• The Mathematical Education
• /
• v.47 no.2
• /
• pp.221-224
• /
• 2008

The article shows that the concept 'weight' and the concept 'heaviness' give rise to different abstractions in the sense of Piaget and that these two concepts are differentiated by set-theoretic devices. The failure of differentiation of these two concepts 'weight' and the 'heaviness' can cause the failure of learning of the difference between reflective abstraction and empirical reflective abstraction. To explain the Piagetian abstrcation in a classroom, the author suggests to use the concept 'color' instead of the concept 'weigtht'.

• Journal of the Economic Geographical Society of Korea
• /
• v.15 no.4
• /
• pp.457-463
• /
• 2012

This study examines the epistemological approach of the economic geography and the approach in the ontology of geography which has been studied based on the region, and thereby aims at the systematization of economic geography. Since 1956, Korean economic geography study has been conducted under the development of studies in developed countries without discussing the uniqueness of the study or the systematization of the research approaches. As a result, the systematization is built after the economic geography is divided into neoclassical economy, geographical political economy, regional structure of the national economy, and local autonomous entity economy on a axis of epistemology and ontology for the systematization of approaches. We should pursue the intellectual change adding the major economic phenomena theories such as the world-system perspective, the regulation theory, network theory, and the institutionalism etc. into the systematization of the economic geography.

• Journal for History of Mathematics
• /
• v.22 no.3
• /
• pp.113-130
• /
• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

• Journal of Educational Research in Mathematics
• /
• v.16 no.3
• /
• pp.179-198
• /
• 2006

In This Paper, I call Johnson & Lakoff (1980; 1999)'s Experientialism or Experiential Realism or, Embodied Realism, Nunez(1995; 1997)'s Ecological Naturalism as Experientialism and try to investigate the possibility of their Experientialism to be a philosophy of mathematical education. This possibility is approached in the respect with the problem of objectivism and relativism. I analyzed the epistemological background of embodied cognition first and then mathematical epistemology of experientialism. Experientialism shares its Philosophical position partly with Dewey and Merleau-Ponty. Experientialists deny the traditional hypothesis of philosophy as such separability of subject and object, and of body and rationality and also They have better position of epistemology than that of Hamlyn, and of Social Constructivism. Therefore, They guarantee wider range of mathematical universality than Hamlyn and Social constructivist. I conclude that the possibility of Experientialism to be a philosophy of mathematical education depends on the success of its supporting the practical study on mathematics education.

• Journal of Christian Education in Korea
• /
• v.66
• /
• pp.11-48
• /
• 2021

This paper is a thesis that explored the necessity and possibility of spiritual teaching that forms the inner side of human beings in the age of AI where objective knowledge is prevalent, focusing on "contemplative pedagogy". For this it first examined the characteristics of objective epistemology of AI and the direction of school education in the AI and explored the necessity and character of spirituality and spiritual teaching as a request for the AI era, and also explores the possibility of realization of spiritual teaching in general school setting through contemplative pedagogy, which actually puts this into practice. As a result of the study, it found that spiritual teaching is not exclusive to a specific area such as religious studies or theology, but is a teaching that should be embodied in all schools and educational fields in today's era where third person knowledge is widespread. It also found that in addition to contemplative teaching, various spiritual teaching models need to be developed and put into practice for this purpose.

• The Journal of Korean Philosophical History
• /
• no.35
• /
• pp.361-384
• /
• 2012

In this study, I considered an important characteristic of system in pre-Qin philosophy that accomplished all categories with the best value. I pointed out misreading that thinkers separated fazhi-theory from shu zhi- theory of Hanfeizi. So I analyzed argument causes of Hanfeizi's shuzhi-theory through epistemology, ethics, military theory. And I proved that understanding the actual conditions and essences of things assured the objective bases on a reward and punishment. There are three things about argument bases of Hanfeizi's shuzi-theory. First, the epistemology that analyzes the actuality of a thing and that endows a duty matching the natural character of a thing. Second, ethics that isn't restricted by a fixed form and is in harmony with a law and that reveals a selfish character freely. Third, military theory, that is a trick that analyzes the quality of a case and a thing accurately. Above the three show that there are an objective basis of reward and punishment and an fair execution about a law in Hanfeizi's shuzhi-theory.

• Research in Mathematical Education
• /
• v.17 no.1
• /
• pp.1-14
• /
• 2013

Stochastic phenomena induce us to construct a probability model and structure our thinking; corresponding models help us to understand and interpret the reality. They in turn equip us with tools to recognize, reconstruct and solve problems. Therefore, various implications in terms of methodology as well as epistemology naturally flow from different adoptions of models for probability. Right from the basic scenarios of different perspectives to explore reality, students are occasionally exposed to misunderstanding and misinterpretations. With realistic examples a multi-faceted image of probability and different interpretation will be considered in mathematical modelling activities. As an exploratory investigation, mathematical modelling activity for probability learning was elaborated through semiotic analysis. Especially, the coherence structure in mathematical modelling discourse was reviewed form a semiotic perspective. The discourses sampled from group activities were analyzed on the basis of semiotic perspectives taxonomical coherence relations.

• Research in Mathematical Education
• /
• v.6 no.1
• /
• pp.1-28
• /
• 2002

This study explored teachers (n = 219) from northern, central, southern and eastern Taiwan concerning their views about children's learning difficulties, mathematical instruction and school mathematics curricular. Results showed that teachers' mathematics knowledge or their instruction methods had no significant influence on their views of children's learning difficulties. Even though teachers indicated that understanding of abstract mathematical concepts was the most prominent difficulty for children, they tended to employ direct instruction rather than constructive and cooperative problem solving in their teaching. However, teachers' views of children's learning difficulties did influence their instructional practice. Results from in-dept interviews revealed that there were some obstacles that prevented teachers from putting constructiveism perspectives of instruction into teaching practice. Further investigation is needed to develop a better understanding of epistemology and teaming psychology as well as to help teachers create constructive learning situations.

• The Mathematical Education
• /
• v.41 no.3
• /
• pp.329-339
• /
• 2002

This study analyzes the epistemological meaning of‘social construction’in mathematical instruction. The perspective that consider the cognition of mathematical concept as a social construction is explained by a cyclic scheme of an academic context and a school context. Both of the contexts require a public procedure, social conversation. However, there is a considerable difference that in the academic context it is Lakatos' ‘logic of mathematical discovery’In the school context, it is Vygotsky's‘instructional and learning interaction’. In the situation of mathematics education, the‘society’which has an influence on learner's cognition does not only mean‘collective members’, but‘form of life’which is constituted by the activity with purposes, language, discourse, etc. Teachers have to play a central role that guide and coordinate the educational process involving interactions with learners in this context. We can get useful suggestions to mathematics education through this consideration of the social contexts and levels to form didactical situations of mathematics.

• Journal of Educational Research in Mathematics
• /
• v.20 no.3
• /
• pp.293-303
• /
• 2010

The purpose of this study is to classify a three-fold role of the history of mathematics through epistemological analysis. Based on the history of infinity and limit, the "potential infinity" and "actual infinity" discourses are described using four different historical epistemologies. The interdependence between the mathematical concepts is also addressed. By using these analyses, three different uses of the history of mathematical concepts, infinity and limit, are discussed: past, present, and future use.