초등학생의 분수 덧셈 뺄셈 계산 과정의 분석을 통해서 다양한 인지적 장애 현상의 유형을 확인할 수 있었다. 이러한 분수 계산에서 나타나는 인지적 장애 현상의 원인을 인식론적, 심리적 요인으로 구분하여 분석하였다. 인식론적 요인으로는 과잉 일반화, 직관의 영향, 언어적 표현의 영향, 부분에만 주목하는 경향을, 심리적 요인으로는 도구적 이해, 오류적 개념 이미지, 자연수 계산에 대한 집착, 문제 조건 변형을 통한 개인적 이해 등을 확인할 수 있었다. 앞의 분석 결과를 바탕으로 학생들이 분수 계산에서 겪는 인지적 장애 극복을 위한 방안과 관련하여 다음의 결론을 얻었다. 첫째, 학생들 스스로 분수 덧셈과 뺄셈에 대한 잘못된 인식을 깨닫고 올바른 이해를 도울 수 있는 지도 방안의 고려가 필요하다. 둘째, 알고리즘과 형식화에 치중하기보다 다양한 활동을 통해 원리를 이해하도록 지도하는 활동이 무엇보다 중요하다. 인지적 장애는 선행 지식과의 관련성 외에 인식론적, 심리적 요인들의 복합적인 작용에 기인하므로 선행지식을 재지도하는 방식을 넘어 다양한 인지적 장애 원인을 고려한 수업 연구가 이루어져야 할 것으로 생각한다.
초등학생의 분수 덧셈 뺄셈 계산 과정의 분석을 통해서 다양한 인지적 장애 현상의 유형을 확인할 수 있었다. 이러한 분수 계산에서 나타나는 인지적 장애 현상의 원인을 인식론적, 심리적 요인으로 구분하여 분석하였다. 인식론적 요인으로는 과잉 일반화, 직관의 영향, 언어적 표현의 영향, 부분에만 주목하는 경향을, 심리적 요인으로는 도구적 이해, 오류적 개념 이미지, 자연수 계산에 대한 집착, 문제 조건 변형을 통한 개인적 이해 등을 확인할 수 있었다. 앞의 분석 결과를 바탕으로 학생들이 분수 계산에서 겪는 인지적 장애 극복을 위한 방안과 관련하여 다음의 결론을 얻었다. 첫째, 학생들 스스로 분수 덧셈과 뺄셈에 대한 잘못된 인식을 깨닫고 올바른 이해를 도울 수 있는 지도 방안의 고려가 필요하다. 둘째, 알고리즘과 형식화에 치중하기보다 다양한 활동을 통해 원리를 이해하도록 지도하는 활동이 무엇보다 중요하다. 인지적 장애는 선행 지식과의 관련성 외에 인식론적, 심리적 요인들의 복합적인 작용에 기인하므로 선행지식을 재지도하는 방식을 넘어 다양한 인지적 장애 원인을 고려한 수업 연구가 이루어져야 할 것으로 생각한다.
This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the...
This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.
This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.
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