• Communications of Mathematical Education
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• v.28 no.1
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• pp.97-130
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• 2014

The purpose of the study was to investigate the aspects of analogy of high school student's thinking process revealed in the inquiry activity with synthetic division. The case study method of qualitative research was conducted with two high school 10th grade students. Structure-mapping model(SMM) of Gentner and similarity frames which were proposed by other researchers were utilized to analyze the data. Two students used analogy as a tool and they could discover synthetic division of more than 2 degrees, but they revealed different levels of mathematics discovery depending on the different degree of analogical thinking. Surface similarity in the process of inquiry activity played a vital role in analogical thinking. We asked students to explore and discover analogy based on structure similarity. Analogy based on the systematic approach made it possible to predict upper domain. Analogy based on the procedure similarity induced internalization. We could conclude that analogy has instrumental, heuristic and reflective characteristics.

• The Mathematical Education
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• v.56 no.3
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• pp.319-340
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• 2017

The purpose of this study is to develop teaching and learning materials for the mathematics project inquiry subject. Since this subject is newly opened in the 2015 revised mathematics curriculum, there are no textbooks and materials. Hence it is required to help teachers plan lessons of the mathematics project inquiry subject. For this study, developing directions and objectives are established. Ten hours of lesson plan and teaching and learning materials are also developed for the two themes of 'big data' and 'industrial mathematics'. Suitability and validity of the developed material are verified positively from a survey of 8 teachers and 2 professionals. The detailed result findings are as follows. First, teaching and learning notes are suggested for each lesson plan. They are comprised of building inquiry plan, doing inquiry, summarizing results, and presentation. Second, driving questions of each theme are developed as "What is the big data and where is it used for ?" and "How various is the use of the industrial mathematics ?" respectively. Third, poster-types of each project product are developed. Fourth, three inquiry activity sheets and examples which are theme selection, inquiry plan, and group activity are developed. Fifth, 4 assessment sheets of self, peer, group, and teacher-use are developed.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.187-206
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• 2009

On this study, the historical flow of the notation was briefly examined and the direction of mathematical investigation activity of the content of notation by analogy was explored and teaching learning materials were developed. Diverse mathematical facts were investigated on the basis of decimal system and binary system which are learned in middle school. First, the way of progressing analytic activity with algebraic material was examined. Second, on the basis of the notation which are learned in the first grade of middle school, the definition of the scale of a -notation, -a -notation, $\frac{1}{a}$notation, $\sqrt{a}$-notation was extended by analogy. The result of this study will be expected to establish the curriculum of mathematics and provide teaching and learning with the meaningful current events.

• School Mathematics
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• v.11 no.3
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• pp.527-546
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• 2009

This study was designed to gain insights into instrumental genesis process of CAS in Korean high school students and to explore its practical potentials in secondary mathematics education. Two activities, such as Concept-Centered Mathematics Activity based on CAS and Problem Solving Activities, were constructed and executed to 10th Grade seven students for twelve class hours. The finding on the students' activities are as follows : it is meaningful in mathematics education, especially in algebra education, in that the CAS based concept centered mathematics activity offers great opportunities to deal with high-qualified application problems. The problem solving activities based on the instrumented CAS may have an influence on the sequence of mathematics curriculum, e.g. the optimization problems may precede the calculus problems such as derivatives in high school. The results of this study to investigate the instrumental genesis of CAS in mathematical activities will give insights into the secondary mathematics curriculum to prepare the CAS in Korea.

• Communications of Mathematical Education
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• v.31 no.4
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• pp.433-456
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• 2017

The purpose of this study is to suggest the directions for the development and improvement of mathematics textbooks in Korea by examining these characteristics of German textbooks. As a result, German mathematics textbooks were free for unit order and names of units. German mathematics textbooks defined a function for various real life and natural phenomena, relation after intuitively knowing the correspondence between two variables through a graph. In addition, it exercises interpreting the characteristics and information of the graph, guides the activity of graphing various functional situations, and contents to convert various expression methods such as graphs, tables, relational expressions, mathematical terms and sentences. In the German mathematics textbooks, mathematical expressions of the functional relations of the materials in various contexts of daily life, and the activities of predicting and predicting the future, were made to feel the usefulness of mathematics. It has raised functional thinking and provided problems related to other subjects, thus enhancing connectivity with other disciplines. It also included open issues and issues that required mathematical communication.

