New Evidence on Causal Relationship between Approximate Number System (ANS) Acuity and Arithmetic Ability in Elementary-School Students: A Longitudinal Cross-Lagged Analysis.

He Y, Zhou X, Shi D, Song H, Zhang H, Shi J - Front Psychol (2016)

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Figure 1: (A) Schematic of the dot-array comparison task used to measure Approximate Number System (ANS) acuity of participants. (B) An example of multiplication task used to measure arithmetic ability of participants.
Mentions: The ANS acuity of the participants was assessed by a non-symbolic dot comparison task, adapted from the second edition of the Test of Early Mathematics Ability (Ginsburg and Baroody, 1983). The task has been used in recent studies (Zhou and Cheng, 2014; Zhou et al., 2015). As shown in Figure 1A, three screens were presented sequentially in this task. Screen 1 and Screen 3 were black screens containing no information; on Screen 2, two sets of dot-arrays with different number of dots were presented. The participants were asked to choose the more numerous dot-array by pressing the corresponding keys on the computer keyboard. The dot-arrays were created following a common procedure to control for the non-numerical, continuous variables in the ANS task (e.g., Halberda et al., 2008; Agrillo et al., 2013). For half of the ANS tasks, the total combined area of all dots in each dot-array was the same; for the other half of the ANS trials, the average area of dots in each set was the same. The dots in each dot-array were randomly distributed within a circle and the sizes of the dots varied randomly. The number of dots in each dot-array varied from 5 to 32, and the ratio between the number of dots in the two dot-arrays was above 1.2 but below 2.0. The second screen with dot-arrays was only presented for 200 ms, which was too short for participants to count the dots individually. There was no time limit for an answer. The test consisted of 120 trials, with 40 trials for each session. The ANS acuity of the participants was measured using the accuracy, rather than other indices, as suggested by Inglis and Gilmore (2014). The Cronbachâ€™s alpha of the ANS acuity task was 0.80 in the current study.

Bottom Line: Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies.The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported.Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences Beijing, China.

ABSTRACT
Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies. However, whether and how these two measures are causally related still remain less addressed. There are two hypotheses about the possible causal relationship: ANS acuity influences mathematical performances, or access to math education sharpens ANS acuity. Evidences in support of both hypotheses have been reported, but these two hypotheses have never been tested simultaneously. Therefore, questions still remain whether only one-direction or reciprocal causal relationships existed in the association. In this work, we provided a new evidence on the causal relationship between ANS acuity and arithmetic ability. ANS acuity and mathematical ability of elementary-school students were measured sequentially at three time points within one year, and all possible causal directions were evaluated simultaneously using cross-lagged regression analysis. The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported. Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.

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