• 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.

• School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2017

In this study we analyse the features of process of problem posing and explore the development of mathematical knowledge of primary preservice teachers as result of their engagement in problem posing activity. Data was collected through the preservice teachers' class discussions. Analysis of the data shows that preservice teachers developed their ability to understand connections among mathematical concepts.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.385-406
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• 2018

The purpose of this study is to investigate the effect of mathematics classes focused on mathematical problem posing activities on 10th grade students' mathematics achievement and affective characteristics of mathematics. This study was conducted in a total of 45 regular mathematics classrooms with 81 students from two classes through a nonequivalent control group design. The results of the study showed that the teaching method based on mathematical problem posing activities had a more positive effect on students' mathematics achievement and the affective characteristics of mathematics than the teaching method that focuses on problem solving. The teaching method based on problem posing activities proposed in this study could induce students' self-reflective learning motivation, which in turn gave them a more solid understanding of the mathematical concepts they had learned. In addition, it was found that students' problem solving ability, mathematical communication ability, and mathematical thinking ability were positively influenced by problem posing activities. Regarding the affective characteristics of mathematics, the mathematical problem-posing activity suggested in this study turned out to be a very effective strategy for improving students' interest in mathematics.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.417-434
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• 2005

본 연구에서 문제제기 수업이 수학학습에 미치는 효과를 알아보기 위하여 문제제기 수업과 기존의 교사 주도식 수업방식에서 문제해결력과 수학적 창의력에 대한 효과를 분석하였다. 중학교 3학년 학생을 대상으로 28주 동안 문제제기 수업을 실시하여 수업을 한 후, 문제해결력 검사지와 수학적 창의력 검사지를 평가한 결과는 다음과 같다. 첫째, 문제제기 수업을 활용한 수업방식이 기존의 교사 주도식 수업방식에 비해 문제해결력 신장에 효과가 있는 것으로 나타났다. 둘째, 문제제기 수업이 교사 주도식 수업에 비해 수학적 창의력 신장에 효과가 있는 것으로 나타났고, 특히 수학적 창의력 하위 요소 중 유창성과 융통성 신장에 효과가 있었다. 따라서 문제해결력 신장과 수학적 창의력 신장을 위해서 학교수업에서 문제제기 수업 활동의 도입을 제언한다.

• School Mathematics
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• v.7 no.4
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• pp.319-336
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• 2005

This study is to find the properties of Diffy activity and to investigate the problems and conjectures which could be posed in the Diffy activity. The Diffy is a simple subtracting activity. But, 1 think it is a field where the mathematical thinking can take place. I proposed some problems and conjectures which can be posed. I solved the problems using excel and the software I developed and proposed the related data. I think such problems and the data will be the good materials for elementary students and gifted to think mathematically with.

• The Journal of the Korea Contents Association
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• v.18 no.2
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• pp.541-552
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• 2018

The purpose of this study was to investigate the effects of 'problem posing from mathematical problems' on the students' affective domain of mathematics, and to conduct evaluation and management of teachers' respectively. The quantitative and qualitative approaches were combined to analyze the changes in the affective achievement of all the students and individual students in the study. The conclusions of this study are as follows: First, problem-posing class improved the problem-solving ability and meaningful experience in the learning activity itself, thus improving students' self-confidence, interest, value, and desire to learn. Second, The students' affective domain of mathematics should be emphasized, and systematic evaluation and management should be carried out from the first grade of middle school to high school senior in mathematics. Third, it is necessary to present and disseminate them in detail on the national-level to evaluation system and method of affective domain of mathematics. Therefore, the teacher should actively implement the problem-posing teaching and learning in the classroom lesson and help students' affective achievement. and teachers need to measure and manage the affective achievement of all students on a regular basis.

• 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 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.

• 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.

• The Mathematical Education
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• v.46 no.1 s.116
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• pp.69-79
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• 2007

Students experience many problem solving activities in school mathematics. These activities have focused on finding the solution whose existence was known, and then again conjecture about existence of solution or posing of problems has been neglected. It needs to put more emphasis on conjecture and problem posing activities in school mathematics. To do this, a model and examples of designing mathematical activities centered on conjecture and problem posing are needed. In this article, we introduce some examples of designing such activities (from the pythagorean theorem, the determination condition of triangle, and existing solved-problems in textbook) and examine suggestions for mathematics education. Our examples can be used as instructional materials for mathematically able students at middle school.