• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.445-458
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• 2010

This study intends to investigate the process of the development of quantity concept and how to deal with the quantity calculus in elementary school, and to find out the implication for improving the curriculum and mathematics textbooks of Korea. There had been the binary Greek categories of discrete number and continuous magnitude in quantity concept, but by the Stevin's introduction of decimal, the unification of these notions became complete. As a result of analyzing of the curriculum and mathematics textbooks of Korea, there is a tendency to disregard the teaching of quantity and its calculus compared to the other countries. Especially multiplication and division of quantity is seldom treated in elementary mathematics textbooks. So these should be reconsidered in order to seek the direction for improvement of mathematic teaching. And Korea's textbooks need the emphasis on the quantity calculus and on constructing quantity concept.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.723-743
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• 2015

In this research, The objective of the present study was to develop a preliminary diagnostic worksheet for use in consultations for learning mathematics. In order to achieve this, the worksheet was constructed with questions designed to assess the students. Through standardization, diagnostic worksheets for primary school students in grades 5 and 6 and secondary school students in grades 7 and 8 were produced. The diagnostic worksheet was divided into three sections, consisting of the psychology of learning mathematics in section 1, the methodology in learning mathematics in section 2, and personal preferences in learning mathematics in section 3. The psychology of learning mathematics was composed of questions on factors such as, "confidence in math learning ability," "math anxiety," and "attitude in learning mathematics." Moreover, factors in methodology in learning mathematics were "self-management in learning mathematics" and "math learning strategies." Those for personal preferences in learning mathematics asked about "motivation" and "preferences" with questions about "math learning habits" and "management methods for learning math." This diagnostic worksheet can be used as basic material in consulting students on learning mathematics.

• School Mathematics
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• v.10 no.3
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• pp.319-337
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• 2008

Intuitions in independence formed by common language help and also hinder the establishment of new conceptual system about independence as a mathematical term. Intuitions which entail such conflicts can be a driving force in explaining independence but at the same time, it is the impedimental factor causing a misconception. The goal of this paper is to help students use the intuitions properly by distinguishing helpful intuitions and impedimental intuitions. This paper suggests that we need to reveal in teaching the misconception resulting not from mathematic but from linguistic interpretation of independence. This paper points out the need for the clear distinction of independence of trials and independence of events and gives an counterexample of the case that sampling with and without replacement shouldn't be specified as a representative example of independence and dependence of events. The analysis of intuition in this parer is based on intuitions classified by Fischbein and this paper analyzed institutions applied to the concept of independence corresponding intuitions classified by Fischbein.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.269-283
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• 2014

Recently, 3S Mathematics Education (Storytelling mathematics education, SMART mathematics education, and STEAM mathematics education) is emphasized. Based on recently published report on Storytelling mathematics textbook, we propose executable expression based SMART storytelling mathematics related to the elementary mathematic curriculum on 3D building blocks. We designed letters and expressions to represent three dimensional shape of 3D building blocks, and we compare its characteristics with that of LEGO blocks. We assert that text-based executable expressions not only construct what students want to make but also teachers can read students thinking process and can support educational help based on students needs. We also present linear function, quadratic function, and function variable concepts using executable expressions based on 3D building block as an example of SMART storytelling mathematics. This research was supported by the collaborated creativity mentoring project between Siheung City and college of education at Seoul National University. We hope designed executable expressions can be used for the development of SMART storytelling mathematics education.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.239-257
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• 2016

The Common Core States Standards was developed by building on the best state standards in the U.S.; examining the expectations of other highperforming countries around world; and carefully studying the research and literature available on what students need to know. The Common Core States Standards for Mathematics are reshaping the teaching and learning of mathematics in California classroom using the California Common Core States Standards for Mathematics(CA CCSSM). The aim of this study is to observe CA CCSSM. The CA CCSSM were established to address the problem of having a curriculum that is 'a mile wide and an inch deep'. And it have two types of standards. One is standards for mathematical practice which are the same at each grade level, the other is standards for mathematical content which are different at each grade level. This study focused on standards for mathematical content, in particular, on Geometry domain in elementary level, using Mathematics Framework for California Public Schools.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.45-61
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• 2009

The powerful role of analogical reasoning in discovering mathematics is well substantiated in the history of mathematics. Mathematically gifted students, thus, are encouraged to learn via in-depth exploration on their own based on analogical reasoning. In this study, 57 gifted students (31in the 7th and 26 8th grade) were asked to formulate or clarify analogy. Students produced fruitful constructs led by analogical reasoning. Participants in this study appeared to experience the deep thinking that is necessary to solve problems made with analogies, a process equivalent to the one that mathematicians undertake. The subjects had to reflect on prior knowledge and develop new concepts such as an orthogonal projection and a point of intersection of perpendicular lines based on analogical reasoning. All subjects were found adept at making meaningful analogues of a triangle since they all made use of meta-cognition when searching relations for analogies. In the future, methodologies including the development of tasks and teaching settings, measures to evaluate the depth of mathematic exploration through analogy, and research on how to promote education related to analogy for gifted students will enhance gifted student mathematics education.

