• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.285-299
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• 2013

Problem posing activity of which a learner reinterprets an original problem via a new problem suggested, is a learning method which encourages an active participation and approves self-directed learning ability of the learner. Especially gifted students need to get used to a creative attitude to modify or reinterpret various mathematical materials found in everyday usual lives creatively in steady manner via such empirical experience beyond the question making level of the textbook. This paper verifies the possibility of lesson on question making strategy utilization for creativity development of gifted class, and analyzes various cases of students' trials to modify the rules of a board game called Rummikub in application of their own mathematics after learning What-If-Not strategy.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.221-235
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• 2007

Open problems can provide experiences for students to yield originative and various products in their level, because it is open with respect to its departure situation, goal situation, or solving method. Teachers need to pose and utilize open problems in forms of solution-finding or proving problems. For this we first have to specify which resource and method to use by concrete examples. In this article, we exemplify a method and procedure of posing an open problem by the two cases in which we pose open problems by reorganizing given closed problems. And we analyze students' responses for the two posed open problems. On the basis of these, we reflect implications for mathematical education of open problems.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.143-157
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• 2016

This study aims to find out the feasibility and effectiveness of mathematical games as a way to provide primary pre-service teachers with doing mathematics. The game had induced the active participation of elementary pre-service teachers. Through transforming the game, the teachers have been able to experience of mathematical problem posing and generating mathematical representation. Based on this, we discuss the role of mathematical games as a method of pre-service teacher education.

• Research in Mathematical Education
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• v.17 no.2
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• pp.119-131
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• 2013

It is the first time that there is a subject, advanced mathematics in the 2009 revised high school curriculum. Therefore it is posing a challenge to the teachers who are teaching it. At the advanced level, it is important for learners to reflect on their mental mathematical activities. This research analysed pre-service secondary teachers' reflective thinking in solving the tasks specific for the teaching and learning of polar coordinates. We report how and through what process mathematical tasks that can create disequilibrium for pre-service secondary teachers enable reflective thinking and expand preservice secondary teachers' thoughts and recognition of defining reflective thinking in looking back on one's problem solving and thinking processes.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.663-677
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• 1998

The development of Science and Technology and the social change require new paradigm in Education. In a traditional paradigm, learners have been regarded as a passive being and knowledge could be transmitted to learner. But within this paradigm, it is difficult to confront the social change and to develop problem solving skills in various context. This results in a new, alternative perspective, Constructive paradigm. As an alternative to the traditional settings, Constructive paradigm emphasizes the learner centered instruction. The reform movement in mathematics education including NCTM's standards revolves around this paradigm and the open education movement in our educational system is based on it. Open education values learner's interest, autonomy and internal motivation in learning. However, open education has been misunderstood by most of the teachers. It should be understood as the change of paradigm. In this study, as a way of helping students connect mathematics to their everyday lives and construct meaningful mathematical knowledge and concept, mathematical modelling is suggested. It consists of posing and specifying the real problem, formulation and constructing a mathematical model, analyzing and solving a mathematical problem. interpreting the solution and comparing with reality and communicating results. In this process, technology like computer can be a powerful tool. It can help students explore various problems more easily and concretely.

• The Mathematical Education
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• v.60 no.4
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• pp.431-449
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• 2021

Elementary mathematics textbooks present contents for enhancing problem solving competency. Still, teachers find teaching problem solving to be challenging. To understand the supports textbooks are suggesting, this study examined tasks from the challenging/thinking and inquiry mathematics. We analyzed 288 mathematical activities based on an analytic framework from the 2015 revised mathematics curriculum. Then, we employed latent class analysis to classify 83 mathematical tasks as a new approach to categorize tasks. As a result, execution of the problem solving process was emphasized across grade levels but understanding of problems was varied by grade levels. In addition, higher grade levels had more opportunities to be engaged in collaborative problem solving and problem posing. We identified three task profiles: 'execution focus', 'collaborative-solution focus', 'multifaceted-solution focus'. In Grade 3, about 80% of tasks were categorized as the execution profile. The multifaceted-solution was about 40% in the thinking/challenging mathematics and the execution profile was about 70% in Inquiry mathematics. The implications for developing mathematics textbooks and designing mathematical tasks are discussed.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.797-820
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• 2013

