• 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.

• 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 the Korean School Mathematics Society
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• v.20 no.2
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• pp.187-210
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• 2017

The animated discussion about mathematical modeling that had studied consistently in Korea since 1990s has flourished, because mathematical modeling was involved in the teaching-learning method to improve problem solving competency on 2015 reformed mathematics curriculum. In an attempt to re-examine the educational value and necessity of application to school education field, this study was to review the literature of mathematical modeling in mathematical competencies perspective. As a result, mathematical modeling could not only be involved the components of problem solving competency, but also support other competencies; reasoning, creativity-amalgamation, data-processing, communication, and attitude -practice. In this regard, This paper suggested the necessity of the discussion about the position of mathematical modeling in mathematical competencies and the active use of mathematical modeling tasks in mathematics textbook or school classes.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.503-522
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• 2013

In the 2009 new curriculum reform, where creativity is the key point, assessment methods for mathematical creativity is recommended. However, lessons for creativity are not carried out well in mathematics classes. One of the reasons for this is the lack of assessment methods for student's creativity and specific instructions on how teachers should evaluate their students using a written test. Therefore, in this paper, we propose a simple way to evaluate student's creativity by differentiating the student's solutions of the posed problems. For validation of the proposed method, we identified the properties of excellent problem solutions cited by both the students group and teachers group. A chi-square test was then carried out to compare any differences in frequency that each of the groups chose as an excellent solution as a result of the student's problem solving

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.15-24
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• 2005

오늘날 제 7차 교육과정은 학습자의 사고과정과 능력을 다양한 평가방식으로 실시하도록 권유하고 있다. 이러한 목적을 구현하기 위하여 수학과 평가는 교수-학습에 유용한 평가, 과정 중심의 평가, 다양한 방법을 활용하는 평가가 되어야 할 것이다. 이는 학습자로 하여금 스스로 학습하도록 가정하는 인식론적 변화에 바탕을 둔 최근의 평가 동향과 맥을 같이 하고 있다. 평가에서 학생의 수학활동 역시 특히 인지적 영역의 다양성을 지닌 개인에 의하여 이루어지기 때문에 수학 평가는 단편적인 정형화된 지식이 아닌 문제 해결의 전략이나 발견술과 같은 요소에서 강조되고 있는 비정형의 문제들을 통한 메타인지적인 발달과정을 고려해야 한다. 본 연구에서는 학생이 준개방형 평가문제를 해결하는 과정을 통해 자신이 얼마나 알고 있는가를 인식하며 자신의 문제 해결 전략을 점검하고 평가하는 인지적 능력에서 일어나는 변화를 알아보는 데 그 목적이 있다. 지금 현재 연구가 진행 중이며 본 연구의 결과는 다음 논문집에 발표할 예정이다.

• School Mathematics
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• v.10 no.4
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• pp.583-601
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• 2008

The creative productivity is regarded as an essential factor to perform the gifted education. While it is very important to cultivate and to expand a creative productivity through mathematically problem solving in gifted education, we have difficulties in actual education of the (mathematically) gifted, even are there few researches/studies which deal with teaching and guiding the creative problem solving in mathematically gifted education, it is hard to find a guideline that provides proper ways (or directions) of learning-instruction and evaluation of the mathematically gifted. Therefore in this study, the researcher would provide a learning-instruction model to expand a creative productivity. The learning-instruction model which makes the creative productivity expanded in mathematically gifted education is developed and named MG-CPS(Mathematically Gifted-Creative Problem Solving). Since it reflected characteristics of academic- mathematical creativity and higher thinking level of the mathematically gifted, this model is distinguished from general CPS. So this model is proper to provide a learning experience and instruction to the mathematically gifted.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.143-159
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• 2018

Since the mathematics learning achievement level is closely related to problem-solving ability, it is necessary to understand the relationship between problem-solving ability and meta-affect ability from the point of view of general mathematics learning ability. In this study, we compared the frequency analysis and the case analysis of the functional aspects of the meta-affect in elementary school students' problem-solving processes according to mathematics learning achievement level in parallel with frequency analysis and case analysis. In other words, the frequency of occurrence of meta-affect, the frequency of meta-affective type, and the frequency of meta-functional types of meta-affect were compared and analyzed according to the mathematics learning achievement level in the collaborative problem-solving activities of small group members with similar mathematics learning achievement level. In addition, we analyzed the representative cases of meta-affect by meta-functional types according to the mathematics learning achievement level in detail. As a result, meta-affect in problem-solving processes of the upper level group acted as relatively various types of meta-functions compared to the lower level group. And, the lower level group, the more affective factors acted in the problem-solving processes.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.419-443
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• 2018

The purpose of this study was to analyze the problem solving strategies of ordinary students, gifted students, pre-service teachers, and in-service teachers with the 'chicken and pig problem,' which has multiple strategies to obtain the solution. For this study, 98 students in the 6th grade elementary schools, 96 gifted students in a gifted institution, 72 pre-service teachers, and 60 in-service teachers were selected. The researcher presented the "chicken and pig" problem and requested them the solution strategies as many as possible for 30 minutes in a free atmosphere. As a result of the study, the gifted students used relatively various and efficient strategies compared to the ordinary students, and there was a difference in the most used strategies among the groups. In addition, the percentage of respondents who suggested four or more strategies was 1% for the ordinary students, 54% for the gifted students, 42% for the pre-service teachers, and 43% for the in-service teachers. As suggestions, the researcher asserted that various kinds of high-quality mathematical problems and solving experiences should be provided to students and teachers and have students develop multi-strategy problems. As a follow-up study, the researcher suggested that multi-strategy mathematical problems should be applied to classroom teaching in a collaborative learning environment and reflected them in teacher training program.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.793-806
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• 2010

In this paper we study meaning and methods of analyzing problems related with equation of high school mathematics. By analyzing problem we can get two types of informations. Based on these informations we suggest some problem solving methods. Especially we try to extract second type information using analysis through synthesis. This second type information can help us to find new non-routine problem solving method.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.433-452
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• 2009

This study investigated the teaching strategies of two exemplary American teachers regarding word problems and their impact on students' ability to both understanding and solving word problems. The teachers commonly explained the background details of the background of the word problems. The explanation motivated the students' mathematical problem solving, helped students understand the word problems clearly, and helped students use various solving strategies. Emphasizing communication, the teachers also provided comfortable atmosphere for students to discuss mathematical ideas with another. The teachers' continuous questions became the energy for students to plan various problem solving strategies and reflect the solutions. Also, this research suggested a complementary model for Polya's problem solving strategies.