• School Mathematics
• /
• v.16 no.1
• /
• pp.111-133
• /
• 2014

This study aims to explore mathematical belief system and core belief factors to be found. The mathematical belief system becomes an auto regulation device for students' using mathematical knowledge in mathematical situations and provides them with the context to perceive and understand mathematics. They have individual mathematical beliefs for each of mathematics subject, mathematical problem solving, mathematical teaching and learning and self-concept, and these beliefs of students construct mathematical belief system according to mutual relationships among the mathematical beliefs. Using correlation analysis and multiple regression, mathematical belief system was structuralized and core belief factors were found. Mathematical belief system is structuralized and, as a result the core belief factors that are psychological centrality of high school students' mathematical belief system are found to be persistence, challenge, confidence and enjoyment. These core belief factors are formed on the basis of personal experiences and they are personal primitive beliefs that cannot be changed with ease and cannot be shared with other people but they are related with many other beliefs influencing them.

• Journal of Elementary Mathematics Education in Korea
• /
• v.6 no.1
• /
• pp.1-21
• /
• 2002

Teachers' teaching behavior is directly influenced by teachers' belief, and students' belief system is directly influenced by teachers' teaching behavior. There has been a question whether curriculum of teacher training university could help preservice teachers form positive belief system. The purpose of this study was to address this issue empirically. First, a questionnaire about mathematical belief was given to freshmen preservice teachers. They generally showed positive belief about mathematics to the degree that is not satisfactory and responded most positively in the sub-area of teaching mathematics from three sub-areas of mathematics itself, studying mathematics, and teaching mathematics. After studying a mathematical philosophy course, the freshmen preservice teachers were given the same questionnaire that they responded before studying the course. Belief about mathematics itself was changed very positively, and increase in the sub-area of mathematics itself was the largest. These results show that the mathematical philosophy course helped preservice teachers form positive belief system in mathematics.

• The Mathematical Education
• /
• v.24 no.2
• /
• pp.105-116
• /
• 1986

For any thought and knowledge, its growth and development has close relation with the society where it is developed and grow. As Feuerbach says, the birth of spirit needs an existence of two human beings, i. e. the social background, as well as the birth of body does. But, at the educational viewpoint, the spread and the growth of such a thought or knowledge that influence favorably the development of a society must be also considered. We would discuss the goal and the function of mathematics education in relation with the prosperity of a technological civilization. But, the goal and the function are not unrelated with the spiritual culture which is basis of the technological civilization. Most societies of today can be called open democratic societies or societies which are at least standing such. The concept of rationality in such societies is a methodological principle which completes the democratic society. At the same time, it is asserted as an educational value concept which explains comprehensively the standpoint and the attitude of one who is educated in such a society. Especially, we can considered the cultivation of a mathematical thinking or a logical thinking in the goal of mathematics education as a concept which is included in such an educational value concept. The use of the concept of rationality depends on various viewpoints and criterions. We can analyze the concept of rationality at two aspects, one is the aspect of human behavior and the other is that of human belief or knowledge. Generally speaking, the rationality in human behavior means a problem solving power or a reasoning power as an instrument, i. e. the human economical cast of mind. But, the conceptual condition like this cannot include value concept. On the other hand, the rationality in human knowledge is related with the problem of rationality in human belief. For any statement which represents a certain sort of knowledge, its universal validity cannot be assured. The statements of value judgment which represent the philosophical knowledge cannot but relate to the argument on the rationality in human belief, because their finality do not easily turn out to be true or false. The positive statements in science also relate to the argument on the rationality in human belief, because there are no necessary relations between the proposition which states the all-pervasive rule and the proposition which is induced from the results of observation. Especially, the logical statement in logic or mathematics resolves itself into a question of the rationality in human belief after all, because all the logical proposition have their logical propriety in a certain deductive system which must start from some axioms, and the selection and construction of an axiomatic system cannot but depend on the belief of a man himself. Thus, we can conclude that a question of the rationality in knowledge or belief is a question of the rationality both in the content of belief or knowledge and in the process where one holds his own belief. And the rationality of both the content and the process is namely an deal form of a human ability and attitude in one's rational behavior. Considering the advancement of mathematical knowledge, we can say that mathematics is a good example which reflects such a human rationality, i. e. the human ability and attitude. By this property of mathematics itself, mathematics is deeply rooted as a good. subject which as needed in moulding the ability and attitude of a rational person who contributes to the development of the open democratic society he belongs to. But, it is needed to analyze the practicing and pursuing the rationality especially in mathematics education. Mathematics teacher must aim the rationality of process where the mathematical belief is maintained. In fact, there is no problem in the rationality of content as long the mathematics teacher does not draw mathematical conclusions without bases. But, in the mathematical activities he presents in his class, mathematics teacher must be able to show hem together with what even his own belief on the efficiency and propriety of mathematical activites can be altered and advanced by a new thinking or new experiences.

