• Journal of the Korean Society of Groundwater Environment
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• v.2 no.2
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• pp.72-77
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• 1995

Flow times of the groundwater in the gneiss near Samkwang mine in Korea were estimated through the development of a mathematical model, the field hydraulic tests, and the analysis of tritium concentration of the groundwater and rainfall sampled in the study positions. Results of this study we as follows: (1) The mathematical model to calculate the age of groundwater was developed considering the tritium concentrations of rainfall precipitated in the studied area for period 1961 to 1993. (2) The ages of the groundwater in the tunnel 44, 92, 102, and 205 m below the surface were estimated at 2, 0, 4.0, 4.5, and 9.0 years, respectively. These results were verified by the data on the tritium concentrations of the groundwater in the tunnel for period 1991 to 1993.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.53-74
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• 2013

The purpose of this paper is to analyze how mathematically gifted middle school students find out the necessary and sufficient condition for a certain hyperbolic line to be parallel to a given hyperbolic line in Non-Euclidean disc model (Poincar$\acute{e}$ disc model) using the Geometer's Sketchpad. We also investigated their characteristic of mathematical thinking and analyze how they express what they had observed while they did mental experiments in the Poincar$\acute{e}$ disc using computer-aided construction tools, measurement tools and inductive reasoning.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.403-419
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• 2004

The perspective on this study assumes that the mathematical modeling activity provides students with the environment which promotes metacognitive thinking. The purposes of this paper are to investigate metacognitive thinking on the mathematical modeling with the result of case study. The study revealed that development of students' model was accompanied with the control and monitoring of modeling activities. Also students refined the model by self-assessment and peer-assessment in small group modeling activities and developed generalizable model.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.581-602
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• 2012

For developing mathematics teachers' professionalism, it is necessary to construct PDS to provide training programs which are appropriate for Korean context and needed by mathematics teachers. This study is a preliminary study for constructing PDS and aims to design PDS model for Korean mathematics teachers. Firstly, components of model were elicited by theoretical review. Secondary, focus group discussion with 8 teachers and individual interview with 1 educational profession and 3 foreign mathematics education researchers were conducted. Finally, by reflecting FGD and interview results, the final version of PDS model was designed. The final model is constructed by 3 components, which are life cycle, program types, and participants. In addition, professional development topics for each life cycle according to PDS model are presented.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.97-118
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• 2011

This study aimed finding effective models for the teaching the concept of function. We selected two models. One is discrete model which focuses on the 'corresponding relation of the elements of the sets(domain and range). The other is continuous model which focuses on the dependent relationship of the two variables connected in variable phenomenon. A vending machine model was used as a discrete model, and a water bucket model was used as a continuous model in our study. We taught 2 times about the concept of function using two models to the 60 students (7th grade, 2 classes) living in Taebak city, and tested it twice, after class and about 3 months later. A vending machine model was helpful in understanding the definition of function in the 7th grade math textbook. Also, it was helpful to making concept image and to recalling it. On the other hand, students who used the water bucket model had a difficultly in understanding the all independent variables of the domain corresponding to the dependent variables. But they excelled in tasks making formula expression and understanding changing situations.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.135-157
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• 2023

Double scale models have been introduced in elementary mathematics textbooks under the 2015 revised mathematics curriculum. However, few studies have examined in detail how students understand or utilize such models. In this study, we analyzed how 154 sixth-grade students who had learned the division of fractions from textbooks containing double scale models understood such models. The results showed that the students tended to identify the components of the model relatively well, but had difficulties exploring the unit or the meaning of the bottom number line of a model. They also had a lot of difficulties using the double scale model to complete the computation process and explain the computation principle. Based on these findings, we discuss the implications of teaching double scale models.

• 전기의세계
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• v.24 no.5
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• pp.6-15
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• 1975

본 고찰은 신경의 생리적 현상을 기능적 측면에서 아나로그 모델로 시뮬레이션 시켜가는 데 있어 모델화의 역사적 발달과정과 기존모델의 특성을 간략하게 요약하고 이들을 비교 검토한 것으로 초기의 모델화에 대한 철학적인 개념으로부터 TR, IC등의 전자부품을 사용한 최근의 모델에 이르기까지 많은 기존모델을 다루어 본 결과 다음과 같은 결론을 얻을 수 있었다. 1. 역사적 발달과정에도 잘 나타난 것처럼 전기, 화학, 역학, 수학등 여러분야의 전문적 지식의 교환없이는 모델화의 정확성, 분석상의 신뢰도, 결과에 대한 보편성이 결여되기 쉽다. 2. 특히 생리적 특성 및 수학적인 면밀한 고찰과 분석이 요구되고 있다. 이는 모델의 특성 결과에 대한 디지탈 전자계산기를 이용한 통계적 처리와 시뮬레이션을 용이하게 할 수 있고, 임상에의 이용 가능성을 높여나가기 위해서이다. 3. 신경 전체에 대한 모델화에 앞서 신경의 구조별 모델화가 선행되어야 한다. 이는 신경의 구조중 수상돌기 및 soma에서의 synaptic inputs에 대한 위치변화에 따른 synaptic potential의 분포상태가 신경의 특성을 규명하는데 매우 유익하다는 사실이 밝혀졌기 때문이다. 4. 신경에서의 synaptic potential의 분포상태는 종전에는 temporal distribution 개념이 지배적이었으나 최근에 와서는 spatial distribution 개념이 우세하게 되었다.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.97-115
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• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• The Mathematical Education
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• v.62 no.3
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• pp.401-416
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• 2023

This study systematically examined the influence of preservice teachers' self-efficacy and AI anxiety, on the intention to use AI programs 'knock-knock! mathematics expedition' in mathematics lessons based on a technology acceptance model. The research model was established with variables including self-efficacy, AI anxiety, perceived ease of use, perceived usefulness, and intention of use from 254 pre-service teachers. The structural relationships and direct and indirect effects between these variables were examined through structural equation modeling. The results indicated that self-efficacy significantly affected perceived ease of use, perceived usefulness, and intention to use. In contrast, AI anxiety did not significantly influence perceived ease of use and perceived usefulness. Perceived ease of use significantly affected perceived usefulness and intention to use and perceived usefulness significantly affected intention to use. The findings offer insights and strategies for encouraging the use of 'knock-knock! mathematics expedition' by preservice teachers in mathematics lessons.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.499-514
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• 2016

As people get to aware that the traditional teacher-centered education can not develop individual students' diversity and creativity and cope with the rapidly changing future society, Korean government has emphasized the learner-centered education since the 7th curriculum. Under this background, we have analyzed the problems of mathematics education that teachers recognized and the features of mathematics textbooks that they developed within the framework of leaner-centered education on the basis of the resources developed from 'Student-centered mathematics textbook improvement teacher research group in 2015.' As a result of using the framework of 'Learner-centered psychological principles (APA, 1997)' for analysis, teachers pointed out the problems related to the principles of Motivational and emotional influences on learning, Individual differences in learning, Developmental influences on learning, Nature of the learning process, and Construction of knowledge, in order. The features of textbook teachers developed reflected the principles of Nature of the learning process, Construction of knowledge, and Motivational and emotional influences on learning, in order. Finally, as we have compared teachers' recognition of the problems with the features of the textbooks developed, most of the problems teachers recognized are reflected in the textbooks; however, the Cognitive and metacognitive factor takes higher possession on the textbooks compared with the problems being recognized, and the Motivational and affective factor takes lower possession on the textbooks compared with the problems being recognized. Accordingly, we have been able to search for the solution to realize the learner-centered education through math textbooks.