• Journal of Engineering Education Research
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• v.14 no.6
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• pp.67-72
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• 2011

This method is a new experimental model for a mathematical education in Engineering students. We compare two different classes; one was recorded the lecture with scenario and the other was not. Also we set up the detailed structures in every lecture for mathematical modeling and solving parts. The purpose for a new model is 1) to improve the students's ability to solve the mathematical problem, 2) how to approach to getting a solution for each problem by system and 3) to provide the lectures anytime to students who want to study more mathematics.

• The Mathematical Education
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• v.61 no.3
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• pp.441-456
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• 2022

The purpose of the current study is to report a part of our larger project whose focus is to understand a relationship between students' units coordination and K-12 school mathematics. In particular, in this paper we report how students who exhibit distinct levels of units coordinations used their knowledge of proportion to solve quadratic function problems of the form y = ax². To this end, three 7th grade students all of whom assimiliated whole number problem situations with three levels of units but showed different levels for fraction problems were chosen. We carried out clinical interviews not only to understand their ability to coordinate units but to understand their problem solving process of proportion and the quadratic function problems. The analysis suggest that their abilities to coordinate units influenced their ways to solving proportion problems, and in turn influenced their ways to solve the specific form of quadratic functions. We have finalized our study by discussing how students' ability to construct and coordinate units, their proportion knowledge, and their knowledge associated with expressing the specific type of quadractic functions could be related.

• Education of Primary School Mathematics
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• v.6 no.2
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• pp.75-84
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• 2002

After entering an elementary school, in fact, a number of children regard mathematics as one of very difficult subjects because of its abstractiveness. This is caused by the fact that their basic thinking power is not yet formed or they can not understand the special quality of mathematics. So this article emphasizes the need to build up the higher logical thought and a basic mathematical concept at the lower grade elementary school stage in which the loaming activity on mathematics begins in earnest, that is, at the stage before having an experience on the calculating activity using numbers. But at present the lower grade elementary school students in our country do not understand the special quality of mathematics composed of a various symbolic system and lay stress upon mathematics learning attached to the calculative activity. In order to make the right mathematical concept of the lower grade elementary school, the basic knowledge and ability as follows is sure to be formed. 1) the foundational logical manipulation activity and knowledge 2) the using ability of the sign and symbolic system At the stage on which mathematics learning activity begins, it is a very important task to make the right concept of the abstractive math and nurse the capability for finding mathematical relations covered under the sign system through the continuos loaming activity on . Through the basic logical manipulation activity and the game activity of sign for lower grade elementary school students mentioned in this article, they can not only foster the higher level logical thinking power and the foundational calculative ability but also bring up the interest on the activity of establishing a new problem solving strategy.

• Communications of Mathematical Education
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• v.34 no.1
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• pp.17-39
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• 2020

The purpose of this study is to analyze the mathematical beliefs of students and teachers by Latent Class Analysis(LCA). This study surveyed 60 teachers about beliefs of 'nature of mathematics', 'mathematic teaching', 'mathematical ability' and also asked 1850 students about beliefs of 'school mathematics', 'mathematic problem solving', 'mathematic learning' and 'mathematical self-concept'. Also, this study classified each student and teacher into a class that are in a similar response, analyzed the belief systems and built a profile of the classes. As a result, teachers were classified into three types of belief classes about 'nature of mathematics' and two types of belief classes about 'teaching mathematics' and 'mathematical ability' respectively. Also, students were classfied into three types of belief classes about 'self concept' and two types of classes about 'School Mathematics', 'Mathematics Problem Solving' and 'Mathematics Learning' respectively. This study classified the mathematics belief systems in which students were categorized into 9 categories and teachers into 7 categories by LCA. The belief categories analyzed through these inductive observations were found to have statistical validity. The latent class analysis(LCA) used in this study is a new way of inductively categorizing the mathematical beliefs of teachers and students. The belief analysis method(LCA) used in this study may be the basis for statistically analyzing the relationship between teachers' and students' beliefs.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.533-551
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• 2015

