• Education of Primary School Mathematics
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• v.26 no.4
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• pp.219-236
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• 2023

This study examined the relationship between preservice teachers' mathematical understanding and problem posing in fractions multiplication and division. To this purpose, 41 preservice teachers performed visual representation and problem posing tasks for fraction multiplication and division, measured their mathematical understanding and problem posing ability, and examined the relationship between mathematical understanding and problem posing ability using cross-tabulation analysis. As a result, most of the preservice teachers showed conceptual understanding of fraction multiplication and division, and five types of difficulties appeared. In problem posing, most of the preservice teachers failed to pose a math problem that could be solved, and four types of difficulties appeared. As a result of cross-tabulation analysis, the degree of mathematical understanding was related to the ability to pose problems. Based on these results, implications for preservice teachers' mathematical understanding and problem posing were suggested.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.717-754
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• 2015

As a design research, this study aims to identify students' collaborative problems solving patterns using the Wiki and design factors triggering MKB(mathematical knowledge building) in virtual environment. For 70 days, 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, solved 10 math problems together using the Wiki. In this study, I considered five design factors; motivation, practice of LaTeX, norms of participation, epistemic agency, and two types of educational settings. The primary pattern emergent in students' collaborative problem solving process is identified as 'solutions and refutations' along the double helix consisting of the constructive line and the critical line, which is very similar to the pattern of 'Conjectures and Refutations'(Lakatos, 1976). Despite that most participants had difficulty in using LaTeX for mathematical expressions, this study shows that Wikis are valuable tools for providing Korean secondary students opportunities to learn social virtue such as humility and courage (Lampert, 1990), which is considered to be have been neglected in Korean educational environment but is emphasized as precious for doing mathematics in the field of mathematics education.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.291-319
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• 2014

The purpose of this study is to investigate students' thinking and understanding through working on Worked-out Examples on numbers and operations, specifically, radical and real numbers and operations in the middle grades. For this purpose, we developed a set of Worked-out Examples; middle school students independently worked on them. Then two students were interviewed. These data were analyzed by using the framework of mathematical proficiency. The data analysis suggested that the students seemed to go through the processes involving a combination of understanding and computation, computation and reasoning, and understanding, computation and reasoning. Also, it appeared that most of the students have difficult solving problems involving with radical and real numbers in related to strategic competence.

• Communications of Mathematical Education
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• v.9
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• pp.299-316
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• 1999

본 논문에서는 스프레드쉬트 프로그램 중에서 가장 활용도가 높은 Excel을 이용하여 만든 여러 가지 모의실험이 확률 통계학습에 어떻게 활용되는 지를 제시함으로써 개념의 지도 및 문제풀이 능력 향상의 효율성을 높이는 방안을 모색하고자 한다. 즉 이는 단순한 이론적 수치계산이 아닌 구체적 경험을 제시하여 학생들에게 확률적 상황에 내재된 확률적 정보의 의미를 파악하게 함으로써 확률의 개념에 대한 이해를 돕고 확률 통계단원에 대한 흥미를 유발케 하고자 한다.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.489-503
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• 2008

It is not an easy matter to develop problems which help students understand mathematical concepts correctly and precisely. The aim of this paper is to review the merits and demerits of three problem types (i.e. one answer problems, multiple choice problems and proof problems) and to suggest some points that should be taken into consideration in problem making. First, we presented the merits and demerits of three types of problems by examining actual examples. Second, we discussed some examples of misleading problems and the ways to make desirable ones. Finally, on the basis of our examination and discussion, we suggested some points that should be kept in mind in problem making. The major suggestions are as follows; i) In making one answer problems, we should consider the possibility of sitting a solution by wrong precesses, ii) In formulating multiple choice tests which are layered for their easiness of grading, we should take into account the importance of checking whether the students are fully understanding the concepts, iii) We may depend on the previous research result that multiple choice tests for proof problems can be helpful for the students who have insufficient math background. Besides those suggestions, we made an overall proposal that we should endeavor to find ways to implement the demerits of each problem type and to develop instructive problems that can help students understanding of math.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.189-209
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• 2014