• Imaging Science in Dentistry
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• v.38 no.1
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• pp.49-56
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• 2008

Purpose: Diagnostic estimation of destruction and formation of bone has the typical limit according to capacity of x-ray generator and image detector. So the aim of this study was to find out how much it can reproduce the shape and the density of bone in the case of using recently developed dental type of cone beam computed tomography, and which image is applied by new detector and mathematic calculation. Materials and Methods: Cone beam computed tomography (PSR 9000N, Asahi Roentgen Ind. Co., Ltd., Japan) and soft x-ray radiography were executed on dry mandible that was already decalcified during 5 hours, 10 hours, 15 hours, 20 hours, and 25 hours. Estimating and comparing of those came to the following results. Results: The change of inferior border of mandible and anterior border of ramus in the region of cortical bone was observed between first 5 and 10 hours of decalcification. The reproduction of shape and density in the region of cortical bone and cancellous bone can be hardly observed at cone beam computed tomography compared with soft x-ray radiography. The difference of decrease of bone density according to hours of decalcification increase wasn't reproduced at cone beam computed tomography compared with soft x-ray radiography. Conclusion: CBCT images revealed higher spatial resolution. However, contrast resolution in region of low contrast sensitivity is the inferiority of images' property.

• Journal of Digital Convergence
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• v.14 no.6
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• pp.143-150
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• 2016

This paper's aim is to suggest the Expert System for analyzing relative combat power in ground operations. Since relative combat power analysis in terms of comparing combat power of friendly forces with one of the enemy can determine how the commander and staffs operate their unit afterwards, it requires fast and rational decision-making process. However, it has relied on manual method so far though Tactical Information Communications Network(TICN) into which numbers of applications can be loaded has been developed over a decade. 3 methods for analyzing relative combat power were expressed as mathematic rules to be used knowledge in the expert system after reviewing previous studies, and it studied how intangible power as well as tangible were reflected on total combat power. The expert system that will be built using EXSYS Corvid tool is expected to lessen error rate, provide faster decision-making, and reflect both intangible combat power and tangible one by using an appropriate weights in analyzing relative combat power. Next research filed includes how to build expert systems related with military personnel and intelligence areas for fast and rational decision-making processes.

• The Mathematical Education
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• v.46 no.3
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• pp.331-349
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• 2007

This study aims to improve the teaching and learning method on the conic sections. To do that the researcher analyzed the impact of dynamic geometry software on students' problem solving of the conic sections. Students often say, "I have solved this kind of problem and remember hearing the problem solving process of it before." But they often are not able to resolve the question. Previous studies suggest that one of the reasons can be students' tendency to approach the conic sections only using algebra or analytic geometry without the geometric principle. So the researcher conducted instructions based on the geometric and historico-genetic principle on the conic sections using dynamic geometry software. The instructions were intended to find out if the experimental, intuitional, mathematic problem solving is necessary for the deductive process of solving geometric problems. To achieve the purpose of this study, the researcher video taped the instruction process and converted it to digital using the computer. What students' had said and discussed with the teacher during the classes was checked and their behavior was analyzed. That analysis was based on Branford's perspective, which included three different stage of proof; experimental, intuitive, and mathematical. The researcher got the following conclusions from this study. Firstly, students preferred their own manipulation or reconstruction to deductive mathematical explanation or proving of the problem. And they showed tendency to consider it as the mathematical truth when the problem is dealt with by their own manipulation. Secondly, the manipulation environment of dynamic geometry software help students correct their mathematical misconception, which result from their cognitive obstacles, and get correct ones. Thirdly, by using dynamic geometry software the teacher could help reduce the 'zone of proximal development' of Vigotsky.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.467-482
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• 2007

In this paper, we surveyed the attitudes of engineering students in 6 universities in Chungcheong area to mathematics by 5-scale degrees and performed a comparative analysis of the results. The results revealed a number of meaningful points which should be applied to college mathematic education. On the basis of the results of the analysis, we made the following suggestions; 1) It is necessary to pay much attention to the students who have insufficient math ability 2) Special teaching methods are required for Freshman engineering students 3) Practical teaching strategies should be developed for engineering students that are based on the research on their math background 4) We should develop more materials in the area of mathematical concept image 5) More attention should be paid to the relation between math concepts and engineering concepts. Besides the above suggestions, we proposed that more research about students' math background and attitudes should be conducted for more efficient college math education.