• Communications of Mathematical Education
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• v.29 no.1
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• pp.131-155
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• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

• School Mathematics
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• v.14 no.4
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• pp.409-429
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• 2012

This paper reports the process two 11th grade students went through in reinventing derivatives on their own via a context problem involving the concept of velocity. In the reinvention process, one of the students conceived a tangent line as the limit of a secant line, and then the other student explained to a peer that the slope of a tangent line was the geometric mean of derivative. The students also used technology to concentrate on essential thinking to search for mathematical concepts and help visually understand them. The purpose of this study was to provide meaningful implications to school practices by describing students' process of reinvention of derivatives. This study revealed certain characteristics of the students' reinvention process of derivatives and changes in the students' thinking process.

• School Mathematics
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• v.19 no.4
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• pp.639-661
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• 2017

The purpose of this study is to investigate the relationship between the distance function average speed and the speed function. Particularly, in this study, we investigate the process of constructing the speed function in the distance function (irrational function, exponential function) which is difficult to weaken the argument in the denominator. In this process, students showed various anxieties and expressions about the procedural knowledge that they constructed first. In particular, if student B can not explain all the knowledge he already knows in this process, he showed his reflection on the process of calculating the differential coefficient. This study adds an understanding of the calculation method of students in differential coefficient learning. In addition, it is meaningful that the students who construct procedural knowledge at the time of calculating the differential coefficient have thought about how to provide opportunities to reflect on the procedure they constructed.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.33-55
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• 2011

This study explores the characteristics of calculus students' and instructors' discourses on the derivative using a communicational approach to cognition. The data were collected from surveys, classroom observations, and interviews. The results show that the instructors did not explicitly address some aspects of the derivative such as the relationship between the derivative function (f'(x)) and the derivative at a point (f'(a)), and f'(x) as a function, and that students incorrectly described or used these aspects for problem solving. It is also found that both implicitness in the instructors' discourse, and students' incorrect descriptions were closely related to their use of the word, "derivative" without specifying it as "the derivative function" or "the derivative at a point." Comparison between instructors' and students' discourses suggests that explicit discussion about the derivative including exact use of terms will help students see the relationship that f'(a) is a number, a point-specific value of f'(x) that is a function, and overcome their mixed and incorrect notion "the derivative" such as the tangent line at a point.

• Journal of the Korea institute for structural maintenance and inspection
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• v.19 no.4
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• pp.116-124
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• 2015

The objective of this study is to evaluate the effects of the replacement levels of grinded fly-ash on the repaired mortar based on a polymer. The main parameters are the curing temperature and replacement levels of grinded fly-ash. The curing temperature and the replacement levels of grinded fly-ash are varied at $40^{\circ}C$, $20^{\circ}C$ and $5^{\circ}C$, and between 0% and 35% of the total binder by weight, respectively. The flow in fresh mortar and compressive strengths according to ages, the relationship of stress-strain, elastic modulus and modulus rupture in hardened mortar, as well as scanning the electron microscopy and the X-ray diffraction of mortar, were measured, respectively. The test results showed that the flow, elastic modulus and modulus rupture are great in mortar specimens with 20~30% of the replacement levels of grinded fly-ash. In addition, compressive strengths according to ages were affected by the replacement levels of grinded fly-ash and the curing temperature indicated that the strength development ratio of mortar with 20% of the replacement levels of grinded fly-ash was greater than others. In the prediction of the compressive strength specified by the ACI 209 code, the strength development at an early and late age can be generalized by the functions of the replacement levels of grinded fly-ash and the curing temperature. In the analysis of scanning the electron microscopy and the X-ray diffraction, the number and intensity of peaks increased and the form of CSH gels on the surface of the particle of grinded fly-ash was observed.

