• The KIPS Transactions:PartA
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• v.14A no.6
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• pp.383-390
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• 2007

This paper describes the e-learning system for science and engineering mathematics using computer algebra system and Bayesian inference network. The best feature of this system is using one of the most recent mathematical dynamic web content authoring model which is called client independent dynamic web content authoring model and using the Bayesian inference network for diagnosing student's learning. The authoring module using computer algebra system provides teacher-user with easy way to make dynamic mathematical web contents. The diagnosis module using Bayesian inference network helps students know the weaker parts of their learning, in this way our system determines appropriate next learning sequences in order to provide supplementary learning feedback.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.63-86
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• 2013

This study aimed to explore how middle school students perceive constructed-response items and how they solve those items and the patterns of the processes. For this purpose, data were collected from middle school students through survey, written responses on those items that were developed for this particular purpose, and interviews. The survey data were analyzed by using Excel and the written responses and interview data qualitatively. The findings about the students' perceptions about the constructed-response items suggested that the middle school students perceive the items primarily as involving writing solutions logically(17%) and being capable of explaining while solving them(7%). The most difficulties they encounter when solving the items were understanding(26%), applying(12%), mathematical writing(25%), computing(23%), and reasoning(14%). The findings about the students' mathematical proficiencies showed that they made an error most in reasoning (35%), then in understanding(31%), in applying(9%), and least in computing(3%).

• East Asian mathematical journal
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• v.23 no.3
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• pp.361-370
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• 2007

The notion of problem-solving in mathematics education effects mathematics teachers notice and its importance in mathematics is getting better. The purpose of this thesis is to consider the mathematical reasoning for improving the ability of problem solving. It is necessary that notion, enforcement method, procedure and evaluation standard of performance assessment should be explained to students. The teachers, improvements of specialty for class and evaluation as well as systematic reeducation for performance assessment are essential.

• Education of Primary School Mathematics
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• v.7 no.2
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• pp.101-116
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• 2003

In recent days, it is stressed that problem solving ability and inference ability to get a higer accomplishment are very important. The purpose of this research is to explore the affective factors related the problem solving ability and reasoning ability. Also, we explored the difference between the two affective factors focusing on 6th graders in primary school.

• Communications of Mathematical Education
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• v.15
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• pp.141-146
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• 2003

중학교 기하교육의 목적은 학생들의 수학적인 상황을 보는 기하학적인 직관과 논리적 추론능력의 향상이다. 그러나 이 두 가지 모두 만족스럽지 못한 실정이다. 본 고에서는 중학교 기하교육의 문제를 직관기하와 형식기하의 단절이라는 보고, 직관기하에서 증명의 학습요소를 미리 학습하여 직관기하와 형식기하를 연결하자는 대안을 제시한다. 이를 위해 7-나 교과서의 증명요소를 분석하고자 하였다. 관련문헌을 검토하여 7가지 증명의 학습요소를 선정한 후, 교과서를 분석하였다. 분석 결과, 기호화를 제외한 다른 증명의 학습요소는 매우 빈약한 것으로 나타났다. 직관기하 영역에 대한 교과서 구성이 개선될 필요가 있음을 알 수 있다.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.459-475
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• 2022

The equal sign and equivalence are the most basic and core concepts in elementary mathematics, but there has been lack of research on how to teach these concepts with textbooks. Given this, this study analyzed elementary mathematics textbooks in terms of three instructional elements (i.e., emphasizing the meaning of the equal sign as a relational symbol, dealing with an equation as an object for reasoning, and using an equation with a missing value). In particular, this study analyzed 10 different mathematics textbook series that are newly used in 2022 and examined the overall trends and characteristics for teaching the equal sign and equivalence. The results of this study showed that the activities emphasizing the meaning of the equal sign as a relational symbol were most noticeable but the activities dealing with an equation as an object for reasoning or using an equation with a missing value were relatively rare. Based on the results of the analysis, this study provides textbook writers with implications on what to further consider in covering the equal sign and equivalence.

• The Mathematical Education
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• v.61 no.2
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• pp.339-357
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• 2022

This study explores pre-service secondary mathematics teachers (PSTs)' noticing competency. 17 PSTs participated in this study as a part of the mathematics teaching method class. Individual PST's essays regarding the question 'what effective mathematics teaching would be?' that they discussed and wrote at the beginning of the course were collected as the first data. PSTs' written analysis of an expert teacher's teaching video, colleague PSTs' demo-teaching video, and own demo-teaching video were also collected and analyzed. Findings showed that most PSTs' noticing level improved as the class progressed and showed a pattern of focusing on each key aspect in terms of the Teaching for Robust Understanding of Mathematics (TRU Math) framework, but their reasoning strategies were somewhat varied. This suggests that the TRU Math framework can support PSTs to improve the competency of 'what to attend' among the noticing components. In addition, the instructional reasoning strategies imply that PSTs' noticing reasoning strategy was mostly related to their interpretation of noticing components, which should be also emphasized in the teacher education program.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.241-263
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• 2013

The purpose of this paper is to investigate high school students' reasoning characteristics in problem solving. To do this, we selected five high school students as participants and presented them some open problems which allow diverse solving approaches, and recorded their problem solving process. Through analyzing their problem solving process relate to their solution, we found the followings: First, students quickly try to calculate without understanding the given problem. Second, students concern whether their solution is right or not rather than consider mathematical warrants for the results of their strategies. Third, students have difficulties to consider more than two conditions at the same time necessary to solve problem. Forth, students are not familiar to use precedence knowledge relate to given tasks. Fifth, students could have difficulties in problem solving because of easy generalization.

• School Mathematics
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• v.19 no.4
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• pp.691-712
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• 2017

It is an important to develop teachers' statistical reasoning or thinking by teacher education. In this study, the "comparing two data sets" tasks is focused as a way to develop pre-service elementary teachers' reasoning about core ideas of statistics such as distribution, variability, center, and spread. 6 teams of each 4 pre-service elementary teachers participated on the tasks and their presentations are analyzed based on Pfannkuch's (2006) teachers' inference model in comparing two data sets. As a result, they paid attention to the distribution and variability in the statistical problem solving by the "comparing two data sets" tasks, and used their contextual knowledge to make a statistical decision. In addition, they used some statistics and graphs as the reference for statistical communication, which is expected to provide implications for improving statistical education. The finding implies that the "comparing two data sets" tasks can be used to develop statistical reasoning of pre-service elementary teachers. Some recommendations are suggested for teacher education by these tasks.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.257-273
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• 2018

In this paper, we deal with the isoprimetric problem of polygons from the point of view of learning materials for elementary gifted students. The isoperimetric problem of the polygon of odd degree can be solved by E-transformation(see Figure III-1) and M-transformation(see Figure III-3). But in the case of even degree's polygon, it is quite difficult to solve the problem because of the connected components of diagonals (here we consider the diagonals forming triangle with two adjacent sides of polygon). The primary purpose of this paper is to give an idea to solve the isoperimetric problem of polygons of even degree using the properties of ellipse. This idea is derived from the programs of the Institute of Science Education for Gifted Students in the Jeju National University.