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

국문 초록 (Abstract)

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.

다국어 초록 (Multilingual 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.

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