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ISSN : 1229-0718
비율 추론(proportional reasoning)은 생활에 만연되어 있는 추론 능력 중 하나로써 둘 이상의 수량간의 상대적 크기(relative quantities)에 대한 관계적 표상(relational representation)을 포함하며 아동의 인지 발달을 기술하고 설명하는데 있어 핵심적 영역이다. 본 논문에서는 비율 추론의 기원과 발달에 관한 서로 다른 주장들과 이를 뒷받침하는 연구 결과를 중심으로 비율 추론의 어려움뿐 아니라 초기 발달의 기원을 살펴보았다. 특히 이전의 연구에서 비율 추론 과제에서의 난이도에 영향을 준 것으로 여겨지는 과제변인들을 규명함으로써 과거 상반된 연구 결과들을 설명하고자 하였다. 제안된 변인으로는 1) 과제가 판단하기를 요구하는 비율간의 관계(등가 대 서열), 2) 아동의 수학적 지식과 기술의 습득, 3) 자극 수량의 유형(연속적 대 비연속적) 그리고 4) ‘반’의 경계의 이용가능성이다. 이들을 직접 검증한 최근의 몇몇 연구들을 논의하였고 나아가 이에 근거하여 수학 교육에 대한 함의와 그 시사점은 논의 했고, 앞으로 진행되어야 할 연구 방향을 제시하였다.
Proportional reasoning is the one of the core abilities prevalent in our everyday life that involves relational representation about relative quantities. A body of literature was reviewed that has produced contrasting views about the onset age of proportional reasoning. Crucially, several task factors that may be responsible for the varying results in the previous studies were suggested. These factors include 1) relation being asked (equivalence vs. ordinality), 2) the acquisition of mathematical convention, 3) quantitative types of stimulus (continuous vs, discrete) and 4) availability of half-boundary. A few recent studies that directly tested the effects of these task factors were discussed. Educational implication on teaching mathematical concepts and the future direction of researches on proportional reasoning abilities are also addressed.
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