• Communications of Mathematical Education
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• v.33 no.2
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• pp.123-139
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• 2019

This study analyzed how problem-posing tasks included in Korean middle school mathematics textbooks were distributed in terms of content area, task type, and context of task to investigate that the mathematics textbooks are giving students ample opportunities for problem-posing activities. The analysis of 10 mathematics textbooks for first grade in middle school according to the revised mathematics curriculum in 2015 found that the problem-posing tasks contained in the textbooks are insufficient in quantity and not evenly distributed in terms of content areas. There were also more problem-posing tasks with relatively moderate constraints than those with strong or weak constraints in terms of mathematical constraints. In addition, there were more problem-posing tasks that were not requiring students to make a new context, and more often camouflage contexts were used. Based on this, implications for improving mathematics problem-posing tasks in mathematics textbook were suggested.

• Journal of the Korean School Mathematics Society
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• v.21 no.1
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• pp.63-89
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• 2018

In this study, the researcher developed a course integrated mathematical problem posing activities in order to enhance pre-service mathematics teachers' ability to carry out problem posing activities in mathematics classroom, and examined the changes of pre-service mathematics teachers' perceptions about problem posing through the course. The problem posing course developed in this study consisted of three stages: education on the theories regarding problem posing; activities with problem posing; development and implementation of problem posing tasks. According to the results of the questionnaires, interviews, and class journals data analysis, the problem posing experiences provided in this study were very effective in improving pre-service mathematics teachers' understanding of the problem posing strategies and the benefit of problem posing activities to student learning. Particularly, the experience in various problem posing activities and the implementation experience of problem posing provided in the course played a key role in the improvement of pre-service mathematics teachers' understanding of problem posing and PCK.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.309-330
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• 2018

The purpose of this study is to identify possibility of a mathematical problem posing ability by presenting problem posing tasks with different degrees of structure according to the study of Stoyanova and Ellerton(1996). Also, the results of this study suggest the direction of gifted elementary mathematics education to increase mathematical creativity. The research results showed that mathematical problem posing ability is likely to be a factor in identification of gifted students, and suggested directions for problem posing activities in education for mathematically gifted by investigating the characteristics of original problems. Although there are many criteria that distinguish between gifted and ordinary students, it is most desirable to utilize the measurement of fluency through the well-structured problem posing tasks in terms of efficiency, which is consistent with the findings of Jo Seokhee et al. (2007). It is possible to obtain fairly good reliability and validity in the measurement of fluency. On the other hand, the fact that the problem with depth of solving steps of 3 or more is likely to be a unique problem suggests that students should be encouraged to create multi-steps problems when teaching creative problem posing activities for the gifted. This implies that using multi-steps problems is an alternative method to identify gifted elementary students.

• The Mathematical Education
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• v.43 no.4
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• pp.399-404
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• 2004

Mathematical creativity is a main topic which is studied within mathematics education. Also it is important in learning school mathematics. It can be important for mathematics teachers to view mathematical creativity as an disposition toward mathematical activity that can be fostered broadly in the general classroom environment. In this article, it is discussed that creativity-enriched mathematics instruction which includes creative problem-solving and problem-posing tasks and activities can be guided more creative approaches to school mathematics via routine problems.

• East Asian mathematical journal
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• v.34 no.4
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• pp.429-449
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• 2018

The purpose of this study is to investigate how the mathematical creativity of middle school mathematical gifted students is represented through the process of problem posing activities. For this goal, they were asked to pose real-world problems similar to the tasks which had been solved together in advance. This study demonstrated that just 2 of 15 pupils showed mathematical giftedness as well as mathematical creativity. And selecting mathematically creative and gifted pupils through creative problem-solving test consisting of problem solving tasks should be conducted very carefully to prevent missing excellent candidates. A couple of pupils who have been exerting their efforts in getting private tutoring seemed not overcoming algorithmic fixation and showed negative attitude in finding new problems and divergent approaches or solutions, though they showed excellence in solving typical mathematics problems. Thus, we conclude that it is necessary to incorporate problem posing tasks as well as multiple solution tasks into both screening process of gifted pupils and mathematics gifted classes for effective assessing and fostering mathematical creativity.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.2
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• pp.101-124
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• 2008

