• Korean Journal of Logic
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• v.21 no.1
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• pp.59-96
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• 2018

${\bot}$It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (${\perp}$). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ${\perp}$. It is, however, not the problem of the intuitionistic approaches to the liar-type paradoxes but the lack of expressive power of the standard intuitionistic natural deduction system. We introduce a meta-level negation, ⊬$_s$, for a given system S and a meta-level absurdity, ⋏, to the intuitionistic system. We shall show that in the system, the inference to ${\perp}$ is not given without the assumption that the system is complete. Moreover, we consider the Double Meta-Level Negation Elimination rules (DMNE) which implicitly assume the completeness of the system. Then, the restriction of DMNE can rule out the inference to ${\perp}$.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.493-509
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• 2010

Researchers have suggested that educators have to focus their attention on variability and reasoning about variation as means of developing students' statistical thinking in school mathematics. This paper investigated knowledge for the teaching of variability and reasoning about variation; what are sources of variability, how to cope with variability, what are types of variability, how to recognize variability, and the relationship between statistical problem solving and variability. The results involve: discussion on the sources of variability and how to cope with variability promotes students' awareness of different types of variability and students' motivation in the following steps in the statistical activity; emphasis on reasoning about variation in teaching representation of data accords with objectives of statistics education; reexamination of curriculum for statistics education is needed, which has a content-oriented arrangement.

• Journal of the Korean School Mathematics Society
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• v.23 no.3
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• pp.323-349
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• 2020

In this study, we conducted eight reciprocal peer tutoring classes where each student took either role of a tutor or a tutee to study covariational reasoning in ninth graders. Students were given the opportunity to teach their peers with their covariational reasoning as tutors, and at the same time to learn covariational reasoning as tutees. A heterogeneous group was formed so that scaffolding could be provided in the teaching and learning process. A total of eight reciprocal peer tutoring worksheets were collected: four quantitative graph type questions and four questions of the qualitative graph to the group. The results of the analysis are as follows. In reciprocal peer tutoring, students who experienced a higher level of covariational reasoning than their covariational reasoning level showed an improvement in covariational reasoning levels. In addition, students enhanced the completeness of reasoning by modifying or supplementing their own covariational reasoning. Minimal teacher intervention or high-level peer mediation seems to be needed for providing feedback on problem-solving results.

• Korean Journal of Cognitive Science
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• v.13 no.2
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• pp.25-36
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• 2002

Two experiments were performed to explore the effects of the types of property and the tasks on the pattern of property inference in a source selection task in which the source objects were to be selected. animals that were globally similar to the target animal was selected as possible sources when the target properties were anatomical. However animals that were strongly associated with the target property were selected when the target properties were about ability In a passive inference task where premises were given. the global similarity between the source objects and the target object differently affected the confidence of the conclusion depending on the types of the target property: The similarity between the source and the target affected the degree of confidence when the target properties were anatomical ones, but did not affect when the target properties were about ability. The results suggested that participants seemed to have primitive understanding of the relevance of sources to the target properties, but did not. spontaneously seek or use the relevant information.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Korean Journal of Cognitive Science
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• v.26 no.2
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• pp.209-239
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• 2015

Previous studies on the effect of incidental semantic priming on judgment, have focused mainly on mutually exclusive hypotheses. However, the present study explored whether incidental semantic activation affects diagnostic inference depending on the type of the hypothesis: mutually exclusive hypotheses vs compatible hypotheses. In Experiment 1, in case of mutually exclusive hypotheses, the final hypothesis was selected according to the incidental semantic priming, but there was no difference in the number of generated hypothesis in comparison with the control. However, for compatible hypotheses (i.e., both hypotheses can be true), the semantic priming affected the number of generated hypotheses, but not the selection of the final hypothesis. The same pattern of results was observed even when the cognitive load was increased. In Experiment 2, we found a boundary condition of incidental semantic activation on diagnostic inference. When cues related to each of the hypotheses were presented simultaneously, the incidental semantic effect disappeared. These results suggest that people consider all possible cues when making diagnostic inference in daily life. In light of these findings, further research on hypothesis generation/evaluation should take the type of hypothesis into account.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.609-627
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• 2008

