• Journal of Educational Research in Mathematics
• /
• v.23 no.3
• /
• pp.335-351
• /
• 2013

This research assumes that abduction is so important as much as all the creative plausible reasoning to be based upon. We expect it to be deeply appreciated and be taught positively in school mathematics. We are noticing that every problem solving process must contain some steps of abduction and thus, we believe that those who are afraid of abduction cannot solve any newly faced problem. Upon these thoughts, we are looking into the middle school mathematics textbooks to see that how strongly various abductions are emphasized to solve problems in it. We modified types of abduction those were suggested by Eco(1983) or by Bettina Pedemonte, David Reid (2011) and investigated those books to see if, we may regard, various types of abduction be intended to be used to solve their problems. As a result of it, we found that more than 92% of the problems were not supposed to use creative abduction necessarily to solve it. And we interpret this as most authors of the textbooks have emphasis more on the capturing and understanding of basic knowledge of school mathematics rather than the creative reasoning through them. And we believe this need innovation, otherwise strong debates are necessary among the professionals of it.

• School Mathematics
• /
• v.17 no.2
• /
• pp.289-308
• /
• 2015

This study analyzed mathematical processes elaborated in the mathematics curricula of Korea, China, Japan, and the US. Ten mathematical processes were extracted: (a) learning of concepts, principles, laws, and skills; (b) problem solving; (c) reasoning; (d) communication; (e) representation; (f) connections; (g) creativity; (h) character-building; (i) self-directed learning; and (j) positive attitude toward mathematics. This study specified the meaning of such processes and their sub-domains, noticing similarities and differences among the curricula. On the basis of the results, this study includes suggestions for the development of next mathematics curriculum in Korea.

• Communications of Mathematical Education
• /
• v.12
• /
• pp.489-507
• /
• 2001

교수 ${\cdot}$ 학습 과정에서 계산 능력 배양이 목표인 영역을 제외하고는, 복잡한 계산, 수학적 개념 ${\cdot}$ 원리 ${\cdot}$ 법칙의 이해, 문제 해결력 향상 등을 위하여 가능하면 계산기나 컴퓨터를 적극 활용하도록 한다. 제 7차 교육과정에서는 수학적 힘의 신장을 구현하기 위한 실천적인 항목 중 다음과 같이 교수 ${\cdot}$ 학습과정에서의 technology의 활용을 적극 권장하고 있다. 이는 곧 수학교육과 실생활이 서로 밀접한 관계를 가지고 있음을 의미하는 것이다. 이런 새로운 움직임에 따라 계산기 활용에 대한 관심과 이를 수업에 이용하려는 방안을 적극 모색하고 있으며 이미 많은 자료들이 간행되고 있다. 그래픽 계산기는 컴퓨터와는 달리 많은 자료를 내장하고 있지는 않지만 휴대가 간편하고 개별적으로 사용할 수 있어 학교 수업시간 중 활용하는 데에 큰 장점을 가지고 있다. 또, 수학의 교수 ${\cdot}$ 학습 과정에서 그래픽계산기는 학생들의 흥미를 자극하고, 시각적인 힘을 활용하고, 수학적 사고력을 향상시키며, 문제를 탐구하는 과정에서의 단순한 계산을 효과적으로 처리할 수 있도록 도와준다. 뿐만 아니라 수학의 내적 영역과 수학의 외적 영역을 연결시키는 힘과 학습 과정에서 학생의 주도력을 강화시켜줄 수 있다. 그러나 계산기의 사용 자체가 목표가 될 수는 없으며 그래픽 계산기의 사용으로 학생들의 계산능력을 하락시켜서도 안된다. 이를 위해서는 적절한 교수 ${\cdot}$ 학습법의 개발과 연구가 끊임없이 지속되어야 할 것이다. 그래픽계산기는 함수, 통계 단원에서 자료를 분석하고 그에 적합한 식을 찾는 과정에 매우 유용하게 이용된다. 이는 재량활동이나 특기적성활동 시간에 조작활동을 통하여 개념에 대한 다양한 창의적인 표현을 할 수 있는 기회를 제공하기도 한다. 다음은 함수식을 이용하여 여러 가지 디자인을 할 수 있는 예를 그래픽 계산기를 통하여 보여준다. 생활 속의 여러 가지 모양들은 대체로 함수식으로 표현될 수 있다. 그래픽 계산기는 함수식을 입력하여 그래프의 형태를 관찰하고 그 특징을 살펴보는데 매우 유용하며 제한된 변역에서 여러개의 함수식을 입력하여 원하는 모양의 디자인을 해 볼 수 있다.

• School Mathematics
• /
• v.12 no.2
• /
• pp.177-191
• /
• 2010

Small Group Collaborative Instruction in school settings has been endorsed by many educational experts over the years. Some studies found that learners greatly benefit from one another through communication and interaction with their peers. These studies previously indicated improvement of a learner‘s academic ability as well as the application of the affective domain when using this type of instruction. Lower-level students with limited mathematical abilities improved their problem-solving and conceptual thinking skills when tasked to work with other learners. On the other hand, the effectiveness of this process was questioned to be less evident with higher-level performers. Therefore, this study was designed to observe the efficacy of Small Group Collaborative Instruction on higher-level students and to explore their learning process as they interact with and teach lower-level students. This study observed that higher-level students use high-level mathematical thinking skills when helping lower-level students, and they improved problem-solving ability as well as communication skills.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.9
• /
• pp.80-87
• /
• 2004

Active control of on-orbit spacecraft jitter is a significant problem for future spacecraft mission requiring stringent pointing performance. Jitter is major disturbance source degrading payload pointing performance. Both passive and active jitter isolation techniques have been studied during the last decade. We present active jitter isolation for a model device in this work. The device provides active control capability by 3 degree-of-freedom control of payload in feedback control strategy. Mathematical modeling of the device is pursued which is naturally used for a baseline controller design. Simulation results are used to validate the designed control law.

