• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.77-98
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• 2001

This study has a purpose to find out how the problem posing activity by presenting the problem situation effects to the mathematical problem solving ability. It was applied in two classes(Experimental group-35, Controlled group-37) of the fourth grade at ‘D’ Elementary school in Bang Jin Chung nam and 40 Elementary school teachers working in Dang Jin. The presenting types of problem situation are the picture type, the language type, the complex type(picture type+ language type), the free type. And then let them have the problem posing activity. Also, We applied both the teaching-teaming plan and practice question designed by ourself. The results of teaching and learning activities according to the type of problem situation presentation are as follows; We found out that the learning activity of the mathematical problem posing was helpful to the students in the development of the mathematical problem solving ability. Also, We found out that the mathematical problem posing made the students positively change their attitude and their own methods for mathematical problem solving.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.321-350
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• 2013

The purpose of this study to analysis of problem posing in 5th and 6th grade mathematics textbooks and to comprehend errors in the problem posing activity of 6th graders in elementary school. For solving the research problems, problem posing contents were extracted from mathematics textbooks and practice books for the 5th and 6th grade of elementary school in the 2007 revised national curriculum, and they were analyzed, according to each grade, domain and type. Based on the analysis results, 10 problem posing questions which were extracted and developed, were modified and supplemented through a pre-examination, and a questionnaire that problem posing questions are evenly distributed, according to each grade, domain and type, was produced. This examination was conducted with 129 6th graders, and types of error in problem posing were analyzed using collected data. The implications from the research results are as follows. First, it was found that there was a big numerical difference of problem posing questions in the 5th and 6th grade, and problem posing questions weren't properly suggested in even some domains and types, because the serious concentration in each grade, type and domain. Therefore, textbooks to be developed in the future would need to suggest more various and systematic of problem posing teaching learning activity for each domain and type. Second, the 'error resulting from the lack of information' occurred the most in the problems that 6th graders posed, followed by the 'error in the understanding of problems', 'technical errors', 'logical errors' and 'others'. This implies that a majority of students missed conditions necessary for problem solving, because they have been used to finding answers to given questions only. For such reason, there should be an environment in which students can pose problems by themselves, breaking from the way of learning to only solve given problems.

• 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.

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.193-204
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• 2017

The purpose of the study was to investigate and develop a practical approach to integrating student-driven mathematical problems posing in mathematics instruction. A problem posing activity was performed during regular mathematics instruction. A total of 540 mathematical problems generated by students were recorded and analysed using systemic procedures and criteria. Of the problems, 81% were mathematically solvable problem and 18% were classified as error type problems. The Mathematically solvable problem were analysed and categorized according to the complexity level; 13% were of a high-level, 30% mid-level and 57% low-level. The error-type problem were classified as such within three categories: non-mathematical problem, statement or mathematically unsolvable problem. The error-type problem category was distributed variously according to the leaning theme and accomplishment level. The study has important implications in that it used systemic procedures and criteria to analyse problem generated by students and provided the way for integrating mathematical instruction and problem posing activity.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.1
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• pp.93-114
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• 2018

The purpose of this study was to analyze mathematical the effects of problem posing activities on students' characteristics toward mathematics to encourage active learning. We will also examine various examples of the characteristics of the problems made by students with different mathematical characteristics. We chose one 6th grade group to conduct this research. From the results of this study, we obtained the following conclusions. First, problem posing activities are effective in improving students' mathematical interest and confidence, value recognition. Second, Students with different mathematical characteristics showed different results in problem posing activities. We confirmed the effectiveness of problem posing activities on students' positive characteristics of mathematics. In this regard, we were able to confirm examples of various problems that students made. In the future, we would like to propose generalization by conducting research on students of various school ages.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.133-144
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• 1999

This study aims at identifying the effect of problem posing on the academic achievement in high school mathematics. As subjects of the study, two classes of first grade in high school were selected. One of them was treated with problem posing learning, the other was treated with learning-in-a-body. Each has 40 students and was also divided into two groups(high- level and low-level) according to their learning-level. Two instruments were used for this study. One was the teaching-learning method developed by the researcher. The other was TTCT(Torrance Test of Creative Thinking). The 't-test' was used for this study and the significant level of test was within 5 percent. The results of this study are as follows: 1. The group with problem posing learning showed significantly higher academic achievement(learning-ability) than the one with learning-in-a-body. 2. There was no significant difference in the academic achievement(creativity) between the two groups. But there was significant difference in the creative factors. 3. There was no significant differences in the academic achievement between high-level-groups in each group. 4. There was significant difference in the academic achievement (learning-ability) between low-level groups in each group. And there was significant difference in the creative factors. On the basis of the results above, the following conclusions could be made. The problem posing learning method was more effective in the academic achievement in highschool mathematics than learning-in-a-body. Especially low-level group was more effective than high-level group. These facts implies that it is more effective for a teacher to adopt the problem posing learning considering the students' learning-levels.

• The Mathematical Education
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• v.43 no.3
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• pp.233-255
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• 2004

Problem solving in math education is of great importance. The interest on problem solving in math education is growing all over the world. Problem solving ability is important throughout the fourth-sixth national curriculum in Korea and this is also necessary in the seventh national curriculum. The writer has implemented a proper model for problem posing and this is also necessary in the seventh national curriculum that emphasizes self-leading for improvement in the classroom. This model has advantages to cultivate a good habit of students who tries to solve the problems with concrete strategies, to take part in the problem solving activity and to change their mathematical attitude.

• Research in Mathematical Education
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• v.27 no.1
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• pp.1-24
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• 2024

In this paper, the author analyzed characteristics of deep mathematics learning in problem solving and problem-posing classroom teaching. Based on a simple wrong plane geometry problem, the author describes the classroom experience how one expert Chinese mathematics teacher guides students to modify geometry problems from solution to investigation, and guides the students to learn how to pose mathematics problems in inquiry-based deep learning classroom. This also demonstrates how expert mathematics teacher can effectively guide students to teach deep learning in regular classroom.

• Education of Primary School Mathematics
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• v.2 no.2
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• pp.133-144
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• 1998

We examined two kinds of problem posing, 'problem making' and 'problem modifying' to find which one is more effective for improving mathematical problem solving ability according to the student's learning-levels and sexes. The results showed that 'problem making' is more effective for high and middle-level groups than 'problem modifying'. There was no big difference according to the sexes. These facts implies that making a problem when a situation was presented is more effective to develop problem solving ability than modifying a problem ： modifying some conditions and contents of given problem.

• Journal of Gifted/Talented Education
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• v.24 no.6
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• pp.1053-1071
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• 2014

Problem posing is used to develop the creativity program and adaption for the gifted, and to screen the gifted students in the selection process. However existing creativity assessment factors(fluence, flexibility, originality) has been recognized to have it's limitation to assess the mathematical creativity. To improve the creativity assessment, we propose new set of assessment factors for mathematical creativity test through problem posing. For this study, we let 19 mathematically gifted students to pose two good mathematical problems for a limited time after solving a certain problem so called a reference problem. A week late, we let the subjects, pre-service teachers, and experts to evaluate the problems posed by the subjects, and leave the reasons for evaluating highest mark and lowest mark. With this date, we propose fluence, flexibility, originality, anti-similarity, complexity, elaboration as the set of mathematics creativity assessment factors.