Problem posing in school mathematics is generally regarded to make a new problem from contexts, information, and experiences relevant to realistic or mathematical situations. Also, it is to reconstruct a similar or more complicated new problem based on an original problem. The former is called as problem generation and the latter is as problem reformulation. The purpose of this study was to explore the co-relation between problem generation and problem reformulation, and the educational effectiveness of each problem posing. For this purpose, on the subject of 33 pre-service secondary school teachers, this study developed two types of problem posing activities. The one was executed as the procedures of [problem generation${\rightarrow}$solving a self-generated problem${\rightarrow}$reformulation of the problem], and the other was done as the procedures of [problem generation${\rightarrow}$solving the most often generated problem${\rightarrow}$reformulation of the problem]. The intent of the former activity was to lead students' maintaining the ability to deal with the problem generation and reformulation for themselves. Furthermore, through the latter one, they were led to have peers' thinking patterns and typical tendency on problem generation and reformulation according to the instructor(the researcher)'s guidance. After these activities, the subject(33 pre-service teachers) was responded in the survey. The information on the survey is consisted of mathematical difficulties and interests, cognitive and affective domains, merits and demerits, and application to the instruction and assessment situations in math class. According to the results of this study, problem generation would be geared to understand mathematical concepts and also problem reformulation would enhance problem solving ability. And it is shown that accomplishing the second activity of problem posing be more efficient than doing the first activity in math class.

• Research in Mathematical Education
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• v.12 no.3
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• pp.215-233
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• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.185-196
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• 1998

This study is undertaken to clarify the evolution of the mathematics regarding the $\pi$ ratio, square root, trigonometric ration which are dealing by approximate value according to the curriculum of Korean Middle School and its subsequent growth of methods for attaining the approximate value. Furthermore a brief survey has been thought for assessing the significance of the core of approximate value and its utility which will be given a guide line to many young learners. I'd better teach these historical background to the students and it makes clear the approximate value and the content about the approximate value. This research should help to improve the student's ability of solving a problem by making them think it mathematically through the life and the effort of the mathematician.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.41-55
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• 2001

The purpose of this study was to compare and analyze the curricula of kindergarten and elementary school and to present a plan for connecting the two curricula. The curricula emphasized mathematical thinking and problem solving instead of fragmentary knowledge and adopted the streamed curriculum based on children’s ability and interest. And both of them consisted of number and operation, geometry, measurement, statistics, and put emphasis on activity such as real life experience, play, manipulation of concrete objects, and communication. However, there are some kinds of differences between them, because the kindergarten curriculum is not included in the common curriculum, from 1st grade to 10th grade. Thus, this study recommended several ideas based. Thus, this study recommended several ideas based on theories to connect the mathematics curricula of kindergarten and elementary school.

• School Mathematics
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• v.9 no.2
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• pp.277-289
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• 2007

This research aims to look into the mathematically gifted 6th and 7th graders spatial visualization ability of solid figures. The subjects of the research was six male elementary school students in the 6th grade and one male middle school student in the 1th grade receiving special education for the mathematically gifted students supported by the government. The task used in this research was the problems that compares the side lengths and the angle sizes in 4 pictures of its two dimensional representation of a regular icosahedron. The data collected included the activity sheets of the students and in-depth interviews on the problem solving. Data analysis was made based on McGee's theory about spatial visualization ability with referring to Duval's and Del Grande's. According to the results of analysis of subjects' spatial visualization ability, the spatial visualization abilities mainly found in the students' problem-solving process were the ability to visualize a partial configuration of the whole object, the ability to manipulate an object in imagination, the ability to imagine the rotation of a depicted object and the ability to transform a depicted object into a different form. Though most subjects displayed excellent spatial visualization abilities carrying out the tasks in this research, but some of them had a little difficulty in mentally imagining three dimensional objects from its two dimensional representation of a solid figure.

• The Mathematical Education
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• v.46 no.4
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• pp.445-464
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• 2007

On considering the mathematical creativity of the gifted in mathematics, some points should be reflected such as the characteristics of leaners, the gifted and of domain-special facts in mathematics. And the clear view of mathematical creativity of the gifted in mathematics makes a way to define the meanings of creative-productive ability and of creative products. Therefore to explicate the concept of mathematical creativity of the gifted in mathematics, researcher reviewed literacies of the concept of creativity in general fields, classical mathematicians, and school mathematics. In conclusion, first, mathematical creativity of the gifted in mathematics should be considered on the aspects of subject-mathematics, object-the gifted, and performing-gifted education. Second, it contains advanced problem solving matters on the school mathematics curriculum but reflect the process of recovery and reinvent and it is suggested in [fig.1] and [fig.2].