Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

Abstract

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics.

Keywords: Approximate number system; Children; Mathematics; Numerical cognition; Symbols; Training.

Figure 1

Schematic depiction of training tasks. Stimulus events are organized horizontally from start (top) to finish (bottom). The numbers indicate the duration of presentation. The horizontal arrows indicate stimulus movement. The vertical arrows indicate the following event.

Figure 2

Average training task performance over time in Experiment 1. a) Average reaction time (in milliseconds) for each condition. b) Average task accuracy (expressed as percent correct) for each condition.

Figure 3

Effects of ratio on average training performance over time in Experiment 1.

Figure 4

Average symbolic arithmetic test performance in Experiment 1. a) Average speed of test completion (in seconds) for each condition b) Average test accuracy (expressed as percent correct) for each condition.

Figure 5

Average training task performance over time in Experiment 2. a) Average reaction time (in milliseconds) for each condition. b) Average accuracy (expressed as percent correct) for each condition.

Figure 6

Average arithmetic and sentence completion test performance in Experiment 2. a) Average speed (in seconds) on each test type for each condition b) Average accuracy (expressed as percent correct) on each test type or each condition.

Figure 7

Average symbolic arithmetic test performance over time in Experiment 2. a) Average speed (expressed in seconds) on each test set for each condition. b) Average accuracy (expressed as percent correct) on each test set for each condition.