• Journal of the Korean School Mathematics Society
• /
• v.15 no.3
• /
• pp.411-428
• /
• 2012

There is no single definition of mathematical creativity. But creativity is a key competency to adapt and live in the future. So, there are so many attentions to develop students' mathematical creativity in school mathematics. In special, mathematical problem posing activity is a good method in enhancing mathematical creativity. The purpose of this paper is to analyse on the students' mathematical creativity using problems which are made by students in problem posing activities. 16 children who consist of three groups(high, middle, low) are participated in this study. They are trained to make the problem by Brown & Walter's 'What if not' strategy. The results are as follows: Total creativity is proportional to general achievement levels. There is a difference total creativity between items contents. The number of problems differs little according to the general achievement levels. According to the qualitative analysis, students make the problems using the change of terms. And there is no problem to generalize. Based on this paper, I suggest comparing the creativity between problem posing activity and other creative fields. And we need the deeper qualitative analysis on the students' creative output.

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

• Communications of Mathematical Education
• /
• v.29 no.3
• /
• pp.533-551
• /
• 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.

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

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.2
• /
• pp.321-350
• /
• 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
• /
• v.59 no.1
• /
• pp.81-99
• /
• 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.

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

• Education of Primary School Mathematics
• /
• v.6 no.1
• /
• pp.29-40
• /
• 2002

Fairy-tales give students opportunities to build connections between a problem-solving situation and mathematics as well as to communicate solutions through writing, symbols, and diagrams. Therefore, the purpose of this paper is to introduce how to use fairy-tales in elementary mathematics classroom in order to develope student's mathematical concepts and process in terms of the following areas: ⑴ reconstructing literature ⑵ understanding concepts ⑶ problem posing activity. To be useful, mathematics should be taught in contexts that are meaningful and relevant to learners. Therefore using fairy-tales as a vehicle to teach mathematics gives students a chance to develope mathematics understanding in a natural, meaningful way, and to enhance problem posing and problem solving ability. Further, future study will continue to foster how fairy-tales literatures will enhance children's mathematics knowledge and influence on their mathematics performance.

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.2
• /
• pp.285-299
• /
• 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 Elementary Mathematics Education in Korea
• /
• v.10 no.1
• /
• pp.1-19
• /
• 2006

It is generally accepted that fostering creative thinking is a core in mathematics education and accumulating research products on that topic is really needed. In this study, I hoped to investigate and verify that in mathematics education it was possible to cultivate creative thinking through various and divergent activities, For this purpose, I delat with some illustrations, in which students learned mathematics through the operational activities using teaching tools, problem solving and problem posing activities, and finally they seemed to foster creative mathematical thinking. In conclusion of this paper, I have suggested that in math education those activities should be used to cultivate students' creative thinking in kindergarten or early elementary school. Also I asserted that it is urgently need to store up research products about various materials and methods for those mathematics teaching and learning.