Visual form perception predicts 3-year longitudinal development of mathematical achievement


Numerous studies have demonstrated an association between approximate number system (ANS) acuity and mathematical performance. Studies have also shown that ANS acuity can predict the longitudinal development of mathematical achievement. Visual form perception in the current investigation was proposed to account for the predictive role of ANS acuity in the development of mathematical achievement. One hundred and eighty-eight school children (100 males, 88 females; mean age = 12.2 ± 0.3 years) participated in the study by completing five tests: numerosity comparison, figure matching, mental rotation, nonverbal matrix reasoning, and choice reaction time. Three years later, they took a mathematical achievement test. We assessed whether the early tests predicted mathematical achievement at the later date. Analysis showed that the ANS acuity measured via numerosity comparison significantly predicted mathematical achievement 3 years later, even when controlling for individual differences in mental rotation, nonverbal matrix reasoning, and choice reaction time, as well as age and gender differences. Hierarchical regression and mediation analyses further showed that the longitudinal predictive role of ANS acuity in mathematical achievement was interpreted by visual form perception measured with a figure-matching test. Together, these results indicate that visual form perception may be the underlying cognitive mechanism that links ANS acuity to mathematical achievement in terms of longitudinal development.

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This research was supported by three Grants from the Natural Science Foundation of China (31671151, 31600896, and 31521063), the 111 Project (BP0719032), and a Grant from the Advanced Innovation Center for Future Education (27900-110631111). The investigation received approval from the institutional review board (IRB) at the State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, as well as from the primary schools.

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Correspondence to Xinlin Zhou.

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Appendix: Examples used in the self-adapted mathematical achievement test

Appendix: Examples used in the self-adapted mathematical achievement test

Arithmetic problem:

9.3 × 6 means to

A: count 9.3 for 6 times

B: count 9.3 for 3 times

C: count 9.3 for 4 times

D: count 9.3 for 5 times

E: count 6 for 9.3 times

Algebraic problem:

Below shows faulty steps used to solve the equation 5x ‒ 40 = 20. From which step did the mistake occur?

Step 1: 5x ÷ 5 ‒ 40 = 20 ÷ 5

Step 2: x ‒ 40 = 4

Step 3: x ‒ 40 + 40 = 4 + 40

Step 4: x = 44

A: Step 1

B: Step 2

C: Step 3

D: Step 4

E: Not sure

Geometric problem:


If the total surface area of the rectangular solid shown above is 24 square centimeters, what is the sum if the red, yellow, and blue areas are added up (expressed in square centimeters)?

A: 10

B: 20

C: 14

D: 16

E: 12

Statistical problem:

There are four kinds of vegetables planted in a field: green peppers, cucumbers, towel gourds, and eggplants. The figure below shows the area used for planting each vegetable.


The percentage of area where green peppers are planted is ( )%.

If the area for planting towel gourds is 300 m2, then area for planting eggplants is ( ) m2.

( ) has the largest area for planting, which is ( )% larger than the area for green peppers.

A: 20; 160; Cucumbers; 25

B: 30; 160; Cucumbers; 125

C: 20; 150; Towel gourd; 5

D: 20; 140; Towel gourd; 5

E: 20; 120; Cucumbers; 125

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Zhou, X., Hu, Y., Yuan, L. et al. Visual form perception predicts 3-year longitudinal development of mathematical achievement. Cogn Process (2020).

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  • Mathematical cognition
  • Approximate number system
  • Visual form perception
  • Mathematical achievement
  • Longitudinal development