink měl vypadat.…”