피아제의 명제논리와 베이지언 인과추론에 근거한 구조구성주의 융합교수학습모형 개발 = Teaching-Learning Model of Structure-Constructivism Based on Piagetian Propositional Logic and Bayesian Causational Inference

다국어 초록 (Multilingual Abstract)

With this article, I would like to introduce the new teaching-learning model synthesizing the Bayesian probabilistic models and Piaget’s propositional ones of learning. I call this new model “Bayesian structure-constructivist Model of Teaching-learning”(abbreviation: BMT). Teaching theory is usually based on analyzing the learning theory. I will first compare and criticise Piagetian learning theory and Bayesian one in terms of historical genesis and formalization. Then, I will present and justifier the main features of BMT. BMT first underlines that learning is an interaction between representation and sampling, that children always distinguish between week sampling and strong sampling, spacially between pedagogical sampling and non-pedagogical. Second, BMT supposes that, to select examples to facilitate learning, teachers have to use the Bayesian mode of pedagogical reasoning, and combine the direct instruction and discovery learning. Finally, Even though children may sometimes learn abstract rules earlier than more concrete ones(the blessing of abstraction), we should accept Piagetian logical grammars as a possible broad language of thought and hierarchical systems of logical levels. This is because the blessing of abstraction is consistent with developmental data: learning more abstract knowledge in most areas depends on first learning more concrete kinds of knowledge.

국문 초록 (Abstract)

본 연구의 목적은 최근 20여 년 동안 진행되어 온 학습이론에 대한 피아제의 명제논리학적 학습이론과 베이즈주의의 확률론적 학습이론의 융합에 근거하는 새로운 융합교수학습모형을 개발하는 것이다. 연구자는 이 새로운 교수학습모델을 “베이지안 구조구성주의 교수학습모형”(Bayesian structure-constructivist Model of Teaching-learning: 이하 약칭 BMT)이라 명명한다. 본고는 역사-비판적 관점 및 형식화적 관점에서 피아제의 명제논리학적 학습모형에서 해석된 학습이론과 베이즈주의의 확률론적 추론모형에서 해석된 학습이론을 일차적으로 분석하고, 논문의 후반부에서는 이를 근거로 교수법의 관점에서 양자의 학습이론을 통합하는 새로운 교수학습모델, 즉 BMT의 중요한 특성들을 세부적으로 제시한다. 몇 가지 핵심만 언급하면, 첫째로, BMT는 개념 학습이든 이론 학습이든 모든 학습은 표상과 샘플링의 상호작용임을 강조한다. 매우 이른 나이에서부터 아동은 학습하기 이전에 자기에게 주어진 예시들이 약한 샘플링인지 강한 샘플링인지, 특히 교육학적 샘플링인지 비교육학적 샘플링인지를 구분한다. 둘째로, 따라서 학습을 촉진시킬 수 있는 샘플을 선택하기 위해서 교사는 교육학적 추론을 위한 베이지안 모델을 활용하면서 직접적인 강의식 수업과 발견학습 수업을 병행해야 한다. 셋째로, 아동은 때때로 구체적인 규칙들보다는 추상적인 규칙들을 먼저 학습하기도 하지만, 대부분의 영역에서 추상적인 지식의 학습은 구체적인 지식의 학습에 의존한다. 따라서 성공적인 학습을 위해서는 피아제가 강조한 보편적 언어로서 논리적 문법과 그들 사이의 위계성을 고려하는 샘플을 개발하고 제시해야 한다.

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