Operational momentum during children’s approximate arithmetic relates to symbolic math skills and space–magnitude association

Preschoolers prior formal mathematics education engage numerical magnitude representation rather than counting principles in symbolic ±1 arithmetic: Evidence from the operational momentum effect

“…First of all, the positive correlation we obtained between magnitude OM and arithmetic accuracy is strongly inconsistent with the imperfect decoding/compression hypothesis. It should be noted that: (1) this correlation was independent of age, and therefore likely of other development factors, such as general executive control; and (2) that similar effects are widespread in other developmental studies (Haman & Lipowska, 2021;Jang & Cho, 2022;Knops et al, 2013;Pinheiro-Chagas et al, 2018). In the study by Pinheiro-Chagas et al, OM in non-symbolic arithmetic was correlated with accuracy in the same task; in Jang and Cho, non-symbolic OM correlated with the performance of symbolic arithmetic; in Haman and Lipowska non-symbolic OM correlated with mastering of CP measured in separate tests; and, finally, present study demonstrated correlation of OM and accuracy in a symbolic task (and its relation to the ability to map between non-symbolic and symbolic modes).…”

“…Other studies of OM to date in this and slightly older age groups have used only non-symbolic materials, showing some form of directional OM (Haman & Lipowska, Experiment 1, 2021;Dunn et al, 2019), but less frequently regular magnitude OM (Haman & Lipowska, 2021, but only to a limited extent in Experiment 2; inverted OM in Knops et al, 2013, in 6−7-year-olds that progressed to regular OM only in older children in Pinheiro-Chagas et al, 2018, c.f. also Jang & Cho, 2022).…”

“…The same authors (Gilmore et al, 2010) also found a positive relation between kindergarten non-symbolic arithmetic measured during the school year and end-of-year math test scores. Interestingly, the aforementioned study by Jang and Cho (2022) showed a positive correlation between non-symbolic OM and symbolic arithmetic performance in first-graders. Park et al (2016) showed the effect of a short non-symbolic arithmetic training on math performance in preschoolers, but, interestingly, a similar effect was not replicated either in adults (Szkudlarek et al, 2021) or in third-and fourth-graders (Bugden et al, 2021).…”

“…The same authors (Gilmore et al., 2010) also found a positive relation between kindergarten non‐symbolic arithmetic measured during the school year and end‐of‐year math test scores. Interestingly, the aforementioned study by Jang and Cho (2022) showed a positive correlation between non‐symbolic OM and symbolic arithmetic performance in first‐graders. Park et al.…”

“…Interestingly, it was positively correlated with accuracy (children who chose the correct result more often also made systematic under/overestimation errors depending on the operation). Also Jang and Cho (2022) showed that non‐symbolic OM in 7‐ to 8‐year‐olds positively correlated with symbolic arithmetic and with the number‐size congruity effect (which is a kind of the spatial‐numerical association) but not with the estimation of the number's position on the number‐line. Note that the number‐line estimation task was designed to investigate the mapping of numerical quantities onto the spatial representation, so it may be expected that it involves the same spatial‐numerical associations, and require the same kind of numerical transformations (e.g., decoding logarithmically scaled representations) as arithmetic.…”