This study intended on analyzing the error patterns of mathematic problem posing sentences by the 100 elementary pre-teachers and discussing about the solutions. The results showed that the problem posing sentences have five error patterns: phonological error patterns, word error patterns, sentence error patterns, meaning error patterns, and notation error patterns. Divided into fourteen specific error patterns, they are as in the following. 1) Phonological error patterns are consisted of the 'ㄹ' addition error pattern and the abbreviated word error pattern. 2) Words error patterns are divided with the inappropriate usage of word error pattern and the inadequate abbreviation error pattern, which are formulized four subgroups such as the case maker, ending of the word, inappropriate usage of word, and inadequate abbreviation of article or word error pattern in detail. 3) Sentence error patterns are assumed four kinds of forms: the reference, ellipsis of sentence component, word order, and incomplete sentence error pattern. 4) Meaning error patterns are composed the logical contradiction and the ambiguous meaning. 5) Notation error patterns are formed four patterns as the spacing, punctuation, orthography of Hangul, and spelling rules of foreign words in Korean. Furthermore, the solutions for these error patterns were discussed: First, it has to be perceived the differences between spoken and written language. Second, it has to be rejected the spoken expressions in written contexts. Third, it should be focused on the learning of the basic sentence patterns during the class. Forth, it is suggested that the word meaning should have the logical development perception based on what it means. Finally, it is proposed that the system of spelling of Korean has to be learned. In addition to these suggestions, a new understanding is necessary regarding writing education for college students.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.373-395
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• 2022

This study aimed to examine how prospective mathematics teachers (PMTs) perceive collaborative problem-posing (CPP) as a method to cultivate students' creativity and character in mathematics education. This is to propose the introduction of CPP at the stage of preparatory math teacher education as one of the ways to reinforce the creativity and character education capacity of PMT), and to attempt to be an opportunity to actively utilize CPP in math teaching-learning in the school field for the education of students' creativity and character. To achieve this objective, I designed PMTs taking the 'Educational Theories for Teaching Mathematics' course, required in the second year of university, to experience CPP tasks. Data were collected through questionnaires or interviews over three years on how PMTs recognized the CPP tasks as a tool to cultivate students' creativity and character in secondary schools. The results of the study are as follows. First, PMTs recognized regardless of their CPP experience that CPP might have a positive impact on improving students' ability to devise various ideas and that it positively influences students' attitudes toward building interpersonal relationships, including teamwork, respect, and consideration. Second, the experience of PMTs participating in the CPP made them more positively aware that CPP is effective in improving students' ability to elaborate on ideas. Third, the PMTs' experience of participating in CPP led to a more positive perception of the impact of CPP on the students' abilities and attitudes, namely, the students' ability to elaborate on ideas and their inner attitudes toward individuals, including honesty, fairness, and responsibility, and the attitude of students regarding logically presenting their opinions and making rational decisions. Finally, if there are downsides to the offline environment, an online environment may be more beneficial.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.345-366
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• 2006

In this study, we investigated the methods of using the Cabri3D program for education of problem solving in school mathematics. Cabri3D is the program that can represent 3-dimensional figures and explore these in dynamic method. By using this program, we can see mathematical relations in space or mathematical properties in 3-dimensional figures vidually. We conducted classroom activity exploring Cabri3D with 15 pre-service leachers in 2006. In this process, we collected practical examples that can assist four stages of problem solving. Through the analysis of these examples, we concluded that Cabri3D is useful instrument to enhance problem solving ability and suggested it's educational usage as follows. In the stage of understanding the problem, it can be used to serve visual understanding and intuitive belief on the meaning of the problem, mathematical relations or properties in 3-dimensional figures. In the stage of devising a plan, it can be used to extend students's 2-dimensional thinking to 3-dimensional thinking by analogy. In the stage of carrying out the plan, it can be used to help the process to lead deductive thinking. In the stage of looking back at the work, it can be used to assist the process applying present work's result or method to another problem, checking the work, new problem posing.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.23-48
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• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.