Learning to run the number line: the development of attentional shifts during single‐digit arithmetic

Abstract

Solving single-digit subtraction and addition problems is associated with left and right shifts of attention in adults. Here, we explored the development of these spatial shifts in children from the third to fifth grade. In two experiments, children solved single-digit addition (Experiments 1 and 2), subtraction (Experiment 1), and multiplication (Experiment 2) problems in which operands and the arithmetic sign were shown sequentially. Although the first operand and the arithmetic sign were presented on the center of a screen, the second operand was presented either in the left or the right visual field. In Experiment 1, we found that subtraction problems were increasingly associated with a leftward bias by the fifth grade, such that problem solving was facilitated when the second operand was in the left visual field. In Experiment 2, we found that children can also associate addition problems with the right side of space by the fourth grade. No developmental increase in either leftward or rightward bias was observed for multiplication problems. These attentional shifts might be due to the increasing reliance on calculation procedures that involve mental movements to the left or right of a sequential representation of numbers during subtraction and addition.

Eye movements reveal that young school children shift attention when solving additions and subtractions

“…However, unlike SNAs in single numbers, SNAs in arithmetic were recently shown to be independent from the orientation of reading and writing direction as monolingual adults of opposite reading directions (i.e., Arabic and French-speaking participants) showed an identical rightward spatial bias for additions and leftward bias for subtractions (Masson et al, 2020). These different underlying roots for single numbers and arithmetic SNAs are in line with recent theoretical proposals suggesting that SNAs, despite their behavioral resemblance, could tap into distinct and independent cognitive mechanisms (Cipora et al, 2018) Mathieu et al (2016), consisting in a task in which children had to solve simple arithmetical problems with the second operand presented to the right or to the left 300 ms after the presentation of the operator (Díaz-Barriga Yáñez et al, 2020). In their first experiment, the authors showed that presenting the second operand on the left facilitated subtraction solving in 5th Graders but not in 3rd and 4th Graders.…”

Priming effects of arithmetic signs in 10‐ to 15‐year‐old children

“…Contrary to what we expected, we did not find any correlation between these two variables, whatever the age of children. It is therefore possible that priming effects, and therefore automated procedures, emerge as a result of development or cognitive maturation rather than increase in arithmetic fluency per se (see also, Díaz‐Barriga Yáñez et al, 2020 for similar results and conclusions). Still, such an interpretation might seem at odds with the way Fayol and Thevenot (2012, Exp.…”

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

“…In turn, in the study by Díaz‐Barriga Yáñez et al. (2020), in single‐digit symbolic arithmetic, a change from a reversed directional OM in younger children (third graders) to regular OM in older children (fifth graders) was shown. In studies with adults, the plasticity of linking arithmetic operations with the direction of attention orienting depending on various factors, such as the size of the operands or, importantly, the method of focusing attention (valid cue, distractor, etc.)…”

“…Haman and Lipowska (2021), in a procedure analogous to the present study, showed a regular directional OM for non-symbolic ± 5 arithmetic and reversed OM in the ± 1 non-symbolic problem, similar to symbolic ± 1 arithmetic in the current study. In turn, in the study by Díaz-Barriga Yáñez et al (2020), in single-digit symbolic arithmetic, a change from a reversed directional OM in younger children (third graders) to regular OM in older children (fifth graders) was shown. In studies with adults, the plasticity of linking arithmetic operations with the direction of attention orienting depending on various factors, such as the size of the operands or, importantly, the method of focusing attention (valid cue, distractor, etc.)…”