비율 추론을 중심으로 본 아동기 형식적-비형식적 양적 추론 체계의 발달
Two Dissociable Systems of Proportional Reasoning and their Development
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본 연구는 비율 추론을 중심으로 아동기 양적 추론의 두 가지 체계(형식적/비형식적)를 제안하여 그 발달적 특징을 기술하고 그간의 갈등적 연구결과들을 설명하고자 한 것이다. 이를 위하여 서로 다른 체계를 활성하도록 조작된 두 가지 유형의 자극(비연속적 자극/연속적 자극)을 이용한 비율 대응 추론 과제를 4, 6, 8, 10세 아동에게 실시하였으며 다음과 같은 결과를 얻었다. 비율 추론의 형식적 체계를 활성화하도록 조작된 비연속적 자극 조건에서의 아동의 수행은 수학교육 경험과 높은 관련성을 나타냈다. 즉, 분수를 비교하기 위한 수리적 규칙을 학습한 10세 아동만이 성공적으로 수행했으며, 4, 6세의 아동들은 자연수세기 학습의 영향으로 절대적 개념에 근거한 오류를 보였다. 반면 비형식적 체계를 활성화하도록 조작된 연속적 자극 조건에서는 가장 어린 4세 아동도 성공적으로 과제를 수행했으며, 수리적 학습의 경험과 유의미한 관련성을 나타내지 않았다. 본 연구 결과에 비추어 비율 추론의 발달적 근원 및 그 발달 과정을 양적 추론의 두 체계에 근거하여 기술하였다.
Abstract
The present study was designed to describe the two dissociable systems(formal and informal systems) of proportional reasoning and their development. For these ends, 4, 6, 8 and 10-year-olds were asked to judge the equivalence of proportions involving continuous or discrete quantities. In discrete condition where formal system may have been activated, only 10-year-olds succeeded; children aged 4, 6 and 8 performed chance level. Most importantly, 4- and 6-year-olds’ tendency to be misled by the absolute number was significantly related to their counting proficiency and 10 year olds’ successful performance was significantly related to their fluency in fraction use, indicating that their performance in discrete condition was influenced by their acquisition of mathematical convention.; In stark contrast, even 4-year-olds succeeded at matching proportions and children's performance gradually increases with age in continuous condition where informal system may have been activated.; children’s errors did not predominantly consist of erroneously choosing the absolute amount match.
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