The purpose of this study is to test if problem posing based on structural approach cooperative learning has a positive effect on mathematical achievement and mathematical disposition. For this purpose, this study carried out tasks as follows: First, we design a problem posing teaching learning program based on structural approach cooperative learning. Second, we analyze how problem posing based on structural approach cooperative learning affects students' mathematical achievement. Third, we analyze how problem posing based on structural approach cooperative learning affects students' mathematical disposition. The results of this study are as follows: First, in the aspect of mathematical achievement, the experimental group who participated in the problem posing program based on structural approach cooperative teaming showed significantly higher improvement in mathematical achievement than the control group. Second, in the aspect of mathematical disposition, the experimental group who participated in the problem posing program based on structural approach cooperative teaming showed positive changes in their mathematical disposition. Summing up the results, through problem posing based on structural approach cooperative learning, students made active efforts to solve problems rather than fearing mathematics and, as a result, their mathematical achievement was improved. Furthermore, through mathematics classes enjoyable with classmates, their mathematical disposition was also changed in a positive way.

• Research in Mathematical Education
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• v.16 no.1
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• pp.15-29
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• 2012

One of the important aims in mathematics education is to enhance mathematical thinking for students. And students posing questions is a vital process in mathematical thinking as it is part of the reasoning and communication of their learning. This paper investigates how students develop their mathematical thinking through working on tasks in fractions and posing their own questions after successfully solved the problems. The teaching was conducted in primary five classes and the results showed that students' reasoning is related to their analogy with what previously learned. Also, posing their problems after solving the problem not only helps students to understand the structure of the problem, it also helps students to explore on different routes in solving the problem and extend their learning content.

• 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.

• The Mathematical Education
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• v.61 no.1
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• pp.157-178
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• 2022

Mathematics teachers' content knowledge is an important asset for effective teaching. To enhance this asset, teacher's knowledge is required to be diagnosed and developed. In this study, we employed problem-posing and problem-solving tasks to diagnose preservice teachers' understanding of fraction multiplication. We recruited 41 elementary preservice teachers who were taking elementary mathematics methods courses in Korea and the United States and gave the tasks in their final exam. The collected data was analyzed in terms of interpreting, understanding, model, and representing of fraction multiplication. The results of the study show that preservice teachers tended to interpret (fraction)×(fraction) more correctly than (whole number)×(fraction). Especially, all US preservice teachers reversed the meanings of the fraction multiplier as well as the whole number multiplicand. In addition, preservice teachers frequently used 'part of part' for posing problems and solving posed problems for (fraction)×(fraction) problems. While preservice teachers preferred to a area model to solve (fraction)×(fraction) problems, many Korean preservice teachers selected a length model for (whole number)×(fraction). Lastly, preservice teachers showed their ability to make a conceptual connection between their models and the process of fraction multiplication. This study provided specific implications for preservice teacher education in relation to the meaning of fraction multiplication, visual representations, and the purposes of using representations.

• The Mathematical Education
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• v.59 no.1
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• pp.81-99
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• 2020

This study examined the types of abduction and the thinking strategies by the mathematics problems posed by students. Four students who were 2nd graders in middle school participated in problem posing on four tasks that were given, and the problems that they posed were classified into equivalence problem, isomorphic problem, and similar problem. The type of abduction appeared were different depending on the type of problems that students posed. In case of equivalence problem, the given condition of the problems was recognized as object for posing problems and it was the manipulative abduction. In isomorphic problem and similar problem, manipulative abduction, theoretical abduction, and creative abduction were all manifested, and creative abduction was manifested more in similar problem than in isomorphic problem. Thinking strategies employed at abduction were examined in order to find out what rules were presumed by students across problem posing activity. Seven types of thinking strategies were identified as having been used on rule inference by manipulative selective abduction. Three types of knowledge were used on rule inference by theoretical selective abduction. Three types of thinking strategies were used on rule inference by creative abduction.