• Journal for History of Mathematics
• /
• v.22 no.3
• /
• pp.113-130
• /
• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

• Journal of Educational Research in Mathematics
• /
• v.27 no.4
• /
• pp.857-888
• /
• 2017

Due to globalization, diversification, and informatization, modern society confronts change and crisis in a variety of areas such as economy, politics, and culture. In that context, mathematics educators seek for how to reform school mathematics for democratic and just society. This research proposes critical mathematics education as an alternative model of school mathematics for democratic society. In particular, this research is an explorative study to construct a model of critical mathematics education program. For the purpose, we conducted a comprehensive literature review to identify goals, contents, and methods of teaching and learning, and method of assessment for critical mathematics education. We checked the validity of the model by using the cases of critical mathematics education. Since this research is explorative in the regard that the model is based on theoretical literatures, further research is necessary to extend the model through design research in school context.

• Communications of Mathematical Education
• /
• v.10
• /
• pp.393-416
• /
• 2000

수학교육세계회의(數學敎育世界會議)(ICME)는 ICME수학교육국제위원회(數學敎育國際委員會)가 4년마다 한 번씩 개최하는 행사이다. 수학교육세계회의(數學敎育世界會議)(ICME-9)는 올해(2000년) 7월 31일(월)${\sim}$8월 6일(일)에 일본의 Tokyo동경(東京) 근교 Chiba의 Makuhari막장(幕張)서 개최된다. 전세계에서 4,000여명이 참가하는 큰 규모의 수학교육 관련 행사로써 아시아에서는 처음으로 열린다. 특히 이번 ICME에서는 우리 나라 수학교육자들이 많이 참여하게 되었다. 권오남, 박한식, 신현용 교수는 정규 강연(Regular Lecture)을 하게 되었고, 강완 교수 등 일곱 사람은 분과 모임(WGA, TSG)의 조직 위원(Organizer) 등을 맡아 이 행사의 준비 단계에서부터 중요한 역할을 하고 있다. 그 동안 수학교육에 나타난 떠들썩한 이론들은 거의 대부분 서양에서 시작하였고 우리는 이것을 받아들이기에 급급하였다. 그러나 우리의 주위를 살펴보면 우리에게도 전세계에 알릴 것들이 많이 있다. 이러한 것을 찾아서 더욱 갈고 다듬어서 소개할 때가 되었다. 불확실하거나 흩어진 자료들은 체계적으로 정리하는 한편 그 동안 축적된 경험과 정보들은 세밀히 분석하고 또 이론을 세워서 내어 놓아야한다. 우리 모두 ICME-9에 적극적으로 참여하여 새 천년의 우리 나라 수학교육을 한 단계 높여 보자.

• Education of Primary School Mathematics
• /
• v.24 no.4
• /
• pp.247-264
• /
• 2021

The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

• Journal of the Korean School Mathematics Society
• /
• v.17 no.1
• /
• pp.73-92
• /
• 2014

This study was performed in part with the task to find measures to improve the defining characteristics of feelings, value, interest, self-efficacy, and others aspects in regards to learning math among elementary and middle school students. For this study, it was essential to understand the appropriate questions that are needed to be asked during a consultation at a math clinic, for students that are having a hard time learning math. As a method for performing this study, the content of scheduled counseling over 2 years from a math clinic were collected and the questions that were given and taken were analyzed in order to figure out the types of questions needed in order to effectively examine students that are facing difficulty with learning math. The analysis was performed using Grounded theory analysis by Strauss & Corbin(1998) and went through the process of open coding, axial coding, and selective coding. For the paradigm in the categorical analysis stage, 'attitude towards learning math' was set as the casual condition, 'feelings towards learning math' was set as the contextual condition, 'confidence in one's ability to learn math' was set as the phenomenon, 'individual tendencies when learning math' was set as the intervening condition, 'self-management of learning math' was set as the action/interaction strategy, and 'method of learning' was set as the consequence. Through this, the questions that appeared during counseling were linked into categories and subcategories. Through this process, 81 concepts were deducted, which were grouped into 31 categories. I believe that this data can be used as grounded theory for standardization of consultation in clinics.

• Communications of Mathematical Education
• /
• v.18 no.3 s.20
• /
• pp.243-253
• /
• 2004

수학은 그 근본이 창조적인 활동이다. 창조성은 그것의 본질적인 아름다움을 통해서나 현실 세계문제에 응용되는 방식 중의 하나로 개발될 수 있다. 수많은 위대한 수학자들은 수학의 응용에 진실로 흥미를 가져왔으며, 물리적 현상의 수학적 규명으로부터 새로운 수학이론개발의 영감을 얻어왔다. 우리는 이번연구에서 수학적 모델이 어떻게 형성되고 사용되는지를 살펴보고 수학의 응용 단계에 대하여 연구해 볼 것이다. 그 수학의 응용 예시로써 스포츠, 환경, 인구에 대해 다루어 볼 것이다.

• Journal for History of Mathematics
• /
• v.19 no.2
• /
• pp.59-76
• /
• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.

• School Mathematics
• /
• v.15 no.1
• /
• pp.61-75
• /
• 2013

This study analyzed Korean students' affective characteristics in mathematical learning according to school and sex by Factor Analysis and Cognitive Diagnosis Theory. In numerical affective achievements by Factor Analysis, there are mean differences between schools, i.e. elementary school and secondary school. And there are sexual differences within schools and boys show more positive achievement than girls. By Cognitive Diagnosis Theory, I investigated 6 affective attributes' proportions that students achieved according to school and sex. Middle school students' proportion is highest in self-control and anxiety and the attribute that students achieved most in all school is cognizing mathematical value. Boys show higher proportion in self directivity, interest and confidence than girls, but girls show higher proportion in anxiety than boys. In personal profiles, the proportion of students who achieved 5 attributes except anxiety is highest.

• Journal of Educational Research in Mathematics
• /
• v.24 no.3
• /
• pp.387-407
• /
• 2014

This study investigeted secondary math teachers' difficulties of technology in geometry class with grounded theory by Strauss and Corbin. 178 secondary math teachers attending the professional development program on technology-based geometry teaching at eight locations in January 2014, participated in this study with informed consents. Data was collected with an open-ended questionnaire survey. In line with grounded theory, open, axial and selective coding were applied to data analysis. According to the results of this study, teachers were found to experience resistance in using technology due to new learning and changes, with knowledge and awareness of technology effectively interacting to lessen such resistance. In using technology, teachers were found to go through the 'access-resistance-unaccepted use-acceptance' stages. Teachers having difficulties in using technology included the following four types: 'inaccessible, denial of acceptance, discontinuation of use, and acceptance 'These findings suggest novel perspectives towards teachers having difficulties in using technology, providing implications for teachers' professional development.

• Bulletin of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.65-76
• /
• 1975