• The Mathematical Education
• /
• v.46 no.3
• /
• pp.315-329
• /
• 2007

The concepts of ratio, rate, and proportion are used in everyday life and are also applied to many disciplines such as mathematics and science. Proportional reasoning is known as one of the pivotal ideas in school mathematics because it links elementary ideas to deeper concepts of mathematics and science. However, previous research has shown that it is difficult for students to recognize the proportionality in contextualized situations. The purpose of this study is to understand how the mathematical concept in the middle school mathematics curriculum is connected with ratio, rate, and proportion and to investigate the characteristics of proportional reasoning through analyzing the concept including ratio, rate, and proportion on the middle school mathematics curriculum. This study also examines mathematical concepts (direct proportion, slope, and similarity) presented in a middle school textbook by exploring diverse interpretations among ratio, rate, and proportion and by comparing findings from literature on proportional reasoning. Our textbook analysis indicated that mechanical formal were emphasized in problems connected with ratio, rate, and proportion. Also, there were limited contextualizations of problems and tasks in the textbook so that it might not be enough to develop students' proportional reasoning.

• Education of Primary School Mathematics
• /
• v.9 no.1 s.17
• /
• pp.43-58
• /
• 2005

The objective of the present study was designed to examine that metacognition education had any promoting effects on the development of students' reasoning ability. Two classes in the 5th grade were asked to participated for the present study. Prior to the metacognition teaching, both the experimental and control group classes were given to the preliminary test in which students' basic ability for mathematical reasoning was graded. Then, the students in the experimental group were given 8hour teaching for the topics on the symmetric properties of geometric figures. The present findings indicate that educational application which motivates metacognition can improve mathematical reasoning ability in elementary students. It is widely accepted that metacognition is an active and conscious mental activity, helps the students perceive voluntarily the study items, and further plays an important role in constructing independent and active thinking processes. Accordingly, the present results implicate that the practical performance of metacognition education into the class indeed contributes to build up or strengthen students' voluntary ways of reasoning.

• Communications of Mathematical Education
• /
• v.23 no.1
• /
• pp.39-51
• /
• 2009

The purpose of this article is to study characteristics of tangram as instructional media in combinatorialgeometric point of view, and to present basic materials and direction for efficient tangram activities in gifted education upon systematical analysis of methods of finding solutions. We can apply x=a+2b+4c to find all possible combination of solutions in tangram activities not as trial-and-error method but as analytical method. Through teacher's questions and problem posing in activities using tangram, we systematically came up with most solution and case of all possible combinations be solution in classifying properties of pieces and combining selected pieces.

• Journal of Korean Society of Environmental Engineers
• /
• v.32 no.1
• /
• pp.97-104
• /
• 2010

At present, the biological nutrient removal (BNR) process for removal of nitrogen and phosphorus is being constructing to keep pace with the reinforced standard of effluent quality and the traditional activated sludge process of preexistence is being promoting to retrofit. At the most case of retrofitting, processes are subjected to be under consideration as alternative BNR process for retrofitting. However, process evaluation methods are restricted to compare only treatment efficiency. Therefore, when BNR process apply, process evaluation was needed various method for treatment efficiency as well as sludge production and aeration cost, and all. In this study, the evaluation method of alternative process was suggested for the case for retrofitting S wastewater treatment plant which has been operated the standard activated sludge process. Three BNR processes for evaluation of proper alternatative process were selected and evaluated with suggested method. The selected $A^2$/O, VIP and DNR processes were evaluated using the mathematical model which is time and cost effective as well as gathered objective evaluation criteria. The evaluation between 5 individual criteria was possible including sludge production and energy efficiency as well as treatment performance. The objective final decision method for selection of optimal process was established through the fuzzy inference.

• Communications of Mathematical Education
• /
• v.21 no.1 s.29
• /
• pp.81-105
• /
• 2007

We need questions that have various answers, not one answer by just mechanical calculation, to improve students' creativity. Such questions usually require inquiry, presumption, logical inference and a variety of problem solving tactics. These questions will be even more effective when they can provide students with multiple experiences by making them engage in lots of activities. We have to make use of diverse teaching aids and tools, or teaching materials in order to get these results. This research searches for teaching materials which improve gifted students' creativity as well as the ways to utilize 4D Frame. Furthermore we intend to present the ways to put such materials and 4D frame into practical use.