• Journal of Elementary Mathematics Education in Korea
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• v.8 no.1
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• pp.1-21
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• 2004

The purpose of this study is analyzing phenomenon of mathematical communication by students applied story shell. Also, this study is obtained teaching indicated in early standardized mathematics classes. It is served we realize the purpose of study and set study subject to be as follows. First, it finds out how to be described activities of students' mathematical communication in the mathematics class applied story shell. Second, it finds out what phenomenon is observed in a behavior side of the mathematics class applied story shell. It is developed 7 story shells for the 6th grade of the elementary school for about 4 months and when applying mathematics classes, it is analyzed the notes and recorded data to get in an each class and when applying mathematics classes. It is analyzed the notes and recorded data to get in an each class. The result of this study is as follows: First, in a mathematics class which applies story shell, students concentrate on the class when hearing and reading mathematics problem. So, they are able to understand a mathematical language included in the problem. Second, in a mathematics class which applies story shell, students participate actively at the mathematics class. And in complicate situation among the students it is served they justify own opinion and persuaded logically. The point which study hints to see such a result is as follows: First, in a mathematics class which applies story shell students have answered more quickly than the old times as hearing and reading the problem in a picture. Second, in a mathematics class which applies story shell, students were used to being the mathematics language intimately and there was to observe to express it by an equation. Third, in a mathematics class which applies story shell students attend to study activity with interest. Forth, in situation of complicate thought, students are persuading and explaining their opinions for the purpose of justification.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.85-99
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• 2017

In order to improve mathematical problem-solving ability, there has been a need for research on practical application of meta-affect which is found to play an important role in problem-solving procedure. In this study, we analyzed the characteristics of the sociodynamical aspects of the meta-affective factor of the successful problem-solving procedure of small groups in the context of collaboration, which is known that it overcomes difficulties in research methods for meta-affect and activates positive meta-affect, and works effectively in actual problem-solving activities. For this purpose, meta-functional type of meta-affect and transact elements of collaboration were identified as the criterion for analysis. This study grasps the characteristics about sociodynamical function of meta-affect that results in successful problem solving by observing and analyzing the case of the transact structure associated with the meta-functional type of meta-affect appearing in actual episode unit of the collaborative mathematical problem-solving activity of elementary school students. The results of this study suggest that it provides practical implications for the implementation of teaching and learning methods of successful mathematical problem solving in the aspect of affective-sociodynamics.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.39-57
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• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Journal of the military operations research society of Korea
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• v.36 no.3
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• pp.135-145
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• 2010

The submarine is very threatening and secretive weapon system that achieves missions under the sea. However, the submarine is faced with danger that can be attacked from the enemy when is detected by sensor or rose to the surface. This study will be planned optimal path to maximize the survival rate that considers submarine navigation capability in underwater and search activity of hostile warships. A mathematical programming model and a heuristic algorithm will be suggested in this study. The mathematical programming model is verified by using ILOG CPLEX. The submarine path, unit time(distance) of navigation, survival rate, and computation time is computed by using a heuristic algorithm.

• Proceedings of the Membrane Society of Korea Conference
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• 1995.09a
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• pp.57-71
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• 1995

A simple mathematical model for gacilitated mass transport with a fixed site carrier membrane was derived by assuming an instantaneous, microscopic concentration (activity) fluctuation, The concentration fluctuation, developed due to reversible chemical reaction between carrier and solute, could acuse the higher chemical potential gradient and the facilitated transport. For mathematical formulation, an analogy was employed between the mass transfer for the facilitated transport with fixed site carrier membrane and the electron transfer in a parallel resistor-capacitor (RC) circuit. For the single RC model, it was assumed that a single capacitor represented the total carrier and a solute could not inter-diffuse between matrix and carrier, allowing only two diffusional pathways, This assumption was relaxed by adopting a serial combination of the parallel RC circuit. Here, a solute diffuses in two elements (matrix or carrier) can exchange its pathway, exhibiting four diffusional pathways. The current models were examined against experimental data and the agreement was exceptional.