The Correlation between Distance Effects from Magnitude/Order Comparison and their relationships with math achievement

최근 수의 순서 정보가 어떻게 표상되는지에 대한 관심이 높아지고 있다. 본 연구는 성인을 대상으로 상징적 숫자와 비상징적 선분을 사용한 순서 비교(Order Comparison, OC) 및 크기 비교(Magnitude Comparison, MC) 과제를 실시하였다. 그리고 각 과제에서 측정한 거리 효과 간 상관관계를 분석하고, 각 거리 효과와 수학 성취도와의 관계성을 검증하였다. 연구 결과, 숫자 OC 과제에서 자극 간 거리가 작을 때 더 효율적인 수행이 관찰되는 역 거리 효과가 나타난 반면, 길이 OC 및 MC 과제에서는 자극 간 거리가 클 때 더 효율적인 수행이 나타나는 고전적 거리 효과가 관찰되었다. 또한, 숫자 OC 과제와 숫자 MC 과제, 길이 OC 과제와 길이 MC 과제, 숫자 OC 과제와 길이 MC 과제의 거리 효과 간 상관관계가 유의하였다. 여러 거리 효과 중에서 숫자 OC 과제의 역 거리 효과만이 수학 성취도를 예측하였다. 본 연구 결과를 선행 연구와 함께 고려하면, 서수와 기수 표상 간에 부분적으로 공유되는 체계가 존재할 가능성이 있으나 수학 성취도에 미치는 영향은 발달 단계 등에 따라 서로 다를 수 있음을 시사한다.

keywords: 서수 표상, 기수 표상, 역 거리 효과, 고전적 거리 효과, 수학 성취도, ordinality, cardinality, reverse distance effect, canonical distance effect, math achievement

Abstract

There has been growing interest in ordinal representations and their contributions to mathematical cognition. The present study measured distance effects based on magnitude/order comparison (MC/OC, respectively) tasks using symbolic numbers and non-symbolic lines as stimuli. We examined whether distance or reverse distance effects from these tasks are correlated with one another as well as with math achievement. A reverse distance effect (i.e., better performance when the distance between stimuli is smaller) was observed from the Number OC task, while canonical distance effects were observed from the Length OC and MC tasks. There were correlations between distance effects from Number OC and MC tasks, between Length OC and MC tasks and between Number OC and Length MC tasks. Among all, only the reverse distance effect from the Number OC task predicted math achievement scores in a linear regression model. These results suggest that cardinal and ordinal representations may depend on partially shared mechanisms, yet they may independently contribute to math achievement during distinct phases of development.

keywords: 서수 표상, 기수 표상, 역 거리 효과, 고전적 거리 효과, 수학 성취도, ordinality, cardinality, reverse distance effect, canonical distance effect, math achievement

참고문헌

Arthur Jr, W., Tubre, T. C., Paul, D. S., & Sanchez-Ku, M. L. (1999). College-sample psychometric and normative data on a short form of the Raven Advanced Progressive Matrices Test. Journal of Psychoeducational Assessment, 17(4), 354-361.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hilsdale. NJ: Lawrence Earlbaum Associates, 2.

De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of experimental child psychology, 103(4), 469-479.

Fias, W., Lammertyn, J., Caessens, B., & Orban, G. A. (2007). Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. Journal of Neuroscience, 27(33), 8952-8956.

Foster, J. L., Shipstead, Z., Harrison, T. L., Hicks, K. L., Redick, T. S., & Engle, R. W. (2015). Shortened complex span tasks can reliably measure working memory capacity. Memory & cognition, 43(2), 226-236.

Franklin, M. S., & Jonides, J. (2009). Order and magnitude share a common representation in parietal cortex. Journal of cognitive neuroscience, 21(11), 2114-2120.

Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N.,... Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PloS one, 8(6), e67374.

Goffin, C., & Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150, 68-76.

Hoffmann, D., Hornung, C., Martin, R., & Schiltz, C. (2013). Developing number-space associations: SNARC effects using a color discrimination task in 5-year-olds. Journal of experimental child psychology, 116(4), 775-791.

10.

Jang, S., & Cho, S. (2016). The acuity for numerosity (but not continuous magnitude) discrimination correlates with quantitative problem solving but not routinized arithmetic. Current Psychology, 35(1), 44-56.

11.

Knops, A., & Willmes, K. (2014). Numerical ordering and symbolic arithmetic share frontal and parietal circuits in the right hemisphere. Neuroimage, 84, 786-795.

12.

Lyons, I., Vogel, S., & Ansari, D. (2016). On the ordinality of numbers: a review of neural and behavioral studies. Progress in brain research, 227, 187-221.

13.

Lyons, I. M., & Beilock, S. L. (2013). Ordinality and the nature of symbolic numbers. Journal of Neuroscience, 33(43), 17052-17061.

14.

Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., & Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714-726.

15.

Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519-1520.

16.

Park, K., Lee, H., Im, H. (2008). Test equating of paper-based and computer-based versions of the Korean Job Aptitude Scale for Adults. Seoul: Korea Employment Information Service.

17.

Reynvoet, B., & Sasanguie, D. (2016). The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol-Symbol Associations. Frontiers in Psychology, 7.

18.

Rubinsten, O., Dana, S., Lavro, D., & Berger, A. (2013). Processing ordinality and quantity: ERP evidence of separate mechanisms. Brain and cognition, 82(2), 201-212.

19.

Turconi, E., Campbell, J. I., & Seron, X. (2006). Numerical order and quantity processing in number comparison. Cognition, 98(3), 273-285.

20.

Vogel, S. E., Remark, A., & Ansari, D. (2015). Differential processing of symbolic numerical magnitude and order in first-grade children. Journal of experimental child psychology, 129, 26-39.

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논문 상세

Vol.30 No.1

기수와 서수 비교의 거리 효과 간 상관 및 수학 성취도와의 관계 분석

The Correlation between Distance Effects from Magnitude/Order Comparison and their relationships with math achievement

초록

Abstract

참고문헌

한국심리학회지: 인지 및 생물