• School Mathematics
• /
• v.7 no.4
• /
• pp.427-444
• /
• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Korean Journal of Child Studies
• /
• v.29 no.5
• /
• pp.113-131
• /
• 2008

This study examined mothers' ratings of everyday rules for their young children. Participants were 294 mothers of 2- to 5-year-old children attending kindergartens and nursery schools in Korea. Data were collected by questionnaire and were analyzed by $x^2$. Results indicated that the majority of mothers' rules for their children pertained to safety, interpersonal issues, and as children got older, social conventions. Mothers endorsed prudential justifications for safety and self-care, moral justifications for interpersonal rules, practical and moral justifications for safeguarding property, and conventional justifications for obedience/order and food/mealtime routines. Analyses of mothers' judgments of rule independence indicated that rules on interpersonal and safety issues were to be kept without exception.

• Journal of Korean Philosophical Society
• /
• v.116
• /
• pp.257-280
• /
• 2010

I try to formalize the system of modal logic and interpret it in view of constructivism through this study. As to the meaning of a sentence, as we saw, Frege endorsed extensions in view of the fact that they are enough to provide for a compositional account for truth, in particular that (1) the assignment of extensions to expressions is compositional ; (2) the assignment of extensions to sentences coincides with the assignment of truth values. But nobody would be willing to admit that a truth value is what a sentence means and that consequently all true sentences are synonymous. So, if what we are after is meaning in the intuitive sense, then extensions would not do. This consideration has later become the point of departure of modal and intensional semantics. So, it is clear that the language of modal logic do not allow for an extensional interpretation. ${\square}$ is syntactically on a par with ${\vdash}$, hence within the extensional framework it would have to denote a unary truth function. This means that if modal logic is to be interpreted, we need a semantics which is not extensional. The first attempt to build a feasible intensional semantics was presented by Saul Kripke. He came to the conclusion that we must let sentences denote not truth values, but rather subsets of a given set. He called elements of the underlying set possible world. Hence each sentence is taken to denote the set of those possible world in which it is true. This lets us explicate necessity as 'truth in every possible world' and possibility as 'truth in at least one possible world'. But it is clear that the system of modal logic is not only an enlargement of propositional logic, as long as the former contains the new symbols, but that it is of an other nature. In fact, the modal logic is intensional, in that the operators do not determine the functions of truth any more. But this new element is not given a priori, but a posteriori from construction by logicist.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.7 no.4
• /
• pp.48-57
• /
• 1997

This paper presents the automatic construction and parameter optimization technique for fuzzy logic controllers using genetic algorithm. In general. the design of fuzzy logic controllers has difficulties in the acq~lisition of expert's knowledge and relies to a great extent on empirical and heuristic knowledge which, in many cases, cannot be objectively justified. So, the performance of the controllers c:an be degraded in the case of plant parameter variations or unpredictable incident which a designer may have ignored, and the parameters of fuzzy logic controllers obtained by expert's control action may not be optirnal. Some of these problems can be resolved by the use of genetic algorithm. The proposed method can tune the parameters of fuzzy logic controllers including scaling factors and determine: the appropriate number of fuzzy rulcs systematically. Finally, we provides the second order dead time plant to evaluate the feasibility and generality of the proposed method. Comparison shows that the proposed method can produce fuzzy logic controllers with higher accuracy and a smaller number of fuzzy rules than manually tuned fuzzy logic controllers.

• Journal of the Korean School Mathematics Society
• /
• v.22 no.4
• /
• pp.439-460
• /
• 2019

In this study, we examined classroom interaction to explore the relationships among teacher questions, turn-taking patterns, and student talks in mathematics classrooms. We analyzed lessons given by three elementary teachers (two first-grade teachers and one second-grade teacher) who worked in the same school using a conversation-analytic approach. We observed individual classrooms three times in a year. The results revealed that when teachers provided open-ended questions, such as "why and how" questions and "agree and disagree" questions, and used a non-IRE pattern (teacher initiation-student response-teacher feedback; Mehan, 1979), students more actively engaged in classroom discourse by justifying their ideas and refuting others' thinking. Conversely, when teachers provided closed-ended questions, such as "what" questions, and used an IRE pattern, students tended to give short answers focusing on only one point. The findings suggested teachers should use open-ended questions and non-IRE turn-taking patterns to create an effective math-talk learning community. In addition, school administrators and mathematics educators should support teachers to acquire practical knowledge regarding this approach.

