• Title/Summary/Keyword: 수학적 창의성

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Thinking for creative problem solving and problem posing (창의적 문제해결과 문제변형을 위한 사고)

  • Kim Yong Dae
    • 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.

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The Effects of Mathematical Problem Solving with Multiple Strategies on the Mathematical Creativity and Attitudes of Students (다전략 수학 문제해결 학습이 초등학생의 수학적 창의성과 수학적 태도에 미치는 영향)

  • Kim, Seoryeong;Park, Mangoo
    • Education of Primary School Mathematics
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    • v.24 no.4
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    • pp.175-187
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    • 2021
  • The purpose of this study is to investigate the effects of solving multi-strategic mathematics problems on mathematical creativity and attitudes of the 6th grade students. For this study, the researchers conducted a survey of forty nine (26 students in experimental group and 23 students in comparative group) 6th graders of S elementary school in Seoul with 19 lessons. The experimental group solved the multi-strategic mathematics problems after learning mathematics through mathematical strategies, whereas the group of comparative students were taught general mathematics problem solving. The researchers conducted pre- and post- isomorphic mathematical creativity and mathematical attitudes of students. They examined the t-test between the pre- and post- scores of sub-elements of fluency, flexibility and creativity and attitudes of the students by the i-STATistics. The researchers obtained the following conclusions. First, solving multi-strategic mathematics problems has a positive impact on mathematical creativity of the students. After learning solving the multi-strategic mathematics problems, the scores of mathematical creativity of the 6th grade elementary students were increased. Second, learning solving the multi-strategy mathematics problems impact the interest, value, will and efficacy factors in the mathematical attitudes of the students. However, no significant effect was found in the areas of desire for recognition and motivation. The researchers suggested that, by expanding the academic year and the number of people in the study, it is necessary to verify how mathematics learning through multi-strategic mathematics problem-solving affects mathematical creativity and mathematical attitudes, and to verify the effectiveness through long-term research, including qualitative research methods such as in-depth interviews and observations of students' solving problems.

Math Creative Problem Solving Ability Test for Identification of the Mathematically Gifted Middle School Students (중학교 수학 영재 판별을 위한 수학 창의적 문제해결력 검사 개발)

  • Cho, Seok-Hee;Hwang, Dong-Jou
    • Journal of Gifted/Talented Education
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    • v.17 no.1
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    • pp.1-26
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    • 2007
  • The purpose of this study was to develop a math test for identification of the mathematically gifted on the basis of their math creative problem solving ability and to evaluate the goodness of the test. Especially, testing reliability and validity of scoring method on the basis of fluency only for evaluation of math creative problem solving ability was one of the main purposes. Ten closed math problems and 5 open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 closed math test items of Type I and the 5 open math test items of Type II were administered to 1,032 Grade 7 students who were recommended by their teachers as candidates for gifted education programs. Students' responses were scored by math teachers. Their responses were analyzed by BIGSTEPS and 1 parameter model of item analyses technique. The item analyses revealed that the problems were good in reliability, validity, item difficulty and item discriminating power even when creativity was scored based on the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creative problem solving ability of the candidates for math gifted education programs. In addition, it was found that the math creative problem solving tests discriminated applicants for the two different gifted educational institutions.

An Analysis of Mathematical Thinking and Strategies Appeared in Solving Mathematical Puzzles (수학퍼즐 해결과정에서 나타나는 수학적 사고와 전략)

  • Kim, Pansoo
    • Journal of Creative Information Culture
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    • v.5 no.3
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    • pp.295-306
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    • 2019
  • Despite the popularity and convenient accessibility of puzzles, the variety of puzzles have led to a lack of research on the nature of the puzzle itself. In guiding certain skills, such as abstractness, creativity, and logic, a teacher should have the thinking skill and strategy that appear in solving puzzles. In this study, the mathematical thinking that appears in solving puzzles from the perspective of experts is identified, and the strategies and characteristics are described and classified accordingly. For this purpose, we analyzed 85 math puzzles including the well-know puzzles to the public, plus puzzles from a popular book for the gifted student. The research analysis shows that there are 6 types of mathematics puzzles in which require mathematical thinking.

