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이종일 한국사회과교육연구학회 2004 사회과교육 Vol.43 No.2
Bruner가 교육의 목적을 지식의 '일반적 전이'라고 주장한 이후 개념 학습은 학문중심 교육과정에서 주요 문제로 대두되었다. 그런데 우리나라에서 개념 학습은 입시에서 지식중심 평가의 영향으로 '일반적 전이'보다는 개념 자체 '이해'에 그치는 경향이 높다. 이 결과 개념 학습은 개념 자체를 아는 정도이면 평가에 아무런 문제가 없기 때문에 그것을 '언어화'하여 타인에게 이야기하는 상태로 나아가는 경우가 드물다. 하지만 개념을 일상성 속에서 언어화하여 사용하는 것이 학습자가 고등사고로 나아가는데 토대가 된다는 점을 이해한다면, 개념 언어화를 위한 질문은 교사의 필수적 자질의 하나라 할 수 있다. 필자는 개념 언어화를 위한 질문으로 Taba의 질문전략을 제시하고, 그의 질문전략이 이후 여러 연구자들의 개념 언어화 질문의 토대가 되고 있음을 밝혀보고자 한다. The concept learning has been highly recognized in a curriculum since Bruner mentioned 'general transfer' of knowledge was the major purpose of education. The way of differentiation of students has been strongly influenced by the entrance examination in Korea. The concept learning has placed more weight on understanding concept itself than 'general transfer'. Many Korean teachers have assumed that students have needed to know the concept itself, and that they have not needed to transfer the concept to others with verbal. However, when the Korean teachers understand that verbalizing concept helps learners to improve their thinking power, they consider the essential disposition of teacher as making questions that encourage students to verbalize concepts. This research utilizes Taba's strategy of Questioning as a method of making Questions that stimulate students to verbalize concepts. It discovers that Taba's strategy of questioning has been adopted in much research dealing with strategies of questionings for verbalizing concept. It suggests that the formation of concepts in textbooks in the USA has followed the Taba's strategy of questioning.
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대수 증명에서 종속적 일반성의 인식 및 특정수 전이에 관한 연구
강정기 ( Jeong Gi Kang ),장혜원 ( Hye Won Chang ) 한국수학교육학회 2014 수학교육 Vol.53 No.1
Algebra deals with so general properties about number system that it is called as ``generalized arithmetic``. Observing students` activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.
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