This study designed and developed a model of ill-structured problem solving and ill-structured problems for the 4th, 5th, and 6th graders. In addition, two sets of ill-structured problems has been explored to 23 4th graders, 33 5th graders, and 23 6th graders in elementary schools in order to investigate their problem solving, creative personality, and mathematical reasoning. The model of ill-structured problem solving was suggested ABCDE (Analyze-Browse-Create-DecisionMaking-Evaluate) model and analyzed participants' problem solving procedure. As results, participants showed improvement between pretest and posttest in problem solving and the high graders showed the greater creative personality.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.67-106
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• 2010

This paper tries to analyze how effective the problem posing method through Brainwriting can be on mathematical problem solving and creativity as a way to seek a new pedagogy to enhance student problem solving levels and creativity in mathematics. The findings of the study can be summarized as follows: First, the Brainwriting problem posing method improved students' abilities to alter problems, suggest new problems from multi-perspectives, and solve them. All procedures for such were obtained through discussions among group members. Second, the Brainwriting problem posing method resulted in positive effects on fluency and originality among components of creativity, but not on flexibility. That is, studying mathematics with this method helped students develop creativity levels not in terms of flexibility but of fluency and originality. Third, the interest rate in mathematics learning rose for those who studied mathematics by adopting the Brainwriting problem posing method. Finally, this study caused the Brainwriting problem posing method to be more deeply understood and appreciated from a new perspective.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.19-38
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• 2021

The purpose of this study is to examine pre-service teachers' noticing when evaluating peers' mathematical problem posing tasks. To this end, 46 secondary pre-service teachers were asked to create real-world problems related to permutation and combination and randomly assigned to evaluate peers' problems. As a result, the pre-service teachers were most likely to notice the difficulty of their peers' mathematics problems. In particular, the pre-service teachers tended to notice particular conditions in order to increase the difficulty of a problem. In addition, the pre-service teachers noticed the clarity of a question and its solution, novelty of the problem, the natural connection between real-world contexts and mathematical concepts, and the convergence between mathematical concepts.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.161-181
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• 2018

This study involved an investigation of prospective elementary teachers' preconceptions and experiences of diagrams and their ability to draw diagrams in solving math word problems. A questionnaire and two math word problems were administered to prospective elementary teachers who began to taking an introductory mathematics education course. The results from the analysis of their responses to the questionnaire items indicate that prospective elementary teachers appreciate the value of diagrams as tools for problem solving and communication. In addition, prospective elementary teachers have the will not only to teach their future students how to use diagrams but also to encourage them to draw diagrams in solving math word problems. However, the results also indicates that prospective elementary teachers neither use diagrams spontaneously in their math problem solving activities nor have confidence in drawing useful diagrams. Prospective elementary teachers also manifested low scores on the questionnaire items asking whether they were taught how to draw useful diagrams or encouraged by their teachers to use diagrams in their previous learning experiences. The results from the analysis of the diagrams that prospective elementary teachers drew in solving math word problems showed that most of them had difficulty drawing diagrams that represent their reasoning and solving process.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.73-83
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• 2009

Mathematics Olympiad aims to identify and encourage students who have superior ability in mathematics, to enhance students' understanding in mathematics while stimulating interest and challenge, to increase learning motivation through self-reflection, and to speed up the development of mathematical talent. Participating mathematical competition, students are going to solve a variety of types of mathematical problems and will be able to enlarge their understanding in mathematics and foster mathematical thinking and creative problem solving ability with logic and reasoning. In addition, parents could have an opportunity valuable information on their children's mathematical talents and guidance of them. Although there should be presenting diversified mathematical problems in competitions, the real situations is that resent most mathematics Olympiads present mathematical problems which narrowly focus on types of solving problems. In order to diversifying types of problems in mathematics Olympiads and making mathematics popular, this study will discuss a Olympiad for problem solving ability, a Olympiad for exploring mathematics, a Olympiad for task solving ability, and a mathematics fair, etc.