• Journal for History of Mathematics
• /
• v.19 no.4
• /
• pp.1-12
• /
• 2006

The Nine Chapters on the Mathematical Art has dominated the history of Chinese mathematics. It served as a textbook not only in China but also in the neighbouring countries and regions. The book is anonymous like many Chinese classics. The Nine Chapters contains 246 problems and their solutions, some of which date back to before the Qin Dynasty $(221\sim207\;B.C)$ and it seems to have been written by various writers over many generations. In this paper, we will investigate the structure of the Nine Chapters from the view points of ancient social environments which entail eventually mathematics in the Nine Chapters.

• Journal of the Korean School Mathematics Society
• /
• v.17 no.3
• /
• pp.359-384
• /
• 2014

The purpose of this study is inquire the reaction and adaptability of the mathematically gifted student, in the case of introduce learning materials based on GeoGebra in real class. The study program using GeoGebra consist of 'construction of fundamental figures', 'making animation with using slider tools' (graph of a function, trace of a figure, definite integral, fixed point, and draw a parametric curve), make up the group report after class. In detail, 1st to 15th classes are mainly problem-solving, and topic-exploring classes. To analyze the application effects of developed learning materials, divide students in four groups and lead them to make out their own creative products. In detail, guide students to make out their own report about mathematical themes that based on given learning materials. Concretely, build up the program to make up group report about their own topics in six weeks, after learning on various topics. Expert panel concluded that developed learning materials are successfully stimulate student's creativity in various way, after analyze of the student's activities. Moreover, those learning programs also contributed to the develop of the mathematical ability to thinking that necessary to writing a report. As well, four creative products are assessed as connote mathematically gifted student's creative thinking and meaningful elements in mathematical aspects.

• Journal of Sensor Science and Technology
• /
• v.5 no.2
• /
• pp.37-46
• /
• 1996

This paper describes a system that can be used to recognize unknown materials regardless of the change in ambient temperature by using temperature response curve fitting and fuzzy neural network(FNN). There are problems with a recognition system which utilize temperature responses. It requires too many memories to store the vast temperature response data and it has to be filtered to remove the noise which occurs in experiments. Thus, this paper proposes a practical method using curve fitting to remove the above problems of memories and noise. Also, the FNN is proposed to overcome the problem caused by the change of ambient temperature. Using the FNN which is learned by temperature responses on fixed ambient temperatures and known thermal conductivity, the thermal conductivity of the material can be inferred on various ambient temperatures. So the material can be recognized via its thermal conductivity.

• The Journal of the Korea Contents Association
• /
• v.8 no.12
• /
• pp.1-9
• /
• 2008

Fuzzy Cognitive Map, one of ways to model, describe and infer reasoning relations, is widely used in the field of reasoning knowledge engineering. Despite of the natural and easy understanding of decision and smooth explanation of relation between front and rear, reasoning relation is organized with mathematical haziness and complex algorithm and rarely has an interactive user interface. This paper suggests an interactive Fuzzy Cognitive Map(FCM) construction support system. It builds a FCM increasingly concerning multiple experts' knowledge. Futhermore, it supports user-supportive environment by dynamically displaying the structure of Fuzzy Cognitive Map which is constructed by the interaction between experts and the system.

• Journal of Educational Research in Mathematics
• /
• v.22 no.1
• /
• pp.101-115
• /
• 2012

Analogy, a plausible reasoning on the basis of similarity, is one of the thinking strategy for concept formation, problem solving, and new discovery in many disciplines. Statistics educators argue that analogy can be used as an useful thinking strategy in statistics as well. This study investigated the characteristics of students' analogical thinking in statistics. The mathematically gifted were asked to construct similar problems to a base problem which is a statistical problem having a statistical context. From the analysis of the problems, students' new problems were classified into five types on the basis of the preservation of the statistical context and that of the basic structure of the base problem. From the result, researchers provide some implications. In statistics, the problems, which failed to preserve the statistical context of base problem, have no meaning in statistics. However, the problems which preserved the statistical context can give possibilities for reconceptualization of the statistical concept even though the basic structure of the problem were changed.