• Journal of Educational Research in Mathematics
• /
• v.11 no.2
• /
• pp.351-362
• /
• 2001

Piaget's genetic epistemology has been known as the basis of the 'New Math' and as the opposite point of view to the historico-genetic principle. But these days Piaget's theory is considered to support the historico-genetic principle so that it influences many studies. This study shows the reason of the difference of interpretations of Piaget's theory.

• Journal of Educational Research in Mathematics
• /
• v.11 no.2
• /
• pp.291-305
• /
• 2001

The major purpose of this study is to show the insufficiency of traditional epistemology and consructivism as epistemology of mathematics education. Traditional epistemology such as empiricism, rationalism, Kant's epistemology, and Piaget's genetic epistemology is not sufficient to explain episteme in educational situation because it regards that epsteme is the phenomenon occurs between the abstract individual subject and the object world. Modern epistemology like constructivism recognize the public or social character of epsteme. So it is more appreciate than traditional epistemology to explain episteme in math educational situation. But constructivist pedagogy derived from constructivist learning theory has the following important shortcoming: The lack of clear criteria by which instructional effectiveness might be evaluated from a constructivist perspective.

• School Mathematics
• /
• v.15 no.2
• /
• pp.221-241
• /
• 2013

This study considers the experiment of Inhelder and Piaget(1963) in various aspects, and reveals the characteristics of the 'the formation of a critical mind', 'the transformation into the research question', 'the translation into the experiment', and 'the interpretation of the result of the experiment' in Piaget's genetic epistemology. According to these analyses, this study discusses the educational implications that the results of the Piaget's experiment support the education which raises the student's awareness.

• Journal of Educational Research in Mathematics
• /
• v.8 no.2
• /
• pp.553-563
• /
• 1998

In this thesis, I examined Bruner's EIS theory from the viewpoint of epistemology based on Piaget's genetic epistemology. Although Bruner's ideal thought which insisted ‘to teach the structure’accepted Piaget's theory in the methodology of realization, it is different from Piaget in understanding knowledge. The difference is shown from understanding the meaning of ‘structure’. Piaget's concept of structure is something that has overcome the realistic viewpoint of the traditional epistemology and is reconstructed through endless self-regulative transformational process. However Bruner's is used as a realistic meaning as we can see in the Plato's recollection theory. Therefore Piaget's ‘stage of development’means the difference of structure which lies in the generative process and it includes the qualitive difference of level. On the other hand, Bruner, who is trying to translate and suggest the fixed structure to the children understood Piaget's stage of development as the difference in the ways of representation. Piaget's operational constructivism insists that the children should ‘construct’the knowledge through their activity, and especially in case of the lohico-mathematical recognition, the source should be internalized activity, that is, operation. In view of this assertion, Burner's idea which insists to accept the structure of knowledge as a fixed reality and to suggest the translated representation proper to the cognitive structure of the children to teach them, has a danger of emphasizing only the functional aspects to deliver the given knowledge ‘quickly’. And it also has the danger of damaging ‘the nature of the knowledge’in the translated knowledge.

• Journal of Educational Research in Mathematics
• /
• v.12 no.3
• /
• pp.409-424
• /
• 2002

The historico-genetic principle has been advocated continuously, as an alternative one to the traditional deductive method of teaching and learning mathematics, by Clairaut, Cajori, Smith, Klein, Poincar$\'{e}$, La Cour, Branford, Toeplitz, etc. since 18C. And recently we could find various studies in relation to the historico-genetic principle. Lakatos', Freudenthal's, and Brousseau's are representative in them. But they are different from the previous historico- genetic principle in many aspects. In this study, the previous historico- genetic principle is called as classical historico- genetic principle and the other one as modern historico-genetic principle. This study shows that the differences between them arise from the historical views of mathematics and the development of the theories of mathematics education. Dewey thinks that education is a constant reconstruction of experience. This study shows the historico-genetic principle could us embody the Dewey's psycological method. Bruner's discipline-centered curriculum based on Piaget's genetic epistemology insists on teaching mathematics in the reverse order of historical genesis. This study shows the real understaning the structure of knowledge could not neglect the connection with histogenesis of them. This study shows the historico-genetic principle could help us realize Bruner's point of view on the teaching of the structure of mathematical knowledge. In this study, on the basis of the examination of the development of the historico-genetic principle, we try to stipulate the principle more clearly, and we also try to present teaching unit for the logarithm according to the historico- genetic principle.

• Journal of Educational Research in Mathematics
• /
• v.14 no.1
• /
• pp.129-142
• /
• 2004

These days, constructivism has become a central theory in mathematics education. A essential concept in constructivism is 'construction' and the meaning of construction of mathematical knowledge is a core issue in mathematics educational field. In the basis of Dewey's epistemology, this article is trying to explicate the meaning of construction of mathematical knowledge. Dewey, Kant and Piaget coincide in construction of knowledge from the viewpoint of the interaction between mind and environment. However, unlike Dewey's concept, Kant and Piaget are still in the line of traditional realistic epistemology. Dewey's concept of construction logically implies teaching-learn learning principles. This can be named as a principle of genetic construction and a principle of progressive consciousness.

• Journal of Korean Elementary Science Education
• /
• v.19 no.1
• /
• pp.85-99
• /
• 2000

Researches have shown that learning science frequently requires the process of conceptual change. As a result, many of the constructivist teaching and loaming approaches focus on this kind of loaming. In approaches that focus on conceptual change, cognitive conflict strategies play a key role. Students, however, still have much difficulty in loaming science. Theoretically, it underlies Piaget's genetic epistemology in which disequilibration demands an interplay between assimilation and accommodation until equilibrium is restored. Also, radical constructivism has its roots in a variety of disciplines, but has been most profoundly influenced by the theories of lean Piaget as interpreted and extended by Glasersfeld. This study is intended to interpret the conceptual change from radical constructivist perspective and explain difficulties of conceptual change which students have in learning science.

• Journal of Educational Research in Mathematics
• /
• v.18 no.1
• /
• pp.1-24
• /
• 2008

The purpose of this study is to uncover weaknesses in the constructivism in mathematics education and to search for ways to complement these deficiencies. We contemplate the relationship between the capability of construction and the performance of it, with the view of the 'Twofold-Structure of Mind.' From this, it is claimed that the construction of mathematical knowledge should be to experience and reveal the upper layer of Mind, the Reality. Based on the examination on the conflict and relation between the structuralism and the constructivism, with reference to the 'theory of principle' and the 'theory of material force' in Neo-Confucianist theory, it is asserted that the construction of mathematical knowledge must be the construction of the structure of mathematical knowledge. To comprehend the processes involved in the construction of the structure of mathematical knowledge, the epistemology of Michael Polanyi is studied. And also, the theory of mathematization, the historico-genetic principle, and the theory on the levels of mathematical thinking are reinterpreted. Finally, on the basis of the theory of twofold-structure, the roles and attitudes of teachers and students are discussed.