• School Mathematics
• /
• v.17 no.1
• /
• pp.99-118
• /
• 2015

The purpose of this study is to investigate teachers' perception of core competencies and affective aspects in mathematics. For this purpose, a nationwide survey was conducted. The survey questionnaire consists of three core competencies including problem solving, reasoning and communication, and two affective aspects including good human nature and attitudes. The survey results were further analyzed based on school level, teaching experience, location of schools, and types of high schools. As a result, four findings were identified. First, elementary school teachers tend to put more emphasis on core competencies and affective aspects than secondary school teachers do. Second, in elementary school level, longer teaching experience is correlated with more positive perception of core competencies and affective aspects. However, there was an opposite tendency in secondary school level. Third, teachers working at schools in metropolitan cities tend to emphasize core competencies and affective aspects more than those at schools located in mid-sized cities and rural areas. Fourth, the school types in high school didn't seem to affect the teachers' perception on core competencies and affective aspects.

• Communications of Mathematical Education
• /
• v.32 no.3
• /
• pp.341-362
• /
• 2018

The purpose of this study is to develop a STEAM education model on the basis of mathematics curriculum using real life context, and to analyze the effect of the class based on developed model to make applicable pedagogical discussion. For this purpose, STEAM class materials that can be used in terms of recognition, connection, extension, and application of mathematical concepts, principles and laws are considered, taking into consideration the ways in which real life contexts and mathematical learning could be harmonized. As a results of using these materials, it was empirically confirmed that students' cognitive thinking and affective aspects abilities were improved. The STEAM instruction centered on the mathematics curriculum and the mathematics class based on the data developed in this study have a unique identity compared to the conventional general mathematics teaching methods using the textbooks. And it is pursuing the future class model which could present desirable creativity and personality education. The result of this study would provide preliminary data and meaningful implications to the researchers for next curriculum and concomitant instructional materials as well as the mathematics teachers.

• Journal of Science Education
• /
• v.38 no.3
• /
• pp.569-584
• /
• 2014

The Purpose of this study was an analysis of high school student's understanding level about concepts of special relativity through in-depth interview. The 8 participants were 10th grade students in H high school in Ulsan city, who were interviewed and analyzed in the results of the interview about basic concepts of special relativity using achievement checklist in 6 situations(principle of constancy of light velocity, principle of relativity, relativity of simultaneity, garage paradox, rocket paradox). As results of the checklist, the participants showed high achievement in the content level of simple phenomena and simple concepts related to special relativity. But they showed low achievement in the concept level for fundamental understanding of special relativity. As results of the interview, it was found that the participants decided the order of events depending on their intuition and had a difficulty to apply the coordinate system to real situation, even though they mathematically understood it. In addition, some participants who could not understand the inertial coordinate system explained paradoxes of relativity depending on their intuition and had learner's chaos. Finally, though high school students usually being in formal operational stage, some students had difficulty to draw phenomena of space and time in two dimensional plane.

• Korean Journal of Logic
• /
• v.8 no.1
• /
• pp.23-46
• /
• 2005

The purpose of the paper Is to discuss and estimate early Popper's theory of probability, which is presented in his book, The Logic of of Scientific Discovery. For this, Von Mises' frequency theory shall be discussed in detail, which is regarded as the most systematic and sophisticated frequency theory among others. Von Mises developed his theory to response to various critical questions such as how finite and empirical collectives can be represented in terms of infinite and mathematical collectives, and how the axiom of randomness can be mathematically formulated. But his theory still has another difficulty, which is concerned with the inconsistency between the axiom of convergence and the axiom of randomness. Defending the objective theory of probability, Popper tries to present his own frequency theory, solving the difficulty. He suggests that the axiom of convergence be given up and that the axiom of randomness be modified to solve Von Mises' problem. That is, Popper introduces the notion of ordinal selection and neighborhood selection to modify the axiom of randomness. He then shows that Bernoulli's theorem is derived from the modified axiom. Consequently, it can be said that Popper solves the problem of inconsistency which is regarded as crucial to Von Mises' theory. However, Popper's suggestion has not drawn much attention. I think it is because his theory seems anti-intuitive in the sense that it gives up the axiom of convergence which is the basis of the frequency theory So for more persuasive frequency theory, it is necessary to formulate the axiom of randomness to be consistent with the axiom of convergence.

• Journal of vocational education research
• /
• v.29 no.3
• /
• pp.41-60
• /
• 2010

The purpose of this study was to investigate the relationships between teachers' characteristics and schools' peculiarities and to analyze relevant variables which influence the organization and implementation of the curriculum in specialized industry high schools. Subject were 414 teachers in specialized industry high school. The main result of this study are as follows. First, according to teachers' sex distinction, position, teaching experience, career of industry-related companies, subtle stress difference were found in establishment of education programs, relevance of educational activity, propriety of equipment. Second, in case of schools' subject of establishment, dormitory, specialized types, number of class, type of the sex of recruitment, subtle difference were found in connectivity of graders and subjects, relevance of the organization of education activity, substantial curriculum, push ahead with specialized high school. Third, measures to support development of specialized curriculum arrange sub-items in order of frequency. The way we understand things on vocational education must be settled without delay.