• School Mathematics
• /
• v.4 no.4
• /
• pp.555-563
• /
• 2002

The purpose of this paper is to try formulating a working definition of connection of informal and formal mathematical knowledge. Many researchers have suggested that informal mathematical knowledge should be connected with school mathematics in the process of learning and teaching it. It is because informal mathematical knowledge might play a important role as a cognitive anchor for understanding school mathematics. To implement the connection of them we need to know what the connection means. In this paper, the connection between informal and formal mathematical knowledge refers to the making of relationship between common attributions involved with the two knowledge. To make it clear, it is discussed that informal knowledge consists of two properties of procedures and conceptions as well as formal mathematical knowledge does. Then, it is possible to make a connection of them. Now it is time to make contribution of our efforts to develop appropriate models to connect informal and formal mathematical knowledge.

• Journal of Information Processing Systems
• /
• v.11 no.2
• /
• pp.184-204
• /
• 2015

Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposing a method that computes the corresponding crisp order for the fuzzy relation in a given fuzzy formal context. The obtained formal context using the proposed method provides a fewer number of concepts when compared to original fuzzy context. The resultant lattice structure is a reduced form of its corresponding fuzzy concept lattice and preserves the specialized and generalized concepts, as well as stability. This study also shows a step-by-step demonstration of the proposed method and its application.

• Journal of Elementary Mathematics Education in Korea
• /
• v.10 no.2
• /
• pp.221-242
• /
• 2006

For teaching division more effectively, it is necessary to know students' informal knowledge before they learned formal knowledge about division. The purpose of this study is to research students' informal knowledge of division and to analyze meaningful suggestions to link formal knowledge of division in elementary school mathematics. According to this purpose, two research questions were set up as follows: (1) What is the students' informal knowledge before they learned formal knowledge about division in elementary school mathematics? (2) What is the difference of thinking strategies between students who have learned formal knowledge and students who have not learned formal knowledge? The conclusions are as follows: First, informal knowledge of division of natural numbers used by grade 1 and 2 varies from using concrete materials to formal operations. Second, students learning formal knowledge do not use so various strategies because of limited problem solving methods by formal knowledge. Third, acquisition of algorithm is not a prior condition for solving problems. Fourth, it is necessary that formal knowledge is connected to informal knowledge when teaching mathematics. Fifth, it is necessary to teach not only algorithms but also various strategies in the area of number and operation.

• Journal of the Korean Society for information Management
• /
• v.16 no.4
• /
• pp.53-74
• /
• 1999

This paper describes concept mapping techniques for eliciting and representing knowledge. Concept mapping techniques range from very informal to very formal. Informal concept mapping techniques are usually very easy to use and understand for humans, but not for computers. Formal concept mapping techniques are computational, but humans usually find them hard to understand and use. A knowledge acquisition and representation tools which handle both kinds, and the transition from informal to formal, would be very useful. It is proposed that concept maps be regarded as basic components of any knowledge-based system, complementing text and image with formal and informl active diagrams.

• Communications of Mathematical Education
• /
• v.32 no.3
• /
• pp.297-314
• /
• 2018

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

• The Mathematical Education
• /
• v.47 no.1
• /
• pp.91-106
• /
• 2008

Interviews with 24 pupils in grade 1-2 were used to investigate awareness of the relation between situation and computation in simple quotitive and partitive division problems as informally experienced. Then it was suggested how to connect children's informal knowledge and formal knowledge of division. Most subjects counted cubes or made drawing, and related these methods to the situation described in the problems. In result, quotitive division was experienced as a dealing situation, where the number of items represented by the divisor was repeatedly taken from the whole number. And estimate-adjust was the most frequently displayed way of experiencing partitive division. Therefore, partitive division with its two measurement variables can be related to a measurement model. And children should be taught column algorithms for division with estimated-adjust which pupils used for partitive division problems.

• Industrial Engineering and Management Systems
• /
• v.9 no.1
• /
• pp.1-9
• /
• 2010

Increasing product variety based on product family and product platform provides a company with a competitive advantage over its competitors. As products become more complex, short-life cycled and customized, the design efforts require more knowledge-intensive, collaborative and coordinating efforts for information sharing. By sharing knowledge, information, component and process across different families of products, the product realization process will be more efficient, cost-effective and quick-responsive. Formal Concept Analysis (FCA) is used for analyzing data and forming semantic structures that are formal abstractions of concepts of human thoughts. A Web Ontology Language (OWL) is designed for applications that need to process the content of information instead of simply presenting information to humans. OWL also captures the evolution of different components of the product family. The purpose of this paper is to develop product variety modeling to increase the usefulness of common platform. In constructing and analyzing product ontology, FCA is adopted for conceptual knowledge processing. For the selected product family, product variety Ontology is constructed and implemented using prot$\'{e}$g$\'{e}$-2000.

• East Asian mathematical journal
• /
• v.25 no.3
• /
• pp.247-262
• /
• 2009

Permutation and combination are the part of mathematics which can be introduced the pliability and diversity of thought. In prior studies of permutation and combination, there treated difficulties of learning, strategy of problem solving, and errors that students might come up with. This paper provides the method so that meaningful teaching and learning might occur through the systematic approach of permutation and combination. But there were little prior studies treated counting numbers that basic of mathematics' action. Therefore this paper tries to help the understanding of permutation and combination with the process of changing from informal knowledge to formal knowledge.

• Asian Journal of Innovation and Policy
• /
• v.4 no.2
• /
• pp.242-262
• /
• 2015

The relationship between geographical proximity and academics' formal and informal knowledge-transfer activities in the network is analyzed with a mixed research method. With social network analysis as a basis, we have explored the networks between academics and firms in the 16 regions of South Korea. The result shows Seoul and Gyunggi are identified as central nodes, meaning that the academics in other regions tend to collaborate with firms in these regions. An econometric analysis is performed to confirm the localization of knowledge-transfer activities. The intensity of formal channels measured by the number of academic papers is negatively, but significantly associated with the geographical proximity. However, we have not found any significant relationship between the formality of the channels and geographical proximity. Possibly, the regional innovation systems in South Korea are neither big enough nor strong enough to show a localization effect.

• Knowledge Management Research
• /
• v.11 no.3
• /
• pp.31-45
• /
• 2010

IT outsourcing studies have centered on the separate effect of formal contract and relational trust on IT outsourcing performance. In addition, previous studies ignored the importance of the relational capability that combine the formal contract and partnership can be able to deliver IT outsourcing effects. In this paper, we propose an IT governance commitment as a mediated role between relational capability and IT outsourcing performance. We collected data from 143 client companies of IT outsourcing and analyzed it using the PLS method. Our findings are revealed as following: At first, relational capability significantly and directly influence IT governance commitment as well as indirectly through formal contract and partnership. Secondly, IT governance commitment mediate between relational capability and IT outsourcing effect, and in turn affect IT outsourcing performance. The results and implications are further discussed.