• Journal of Korean Philosophical Society
• /
• v.147
• /
• pp.215-237
• /
• 2018

The purpose of this study is to illuminate the precise nature and the central line of Kant's proof of the causal principle stated in the Second Analogy of the 2nd. edition of the Critique of Pure Reason. The study argues for the following thesis: 1. The proof of the Second Analogy concerns only the causal principle called the "every-event-some-cause" principle, and not the causal law(s) called the "same-cause-same-event" principle. 2. The goal of the proof is to establish the possibility of knowledge of an temporal order of successive states of an object. 3. The proof is broadly an single transcendental argument in two steps. The 1st. step is an analytic argument that infers from the given perceptions of an oder of successive states of an objects to the conclusion that the causal principle is the necessary condition for the objectivity of dies perceived order. The 2nd. step is a synthetic argument that infers from the formal nature of time to the conclusion that the causal principle is a necessary condition for die possibility of objective alterations and of empirical knowledge of these alterations. 4. The poof involves not the 'non sequitur' assumed by P. F. Strawson, that is, Kant infers not directly from a feature of our perceptions to a conclusion regarding the causal relations of distinct states of affairs that supposedly correspond to these perceptions.

• Korean Journal of Logic
• /
• v.14 no.2
• /
• pp.39-76
• /
• 2011

We explain some basic elements of Martin-L$\ddot{o}$f's type theory and examine the distinction between propositions and judgments. In section 1, we introduce the problem. In section 2, we explain the concept of proposition in the intuitionistic type theory as a development of the intuitionistic conception of proposition. In section 3, we explain the concept of judgment in the intuitionistic type theory. In section 4, we explain some basic inference rules and examine a particular derivation in the theory. In section 5, we examine one route from the Fregean distinction between propositions and judgments to the distinction between them in the intuitionistic type theory, paying attention to the alleged necessity for introducing different forms of judgments.

• The Journal of the Korea Contents Association
• /
• v.22 no.8
• /
• pp.200-210
• /
• 2022

The purpose of this paper is to analyze Hirata Oriza's three plays, "Scientific Minds," "Monkeys on the Northern Limit Line" and "Balkan Zoo" with Lyotard's postmodern scientific view. Liotar, who claims that science and narratives follow the rules of their own pragmatic use, talks about the incommensurable parallelism between the two. Hirata Oriza points out that humans rely on narratives in the postmodern world. This paper analyzes Hirata Oriza's plays in three aspects. First, in the postmodern world where the master narrative has disappeared, it identifies the point where the boundaries that define the identity of human beings under the lost and developing science technology are fading. Second, we look at the pattern in which the parallelism between scientific knowledge and narrative knowledge is constantly diluted due to the characteristics of humans who understand the world by leaning on narrative. Finally, the aspects of small narratives are idetified, raised by individuals to comfort themselves toward a world where the master narrative disappears and is justified only by maximizing performance.

• School Mathematics
• /
• v.14 no.1
• /
• pp.85-107
• /
• 2012

Problem solving is important in school mathematics as the means and end of mathematics education. In elementary school, inductive reasoning is closely linked to problem solving. The purpose of this study was to examine ways of improving problem solving ability through analysis of inductive reasoning process. After the process of inductive reasoning in problem solving was analyzed, five different stages of inductive reasoning were selected. It's assumed that the flow of inductive reasoning would begin with stage 0 and then go on to the higher stages step by step, and diverse sorts of additional inductive reasoning flow were selected depending on what students would do in case of finding counter examples to a regulation found by them or to their inference. And then a case study was implemented after four elementary school students who were in their sixth grade were selected in order to check the appropriateness of the stages and flows of inductive reasoning selected in this study, and how to teach inductive reasoning and what to teach to improve problem solving ability in terms of questioning and advising, the creation of student-centered class culture and representation were discussed to map out lesson plans. The conclusion of the study and the implications of the conclusion were as follows: First, a change of teacher roles is required in problem-solving education. Teachers should provide students with a wide variety of problem-solving strategies, serve as facilitators of their thinking and give many chances for them ide splore the given problems on their own. And they should be careful entegieto take considerations on the level of each student's understanding, the changes of their thinking during problem-solving process and their response. Second, elementary schools also should provide more intensive education on justification, and one of the best teaching methods will be by taking generic examples. Third, a student-centered classroom should be created to further the class participation of students and encourage them to explore without any restrictions. Fourth, inductive reasoning should be viewed as a crucial means to boost mathematical creativity.

• Journal of Educational Research in Mathematics
• /
• v.22 no.4
• /
• pp.619-636
• /
• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.