• School Mathematics
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• v.18 no.3
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• pp.711-731
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• 2016

The purpose of this study is to investigate how pre-service secondary mathematics teachers modify mathematical tasks from a textbook and learning opportunities they have during the task modification. In the pursuit of this purpose, tasks was selected from derivative units in a textbook and five pre-service teachers was asked to modify the tasks. The findings from analysis are as follows. First, the cognitive demands of modified tasks were maintained or higher than those of the originals. Pre-service teachers' tendency toward conceptual understanding of derivative seems to make the result. Second, task modification provided a lot of learning opportunities for pre-service teachers. They tried to know intention of curriculum and textbook, realized the importance of predicting students' responses, and had opportunities for cooperation and reflective thinking.

• School Mathematics
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• v.12 no.2
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• pp.239-257
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• 2010

In school mathematics the derivative concept is intuitively taught with the tangents and the concept of instantaneous velocity. In this paper, I investigated the long historical developments of the derivative concepts and analysed the relationships between the definition of derivative and the related elements. Finally I proposed some educational implications based on the analysis.

• Journal of the Korea institute for structural maintenance and inspection
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• v.26 no.2
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• pp.18-27
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• 2022

In this study, the time-dependent chloride ingress behavior in GGBFS concrete was evaluated considering marine exposure conditions and the properties of concrete mixtures. The concrete mixture for this study had 3 levels of water to binder ratio and the substitution rate of GGBFS, and outdoor exposure tests were performed considering submerged area, tidal area, and splash area. According to the evaluation results of diffusion coefficient considering properties of concrete mixtures, as the substitution rate of GGBFS increased, the decreasing rate of the diffusion coefficient decreased based on exposure periods of 730 days(2 years). As the evaluation result of the diffusion behavior according to the marine exposure conditions, the diffusion coefficient was evaluated in the order of submerged area, tidal area, and splash area. In tidal area, a relatively high diffusion coefficient was evaluated due to the repetition of wet and dry seawater. In this study, the effects of GGBFS substitution rate on the decreasing behavior of apparent chloride diffusion coefficient was analyzed in consideration of exposure conditions and periods. Linear regression analysis was performed with apparent chloride diffusion coefficient as output value and GGBFS substitution rate as input value. After 730 days of exposure, the effect of GGBFS on diffusion coefficient was significantly reduced. Even for OPC concrete, after 730 days, the diffusion coefficient was as low as that of GGBFS concrete, so the gradient of the regression equation decreased significantly. It is thought that improved durability performance for chloride ingress can be secured before 730 days through the use of GGBFS.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.335-354
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• 2019

The purpose of this study is to explore alternative ways of teaching derivatives in a way that emphasizes intuition. For this purpose, the contents related to derivatives in Korean curriculum and textbooks were analyzed by comparing with contents in Singapore Curriculum and textbooks. Singapore, where the curriculum deals with derivatives relatively earlier than Korea, introduces the concept of derivatives and differentiation as the slope of tangent instead of the rate of instantaneous change in textbook. Also, Singapore use technology and inductive extrapolation to emphasize intuition rather than form and logic. Further, from the results of the exploration of other foreign cases, we confirm that the UK and Australia also emphasized intuition in teaching derivatives and differentiation. Based on the results, we discuss the meaning and implication of introducing derivatives and teaching differentiation in a way that emphasizes intuition. Finally, we propose the implications for the alternative way of teaching differentiation.

• Journal of the Korea institute for structural maintenance and inspection
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• v.14 no.4
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• pp.160-168
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• 2010

Recently, there are a lot of researches related to the high-fluidity concrete (HFC) with field applications. However, most applications and studies are with concretes with high strength level so there are little studies about durability evaluations such as chloride ion penetration properties with normal strength concrete. Therefore, to evaluate the durability of HFC with normal strength level, this study performed the chloride ion penetration test and observed the micro pore distribution with normal strength HFC which contains limestone powder. Experimental results showed that most micro-pores have diameters between 0.005 to 0.05 ${\mu}m$ with HFCs using limestone powder and the average diameter becomes larger with the increase of limestone powder content. Also, it was shown that, with the increase of the limestone powder content, penetration depth and diffusion coefficient of chloride ion increased and diffusion coefficient had good relationships with compressive strength and average pore diameter with the coefficient of determination over 0.90.