The purpose of this research was to investigate the relationship between the students' strategy types and the recognition for proportional situations. The students' strategy types which were based on the results of ratio and proportion tests were divided into an additive type, a multiplicative type, and a formal type. This research analyzed the students' activities of categorization when were given the proportional problems and nonproportional problems to the students. And it also explored how to develop students' recognizing for the discrimination between the proportional situations and nonproportional situations. The results was the following. First, the students didn't discriminate the proportional situations and the nonproportional situations in the initial state but they came to discriminate little by little. Secondly, the students didn't discriminate the direct proportions and the inverse proportions until the last stage. Third, the multiplicative type was outperformed more than the formal type in solving the ratio and proportion problems but the formal type was outperformed more than the multiplicative type in discriminating between proportional situations and nonproportional situations. These results are interpreted as showing that solving ratio and proportion tasks and recognizing proportional situations are different aspects of proportional reasoning and it is necessary to understand multiplicative strategy with formal strategy in recognizing proportional situations.

• The Transactions of the Korea Information Processing Society
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• v.5 no.3
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• pp.662-670
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• 1998

In order to overcome the problems with first generation expert systems at the symbol level, recently various knowledge level development techniques of second generation expert systems have been proposed. But, these techniques are conceptual modelling techniques. This paper modifies and complements these conceptual modelling techniques and proposes a Task Object Modelling (TOM) technique as a practical knowledge level expert system development technique. This paper defines a Task Object(TO) as a knowledge unit consisted of a goal, execution conditions, behaviour knowledge, and so on. And, we define a Task Object Diagram(TOD) to depict structual, dynamic, and functional aspects of TO easily. We also define Inference Types as basic units to describe behaviour knowledge of TOs. In order to utilize the proposed TOM technique as not a simple conceptual modelling technique but a practical second generalion expert system development technique, we implement a TOD editor, a TO editor, and TO processing algorithm based on the state of TOs. Also we implement a Inference Types Library, in which each inference type is corresponded to an IRE(Jntelligent Rules Element) method, to transform the defined inference types into IRE methods automatically.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.263-287
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• 2010

The purposes of the study were to investigate how children define a triangle, their reasoning types in identifying examples and non-examples of a triangle, and the relationship between their reasoning types and geometrical levels. Twenty-nine students consisted of 3th to 6th grades were involved in the study. Using the van Hiele levels of geometrical thought, children's reasoning types for identifying a figure as a triangle or non-triangle were categorized into visual reasoning, reasoning based on the figure's attributes and formal reasoning. The figure's attributes were further divided into critical and non-critical attributes. Most children identified a figure as a triangle or non-triangle based on critical attributes of the figure(e.g. closed figure, three, vertices, straight sides etc.) Some children identified a figure based on non-critical attributes of the figure(e.g. the length of the sides, the measurement of the angles, or the orientation of the figure). Particularly, some children who had lower levels of geometry identified a figure using visual reasoning, taking in the whole shape without considering that the shape is made up of separate components.

• The Journal of the Convergence on Culture Technology
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• v.10 no.2
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• pp.373-382
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• 2024

This study attempted to identify the relationship between nursing competency, clinical reasoning competence, and empathy ability according to the center of enneagram power for nursing students. The subjects of the study were 218 students enrolled in the department of nursing at two universities located in one region, data collection was conducted from 16 October to 27 October 2023. Data analysis was performed using SPSS/WIN version 26.0 program, descriptive statistics, and difference verification were analyzed by t-test, ANOVA, pearson's correlation coefficient, Results, The enneagram personality type of the subjects of this study was the most common type 9. And in the enneagram center of power, the instinct-centered type had the highest nursing competence, the thought-centered type had the highest clinical reasoning competence, and the emotion-centered type had the highest empathy ability. In addition, nursing competence and clinical reasoning competence showed a significant positive correlation, and clinical reasoning competence and empathy ability were also found to be positively correlated. Therefore, it is important to continue to develop and apply individualized competency building programs that reflect personality type tests to nursing students. In addition, the higher the empathy ability, the higher the clinical reasoning competence, so it is thought that it is necessary to develop a standardized curriculum that can improve nursing competence and clinical reasoning competence and verify its effectiveness.