• Research in Mathematical Education
• /
• v.11 no.2
• /
• pp.127-141
• /
• 2007

This paper compares and analyzes mathematics teachers' understanding of students' mathematical comprehension after experiences with the Cognitively Guided Instruction (CGI) or the Development of Mathematical Ideas (DMI) teaching strategies. This report sheds light on current issues confronted by the educational system in the context of mathematics teaching and learning. In particular, the declining rate of mathematical literacy among adolescents is discussed. Moreover, examples of CGI and DMI teaching strategies are presented to focus on the impact of these teaching styles on student-centered instruction, teachers' belief, and students' mathematical achievement, conceptual understanding and word problem solving skills. Hence, with a gradual enhancement of reformed ways of teaching mathematics in schools and the reported increase in student achievement as a result of professional development with new teaching strategies, teacher professional development programs that emphasize teachers' understanding of students' mathematical comprehension is needed rather than the currently dominant traditional pedagogy of direct instruction with a focus on teaching problem solving strategies.

• The Journal of Fisheries Business Administration
• /
• v.47 no.3
• /
• pp.71-92
• /
• 2016

This study examines the effects of consumer beliefs for food certifications on the behavioral intentions and the behavioral intention biases to purchase the certified seafoods by a subjective probability model which is on the basis of the mathematical probability model and the covariance model. The food certifications used on this study are 'Organic foods', 'Traceability system of food products' and. 'HACCP'. The representative foods of fishery products on this study is seasoned laver. The current study showed the following results. First, consumers have more than two different beliefs each for all certifications which are the subjects of this study. The beliefs of the certifications have an impact on the consumers when they consider to buy the certified seafood products. Second, consumers try to persuade by themselves to ensure that their particular belief about the certification could lead to a purchase the seafood products. Consumer beliefs of the "environmentally friendly production" on the organic foods certification is an important factor as much as the "guarantee of food safety" belief making a positive purchasing behavior intentions(PBI) bias for the organic seafood products. Consumers also have a positive PBI bias for certified seafood products in all certifications as long as a certification is considered to "guarantee the transparency of the food distribution process" as its belief. 'Traceability system' was the only one which didn't generate a positive PBI bias from the belief of "guarantee of food safety" out of three certifications.

• Research in Mathematical Education
• /
• v.19 no.1
• /
• pp.19-41
• /
• 2015

Previous studies indicated that students tended to hold less satisfactory beliefs about the discipline of mathematics, beliefs about themselves as learners of mathematics, and beliefs about mathematics teaching and learning. However, only a few studies had developed curricular interventions to change students' beliefs. This study aimed to examine the effect of a problem-solving curriculum (i.e., Mathematical Problem Solving for Everyone, MProSE) on Singaporean Grade 7 students' beliefs about mathematical problem solving (MPS). Four classes (n =142) were engaged in ten lessons with each comprising four stages: understand the problem, devise a plan, carry out the plan, and look back. Heuristics and metacognitive control were emphasized during students' problem solving activities. Results indicated that the MProSE curriculum enabled some students to develop more satisfactory beliefs about MPS. Further path analysis showed that students' attitudes towards the MProSE curriculum are important predictors for their beliefs.

