• 한국수학사학회지
• /
• 제32권6호
• /
• pp.281-299
• /
• 2019

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

• 한국지구과학회지
• /
• 제36권5호
• /
• pp.484-499
• /
• 2015

This study explores the impact of a STEM integration teacher professional development program focusing on teachers' perception of engineering and their attitudes toward integrating engineering into teaching. A total of sixty-eight teachers from ten schools participated in the program for five days. Data are collected from three main sources including (1) pre and post concept maps probing teachers' perceptions about the engineering discipline, (2) a pre and post survey measuring teachers' self-efficacy of teaching science/mathematics within the engineering context, and (3) engineering integrated science and (or) mathematics lesson plans and teaching reflections. This study utilizes both qualitative and quantitative research methods depending on the data we have collected. The results show that both science and math teachers thought that integrating engineering into teaching provided valuable outcomes, i.e., promoting students' learning about engineering and improving their interest in science or math through real-world problem solving exercises. Participants also felt more comfortable about integrating engineering in their teaching after the program. The results also imply that the teachers' understandings of engineering become more concrete after the program. This study also provides an overview of the challenges and advantages of teaching engineering in K-12 science and mathematics classrooms.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.1149-1159
• /
• 2008

Blind source extraction (BSE) is a special class of blind source separation (BSS) methods, which only extracts one or a subset of the sources at a time. Based on the time delay of the desired signal, a simple but important extraction algorithm (simplified " BC algorithm")was presented by Barros and Cichocki. However, the performance of this method is not satisfying in some cases for which it only carries out the constrained minimization of the mean squared error. To overcome these drawbacks, ICA with reference (ICA-R) based approach, which considers the higher-order statistics of sources, is added as the second stage for further source extraction. Specifically, BC algorithm is exploited to roughly extract the desired signal. Then the extracted signal in the first stage, as the reference signal of ICA-R method, is further used to extract the desired sources as cleanly as possible. Simulations on synthetic data and real-world data show its validity and usefulness.

• Journal of applied mathematics & informatics
• /
• 제5권2호
• /
• pp.373-382
• /
• 1998

Most of the works in Time Series Analysis are based on the Auto Regressive Integrated Moving Average (ARIMA) models presented by Box and Jeckins(1976). If the data exhibits no ap-parent deviation from stationarity and if it has rapidly decreasing autocorrelation function then a suitable ARIMA(p,q) model is fit to the given data. Selection of the orders of p and q is one of the crucial steps in Time Series Analysis. Most of the methods to determine p and q are based on the autocorrelation function and partial autocor-relation function as suggested by Box and Jenkins (1976). many new techniques have emerged in the literature and it is found that most of them are over very little use in determining the orders of p and q when both of them are non-zero. The Durbin-Levinson algorithm and Innovation algorithm (Brockwell and Davis 1987) are used as recur-sive methods for computing best linear predictors in an ARMA(p,q)model. These algorithms are modified to yield an effective method for ARMA model identification so that the values of order p and q can be determined from them. The new method is developed and its validity and usefulness is illustrated by many theoretical examples. This method can also be applied to an real world data.

• 한국수학사학회지
• /
• 제20권4호
• /
• pp.153-174
• /
• 2007

함수 개념은 그 자체만으로 이루어진 단일한 개념이 아니라 산술, 기하와 같은 수학의 여러 주제가 통합된 개념이다. 따라서 함수는 수학의 밑바탕에 폭넓게 스며 있는 기본적인 개념일 뿐 아니라 변화하는 현실 세계를 이해하기 위한 개념적인 수단으로서 다양한 변화 현상을 '보기' 위해서 생각하지 않을 수 없다. 이에 따라 본 논문에서는 역사적인 고찰을 통해 통합개념으로서 함수 개념에 대해 고찰하였다. 특히 함수 개념과 관련된 표현이 보다 명백히 드러난 중세에서부터 19세기까지 함수 개념의 변화를 통해 통합개념으로서 함수의 모습을 살펴보았다.

