• The Mathematical Education
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• v.52 no.4
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• pp.549-565
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• 2013

To help students understand the deduction system in the proof, we analyzed the textbook on mathematics at first. As results, we could find that the textbook' system of deduction is similar with the Euclid' system of deduction. The starting point of deduction is different with each other. But the flow of deduction match with each other. Next, we searched for the example of circular argument and analyzed. As results, we classified the circular argument into two groups. The first is an internal circular argument which is a circular argument occurred in a theorem. The second is an external circular argument which is a circular argument occurred between many theorems. We could know that the flow of deduction system is consistent in internal-external dimension. Lastly, we proposed the desirable teaching direction to help students understand the deduction system in the proof.

• School Mathematics
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• v.15 no.2
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• pp.389-404
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• 2013

Researchers have suggested that students should be experienced in progress of geometric thinking set out in naive and intuitive level and deduced throughout gradual formalization rather than completed mathematics are conveyed to students for students' understanding. This study examined naive and intuitive thinking of students by investigating students' geometric problem solving without diagrams. The students showed these naive thinking: lack of recognition of relation between problem and conditions, use of intuitive judgement depending on diagrams, lacking in understanding of role of specific case, and use of unjustified assumption. This study suggests implication for instruction in geometry.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.111-127
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• 2004

In this note we examined some terms, parallel lines and angles in elementary school mathematics and middle school mathematics respectively. Since some terms are represented early in elementary school mathematics and not repeated after, some students are not easy to apply the terms to their lesson. Also, since the relation between parallel lines and angles are treated intuitively in 7-th grade, applying the relation for a proof in 8-th grade would be meaningless. For the variety of mathematics education, it is desirable that the relation between parallel lines and angles are treated as postulate. Also, for out standing students, it is desirable that we use deductive reasoning to prove the relation between parallel lines and angles as a theorem. In particular, the treatments of vertical angles and the relation between parallel lines and angles in 7-th grade text books must be reconsidered. Proof is very important in mathematics, and the deductive reasoning is necessary for proof. It would be efficient if some properties such as congruence of vertical angles and the relation between parallel lines and angles are dealt in 8-th grade for proof.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2009.11a
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• pp.45.2-45.2
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• 2009

최근 제품에 있어서 가치는 기능성을 제공하는 측면에서 점차 사용성과 감성을 중요시하는 방향으로 변화하고 있다. 최근의 혁신적인 제품을 보면 사용성과 감성적인 가치가 기술개발의 방향성까지 결정하는 등 제품개발에 있어서 감성과 사용성 가치의 중요성은 더 더욱 커지고 있다. 또한 감성과, 사용성에 대한 정확한 예측은 제품의 개발 방향뿐만 아니라, R&D의 방향성을 결정짓기 때문에 이와 같은 Value를 표현할 수 있는 정확하고 신뢰성 있는 모델의 중요성 갈수록 높아지고 있다. 하지만 제품개발에 있어서 감성과 사용성으로 대변되는 User Experience 가치 제공은 기능성, 신뢰성 등의 기존가치와는 달리 소비자, 사용자로 대변되는 Human에 대한 더 높은 이해가 필수적이나, 관련 지식의 부족 및 통계적 정량화, 객관화 어려움 등으로 제품의 가치로 연결시키기에는 많은 어려움이 있는게 사실이다. 본 논문에서는 감성과 사용성 등을 고려한 제품 가치 체계(Product Value Structure)에 대해서 살펴보고, 아울러 이러한 가치를 고려한 제품개발 패러다임의 변화에 대해서 살펴보고자 한다. 또한 기존의 감성 사용성에 대한 방법론에 널리 활용되는 통계적 귀납적 방법론 외에 인지과학(Coginition Technology)을 활용하여 연역적 방법론에 대해서도 고민해보고자 한다. 특히 Iphone의 UI 특성을 통해 Innovation Company가 인지과학적인 Approach를 어떻게 제품개발에 적용하고 있는지에 대해서 알아보고자 한다.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.135-148
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• 2011

Middle school mathematics treats axiom as mere fact verified by experiment or observation and doesn't mention it axiom. But axiom is very important to understand the difference between empirical verification and mathematical proof, intuitive geometry and deductive geometry, proof and nonproof. This study analysed textbooks and surveyed gifted students' conception of axiom. The results showed the problem and limitation of middle school mathematics on the treatment of axiom and proof.

• School Mathematics
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• v.9 no.1
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• pp.99-117
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• 2007

In this paper it is discussed how children develop their logical reasoning beyond difficulties in the process of making sense of division with decimals in the classroom setting. When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter levels, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school should be clarified. This study focuses on the teaching and learning of division with decimals in a 5th grade classroom, because it is well known to be difficult for children to understand the meaning of division with decimals. It is suggested that children begin to conceive division as the relationship between the equivalent expressions at the hypothetical-deductive level detached from the concrete one, and that children's explanation based on a reversibility of reciprocity are effective in overcoming the difficulties related to division with decimals. It enables children to conceive multiplication and division as a system of operations.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.327-344
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• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

• Journal of the Korean earth science society
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• v.31 no.7
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• pp.785-797
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• 2010

This study identified the linguistic features of Earth science treatises through the analysis of the register. Data included three Korean treatises that were in geology, atmospheric science, and oceanography. The register of Earth science treatise was as follows: First, there were semantic, referential connections between Themes and Rhemes, that the messages and main points of the texts were expressed coherently and cohesively. Second, some predicates were used which were related to deductive inference, abductive inferences, or causal relation according to the genre elements of each text. The logical relations were not represented by the conjunctions but by the types of predicates. Third, most texts in the treatises showed interpersonally weak relationship using mental predicates related to possibilities, which meant scientists expressed indirectly their interpretation, explanation, or arguments. From these results, we argued that some activities of unpacking the language of science be included in science curriculum in order to improve students' literacy of science texts and understanding scientists' knowledge construction.

• Journal of the Korean earth science society
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• v.26 no.8
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• pp.751-758
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• 2005

The purpose of this study was to develop an inquiry analysis framework based on the features of earth science inquiry methodology and to analyze inquiry activities in the 8th grade 'Earth History and Diastrophism' unit by using this framework. The framework classified earth science methods as logical inference, hermeneutic, and historical methods, each of which was subdivided in consideration of its subordinate methods and characteristics. The analysis revealed that the logical inference method reflected in the unit as the 'abductive method' (70%) was used more frequently than the 'inductive' (23%) and 'deductive' (22%) methods. The hermeneutic method was found in terms of the 'forestructures of understanding' (92%), 'circular reasoning' (9%). and 'historical nature of human understanding' (17%). The historical method also used as the 'constructing proper taxonomy' (53%), 'adhering to the modem principle of uniformitarianism' (47%), and 'relic interpretation' (41%) were identified with ratios more fester than those for the 'place substituting for time in stage theorizing' (3%) and 'evaluating independent lines of inquiry for convergence' (3%).