수학적 창의성과 개방형 문제(open ended problem)

  • Gwon, O-Nam;Jo, Yeong-Mi;Park, Jeong-Suk;Park, Ji-Hyeon;Kim, Yeong-Sil
    • Communications of Mathematical Education
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    • v.16
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    • pp.217-218
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    • 2003
  • 제7차 교육과정의 기본방향인 '21세기의 세계화 정보화 시대를 주도할 자율적이고 창의적인 한국인 육성'에서 볼 수 있듯이, 새로운 교육과정에서는 학생들의 창의력을 신장시키기 위한 방안으로 교과별 교육과정이나 재량활동 운영 등을 제시한 바 있다. 수학교육에서도 이러한 시대적 흐름에 발맞추어 수학적 창의력의 신장이 강조되고 있는 상황이다. 그동안 이론적인 측면과 실제적인 측면에서 수학적 창의성에 대한 성과가 축적되었다. 이론적인 측면에서 볼 때, Haylock(1987)등에 의해 창의력과 수학적 창의력의 구분되었으며, 특히 '수학적' 창의력에 대한 다양한 정의가 제안되었다. 실제적인 측면에서도 수학적 창의력을 측정하려는 평가 도구들이 그 동안 여러 가지로 개발하였다. 그러나, 이러한 수학적 창의력에 관한 전반적인 연구는 종국적으로 교실 수학수업에 반영되어야 함에도 불구하고, 그리 만족스럽지 못한 상황이다. 특히, 교실에서 수학수업을 실제로 담당하는 교사들이 수학적 창의력을 위한 수업을 하고자 하더라도 당장 가까이에서 구할 수 있는 교수 학습 자료가 여전히 부족한 상황이다. 물론 그 동안 교실 수학수업에서 사용할 수 있는 창의력 개발 프로그램이 전무한 것은 아니다. 그런데 그들 대부분은 게임이나 퍼즐을 이용한 것으로 그 수준이 단순 흥미유발에 그치고 있거나 소수의 영재아를 위한 소재를 중심으로, 특히 수학적 사고 과정을 따르기보다는, 시행착오를 거쳐 원하는 결과를 얻을 가능성이 많으며, 수학과의 연계성이 불분명한 채로 단순놀이에 그치는 경우가 적지 않아, 수업과 연관되어 창의력의 신장이라는 측면에서 볼 때, 적용하기 어려운 사례가 많다. 이러한 상황을 개선하는 데 기여하고자, 현재 교과교육공동연구 지원사업의 하나로 한국 학술 진흥재단의 지원을 받아, '개방형 문제(open-ended problems)'를 중심 소재로 한 '수학적 창의성'을 신장하기 위한 교수학습 프로그램을 개발하여, 중학교 1학년을 대상으로 연구를 진행하고 있다. 개방형 문제라 함은 명백한 정의가 어렵지만 Pehkeon(1995)는 개방형문제의 정의를 명백히 하기위한 시도로서 그 반대로 닫힌 문제에 대한 정의로부터 시작하여, 어떤 문제가 닫혀있다고 하는 것은 그 문제의 출발 상황과 목표 상황이 닫혀 있는 것, 즉 명백히 설명되어있을 때라면 개방형 문제는 이와 반대의 개념임을 시사하였다. Silver(1995)는 개방형 문제를 문제 자체가 다른 해석이 가능하거나 서로 다를 인정할만한 답을 가질 수 있는 문제 또는 풀이과정이 다양한 문제, 자연스럽게 다른 문제들을 제안하거나 일반화를 제시할 수 있는 문제라고 정의하였다. 따라서 개방형 문제란 출발상황이나 목표 상황의 일부가 닫혀있지 않을 때를 말하고 문제의 조건을 만족하는 해답이 여러 가지로 존재하는 문제를 뜻한다. 수학적 창의력을 개발하는 데, 다른 문제 유형보다도, 개방형 문제가 유리하다는 점은 이미 여러 학자들에 의해 주장되어왔다. 미국 국립영재교육센터(NRCG/T)는 기존의 사지선다형이나 단답형 문제와 질문들은 학생들의 사고 능력에 관한 정보를 거의 알려주지 못하기 때문에 한 가지 이상의 답을 요구하는 ‘open-ended' 또는 ’open-response' 문제와 질문을 가지고 수학 분야에서의 창의적 사고 능력과 표현능력을 측정해야 한다고 하였고, 개방형 문제가 일반적으로 정답이 하나인 문제보다 고차원적인 사고를 요구하게 하는 문제 형태라고 하였다. 본 연구에서는 이러한 근거를 바탕으로 개방형 문제의 유형을 다양한 답이 존재하는 문제, 다양한 해결 전략이 가능한 문제, 답이 없는 문제, 문제 만들기, 일반화가 가능한 문제 등으로 보고, 수학적 창의성 중 특히 확산적 사고에 초점을 맞추어 개방형 문제가 확산적 사고의 요소인 유창성, 독창성, 유연성 등에 각각 어떤 영향을 미치는지 20주의 프로그램을 개발, 진행하여 그 효과를 검증하고자 한다. 개방형 문제를 활용한 수학적 창의력 신장 프로그램을 개발하고 현장 학교에 실험 적용하여 그 효과를 분석하고자 하는 본 연구는 창의력 신장에 비중을 두는 수학과 교수-학습 과정에 실제적인 교수 학습 자료를 제공하는 것뿐만 아니라 교사들에게는 수학교실에서 사용 가능한 실제적인 활용방안을, 학생들에게는 주어진 문제를 여러 가지 각도에서 생각하면서 다양한 사고를 경험하는 기회를 가질 수 있어, 수학을 보는 학생들의 태도에도 긍정적인 변화를 가져올 수 있을 것이라 기대한다.