• 한국학교수학회논문집
• /
• 제17권4호
• /
• pp.657-677
• /
• 2014

본 연구의 목적은 실험수업에 참여한 세 명의 중학교 1학년 학생들의 모델 정교화 과정을 질적 사례연구를 통하여 살펴보고 모델 정교화에 영향을 미치는 요인을 분석하여 이에 관한 정보를 제공하고자 함이다. 분석 결과 학생들의 수학적 모델링의 정교화 과정은 각 단계가 단선적으로 일어나는 것이 아니라 모델 내에서 해를 구할 수 없거나 구한 해가 의미가 없는 경우 실제 문제 구성 단계로 돌아가 실제 문제를 수정하거나 수학적 모델 구성 단계로 돌아가 모델을 수정 또는 정교화하는 것을 알 수 있었으며, 모델 정교화 과정에 영향을 미치는 요인으로는 모델링 문제, 메타인지적 사고, 교사 동료와의 의사소통 및 교사의 역할 등이 복합적으로 작용함이 나타났다.

• 대한수학교육학회지:수학교육학연구
• /
• 제14권3호
• /
• pp.267-281
• /
• 2004

방정식의 활용 문제로 다루어지는 문장제는 학생들의 흥미를 유도하고 수학의 유용성을 보여줄 수 있는 것이지만, 학생들이 해결하기에는 여러 어려움이 있다. 본 연구는 학생들이 수학 문장제를 해결하는데 영향을 줄 수 있는 요인들을 언어적 측면과 인지적 측면에서 조사하였다. 언어적 요인에는 텍스트 기반, 실세계, 상황 모델이 있었는데, 학생들은 문장의 텍스트 기반에서 방정식의 상황 모델로 해석하는 것을 어렵게 생각하고 있었으며, 상황 모델에서 학생들은 많은 오류를 보였다. 인지적 측면에서는 방정식을 세우는 스키마와 해결 전략, 식의 복잡성 수준을 조사하였는데, 방정식을 세울 때 학생들은 복잡성 수준을 고려하기보다는 교사의 지도 내용에 따라 전략을 선택하는 경향이 있었다. 그리고 설탕의 양이나 농도, 설탕물의 양을 혼동하는 경향이 강했다. 본 연구의 결과를 통해 문장제에서 학생들에게 제시되는 문제가 해결하기에 얼마나 복잡한지, 학생들이 주로 어떤 전략을 선택하는지, 방정식의 문제 유형별로 발생하는 오류에 대해 알 수 있었다.

• 대한수학교육학회지:학교수학
• /
• 제3권2호
• /
• pp.373-399
• /
• 2001

The function is a basic and key concept to understand mathematical problems. However, many students have difficulties to expand the knowledge to other related concepts and to transfer the knowledge to real world problems. The reasons for the problem may be that the concept of function is taught by simplified and abstracted formula without fully understanding of the reasoning process. Also, the examples for the concepts are artificial and not related to students' experiences. Situated learning theory provides great implications to solve these problems. So, this study was designed to teach the concept of function more meaningful to students by appling situated learning theory. Thirty-eight middle school students were participated in this study. Students were provided the instruction designed according to the principles of situated learning theory. Then, they were asked to complete attitude survey questionnair and a performance assessment task. The result showed that the instruction based on situated learning theory was useful to Promote students' understanding and motivation for learning. More implications of the study was provided in the paper.

• ETRI Journal
• /
• 제38권2호
• /
• pp.397-404
• /
• 2016

In group-oriented applications, it is often required to verify a group of signatures/messages. The individual verification of signed messages in such applications comes at a high cost in terms of computations and time. To improve computational efficiency and to speed up the verification process, a batch verification technique is a good alternative to individual verification. Such a technique is useful in many real-world applications, such as mail servers, e-commerce, banking transactions, and so on. In this work, we propose a new, efficient identity-based signature (IDS) scheme supporting batch verifications. We prove that the proposed IDS scheme and its various types of batch verifications is tightly related to the Computational Diffie.Hellman problem under a random oracle paradigm. We compare the efficiency of the proposed scheme with related schemes that support batch verifications.

• Journal of applied mathematics & informatics
• /
• 제4권1호
• /
• pp.135-135
• /
• 1997

Times series modeling plays an important role in the field of engineering, Statistics, Biomedicine etc. Model identification is one of crucial steps in the modeling of an AutoRegreesive Moving Average(ARMA(p, q)) process for real world problems. Many techniques have been developed in the literature (Salas et al., McLeod et al. etc.) for the identification of an ARMA(p, q) Model. In this paper, a new technique called The Generalised Parameters Technique is formulated for seasonal and non-seasonal ARMA model identification. This technique is very simple and can e applied to any given time series. Initial estimates of the AR parameters of the ARMA model are also obtained by this method. This model identification technique is validated through many theoretical and simulated examples.