• Korean Journal of Remote Sensing
• /
• v.10 no.2
• /
• pp.37-48
• /
• 1994

In spatial information processing, particularly in non-renewable resource exploration, the spatial data sets, including remote sensing, geophysical and geochemical data, have to be geocoded onto a reference map and integrated for the final analysis and interpretation. Application of a computer based GIS(Geographical Information System of Geological Information System) at some point of the spatial data integration/fusion processing is now a logical and essential step. It should, however, be pointed out that the basic concepts of the GIS based spatial data fusion were developed with insufficient mathematical understanding of spatial characteristics or quantitative modeling framwork of the data. Furthermore many remote sensing and geological data sets, available for many exploration projects, are spatially incomplete in coverage and interduce spatially uneven information distribution. In addition, spectral information of many spatial data sets is often imprecise due to digital rescaling. Direct applications of GIS systems to spatial data fusion can therefore result in seriously erroneous final results. To resolve this problem, some of the important mathematical information representation techniques are briefly reviewed and discussed in this paper with condideration of spatial and spectral characteristics of the common remote sensing and exploration data. They include the basic probabilistic approach, the evidential belief function approach (Dempster-Shafer method) and the fuzzy logic approach. Even though the basic concepts of these three approaches are different, proper application of the techniques and careful interpretation of the final results are expected to yield acceptable conclusions in cach case. Actual tests with real data (Moon, 1990a; An etal., 1991, 1992, 1993) have shown that implementation and application of the methods discussed in this paper consistently provide more accurate final results than most direct applications of GIS techniques.

• Journal of Distribution Science
• /
• v.15 no.8
• /
• pp.15-28
• /
• 2017

Purpose - Many researchers analyze VMI as a supply chain collaboration program to reveal its true value. Most of them focus on the dyadic relationship in two stage supply chain systems. This study examines the effect of VMI when it is applied to the different parts of three stage supply chain systems. Research design, data, and methodology - Based on three stage supply chain, this study compares three different systems including full VMI, partial VMI, and non-VMI by using mathematical models. The performances of three systems are compared with the numerical examples of the proposed supply chain models. Results - The numerical examples reveal that full VMI where the manufacturer controls inventories at all stages outperforms any other systems in terms of the system profit and enables all individual members to gain greater profits than non-VMI. Meanwhile, under partial VMI where VMI is implemented between the wholesaler and retailer, only these two members improve their performances and the manufacturer who does not belong to VMI makes less profit than even under non-VMI. This study also examines the impact of market size and profit margin on the system performance. Conclusions - The result of this study supports the common belief that VMI secures the best result when it is applied to the entire supply chain system. The additional findings from the numerical analysis are discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.5 no.1
• /
• pp.7-12
• /
• 2005

This paper deals with the fuzzy modeling for the complex and uncertain nonlinear systems, in which conventional and mathematical models may fail to give satisfactory results. Finally, we provide numerical examples to evaluate the feasibility and generality of the proposed method in this paper. The expert system which introduces fuzzy logic in order to process uncertainties is called fuzzy expert system. The fuzzy expert system, however, has a potential problem which may lead to inappropriate results due to the ignorance of some information by applying fuzzy logic in reasoning process in addition to the knowledge acquisition problem. In order to overcome these problems, We construct fuzzy inference network by extending the concept of reasoning network in this paper. In the fuzzy inference network, the propositions which form fuzzy rules are represented by nodes. And these nodes have the truth values representing the belief values of each proposition. The logical operators between propositions of rules are represented by links. And the traditional propagation rule is modified.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.4
• /
• pp.423-442
• /
• 2011

The purpose of this study was to examine the effects of tasks setting for mathematical modelling in the complex real situations. The tasks setting(MMa, MeA) in mathematical modelling was so important that we can't ignore its effects to develop meaning and integrate mathematical ideas. The experimental setting were two groups ($N_1=103$, $N_2=103$) at public high school and non-experimental setting was one group($N_3=103$). In mathematical achievement, we found meaningful improvement for MeA group on modelling tasks, but no meaningful effect on information processing tasks. The statistical method used was ACONOVA analysis. Beside their achievement, we were much concerned about their modelling approach that TSG21 had suggested in Category "Educational & cognitive Midelling". Subjects who involved in experimental works showed very interesting approach as Exploration, analysis in some situation ${\Rightarrow}$ Math. questions ${\Rightarrow}$ Setting models ${\Rightarrow}$ Problem solution ${\Rightarrow}$ Extension, generalization, but MeA group spent a lot of time on step: Exploration, analysis and MMa group on step, Setting models. Both groups integrated actively many heuristics that schoenfeld defined. Specially, Drawing and Modified Simple Strategy were the most powerful on approach step 1,2,3. It was very encouraging that those experimental setting was improved positively more than the non-experimental setting on mathematical belief and interest. In our school system, teaching math. modelling could be a answer about what kind of educational action or environment we should provide for them. That is, mathematical learning.