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Comparative Study between Gifted Math Elementary Students and Non-Gifted Students in Emotional Intelligence and Creative Nature (초등수학영재와 일반학생의 정서지능과 창의적 성향 비교)

  • Lee, Eun Hee;Ryu, Sung Rim
    • School Mathematics
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    • v.16 no.1
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    • pp.181-199
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    • 2014
  • This study set out to analyze and compare gifted elementary students and non-gifted students in emotional intelligence and creative nature. To understand the characteristics of the former, and provide assistance for career education for both groups. For this purpose, the three following research questions were set: First, what kind of difference is there in emotional intelligence between gifted elementary students and non-gifted students? Second, what kind of difference is there in creative nature between gifted elementary students and non-gifted students? Third, what is the connection between emotional intelligence and creative nature in gifted elementary students and non-gifted students? For this study, 102 students from the gifted class and 132 students from non-gifted classes were selected. In total 234 questionnaires were distributed, and the results were analyzed. The results of this study were as follows. First, as a result of the independent sample T-test, there were noticeable differences in giftedness. Gifted students scored significantly higher than non-gifted students in creative nature. Second, as a result of the independent sample T-test, there were noticeable differences in the creative nature of gifted and non-gifted students. Gifted students scored significantly higher than non-gifted students in creative nature. Third, by analyzing the results found for emotional intelligence and creative nature with Pearson's product-moment correlation, there was a positive correlation between both emotional intelligence and creative nature in both groups of results.

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A study on the Circular art using a numeral operation for the mathematical gifted - Focused on the design of a circle using GSP - (초등수학 영재학생의 자연수의 연산을 활용한 원형 디자인 - GSP를 활용한 원 디자인을 중심으로 -)

  • Park, Joog-Youll;Lee, Heon-Soo
    • Education of Primary School Mathematics
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    • v.15 no.1
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    • pp.31-40
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    • 2012
  • In this paper, we developed teaching learning models using a numeral operation for the mathematical gifted focused on the design of a circle using GSP and investigated effects of this models. This model gave gifted-students to be able to produce creative outputs with mathematical principles and practicality and beauty of mathematics. We found following facts. Firstly, a developed teaching-learning model improves a mathematical gifted student's mathematical creativity as analytic thinking and deductive inference. Secondly, a circular design using GSP helps gifted students to understand the abstract rules because mathematical patterns was represented visually by a circular design. Lastly, a circular design using a numeral operation is helpful to gifted students revealing to creativity and beauty of mathematics.

The analysis of mathematics teachers' teaching behavior for fostering creativity (초.중등학교 수학교사의 창의성 신장 교수 행동에 대한 분석)

  • Lee, Bong-Ju
    • Journal for History of Mathematics
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    • v.25 no.3
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    • pp.77-95
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    • 2012
  • The purpose of this study is to draw implication for the teacher education program in association with creativity through analysing teaching behavior for fostering creativity of the mathematics teachers at the primary and secondary schools. In order to do so, a survey was performed by sampling primary, middle, and high school teachers. According to the results, there is significant difference in teachers' behavior for fostering creativity in the perspective of school classification (primary and secondary school), but not gender, region, and career of teachers. In other words, there is significant difference in teaching behaviors for fostering creativity between primary and secondary school teachers, herein the score of teaching behavior of former is higher than latter. Furthermore, the result of teachers' recognition survey on the possibility of fostering students' creativity via education shows that the teachers of primary schools are more relatively positive than those of secondary schools on the matter.

수학교육과 수학적 창의성

  • Hwang U-Hyeong;Choe Gye-Hyeon;Kim Gyeong-Mi;Lee Myeong-Hui
    • Proceedings of the Korea Society of Mathematical Education Conference
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    • 2006.10a
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    • pp.109-110
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    • 2006
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