• Journal of Elementary Mathematics Education in Korea
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• v.6 no.1
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• pp.41-58
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• 2002

This study examines effects of small group cooperative learning on areas of mathematics such as number and calculation, figure, and measurement, and changes of attitude-interest in math in elementary schools. Seventy eight second graders from Jinhae City were divided into the experimental group and the control group. The experimental group was subdivided into small groups of four students who belonged in different levels of math performance. The subdivision was renewed whenever each area was covered. An examination paper which had been developed by Ministry of Education & Human Resources Development and Kyeongsangnamdo Office of Education was given to the subjects. Also, a questionnaire was developed and given to the participants. The results show that, in general, the small group cooperative learning had good effects on the students' ability to solve math problems and, in articular, greater effects on the ability of low-level students. It is revealed that the interaction between the students in small groups affected their attitudes toward and interest in mathematics in a positive way, but did not make perceivable changes in self-confidence of the young Learners.

• 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.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.63-80
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• 2009

This paper has a purpose to find out the important points about linguistic factors suited to the assessment purpose and mathematics teaching/learning that a word-problem sentence has to possess. We also examine the degree of understanding of sentence and the perceptive/emotional reactions of students toward two different kinds of word-problem sentences that have same mathematical contents, but different linguistic structures. The objects of this thesis are 124 students from the third to sixth grade in an elementary school. We execute assessment of simple-sentence-word-problem and complex-sentence-word-problem that have same mathematical contexts, but different linguistic structures. Then we have compared and examined their own process of solving the two types word-problems and we make up questionnaire and have an interview with them. The conclusions are as followings: First, simple-sentence-word-problem is more successful to suggest an information for solving a problem than complex one. Second, it is hard to find the strategy for solving a problem in complex-sentence-word-problem than simple one. Third, students think that suggested information and mathematical knowledge are different according to the linguistic structure in the process of perceiving the information after reading a word-problem. Fourth, in spite of same sentence type, the negative mental reaction is showed greatly to complex-sentence-word-problem even before solving a problem.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.563-588
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• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• Journal of Gifted/Talented Education
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• v.11 no.3
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• pp.245-270
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• 2001

Math and Science Olympians participated in a study of the role of environmental influences in their talent development. The questions they got was about family and school factors contribute / or hinder to the development of their scientific talents, and the parents' child rearing styles. The questionnaires were originally developed by Campbell(1996) for cross-cultural studies. The major findings were as follows: ⑴ The professional job of the Olympians'father, the high SES, Their parents'discovering their child's talents were positive factors, ⑵ Their family support and learning environment were reported strong and positive, especially books and reading atmosphere, ⑶ The Olympians participated in the accelerated and enriched educational programs, ⑷ The quality of the class and the rigidity of the curriculum were hindering factors, ⑸ Their parents'rearing style were permissive, affective, and supportive.

• Communications of Mathematical Education
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• v.28 no.2
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• pp.255-279
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• 2014

This study is to investigate the change of intelligent and affective domains through the student self-evaluation to identify causes of wrong answers. Through this evaluation, students could have opportunities to solve the given mathematical problems basically and to reflect their problem-solving process, and further to recognize which mathematical content(concepts or expressions, symbols, etc.) led them to solve the problems incorrectly or wrong. Through this process, they would correct their wrong process and answers and to reinforce the prerequisite knowledges relevant to the problems, and furthermore, to enhance problem-solving abilities. To accomplish this, this study was executed as a case study on the subject of four tenth graders. The subject consisted of two boys and two girls. In this study, three essay types of mathematical problems in tenth grade level were chosen from several domestic tests in Korea. Based on the original three essay type of problems, three types of similar problems, namely equivalent problem, similar problem, and isomorphic problems were reconstructed, respectively by the researchers. The subjects were guided to solve the original three problems, and they corrected their wrong parts of the first problem of the three problems. They solved an equivalent problem of the first problem and executed self evaluation and also corrected wrong parts. Next, they dealt with a similar problem of the first problem and executed self evaluation and also corrected wrong parts. Next, while dealing with an isomorphic problem of the first problem, the subjects did the same things. Thus, for the second and third original problems, the study was implemented in the same way. To explore their intelligent and affective domains through student self-evaluation in-depth, the subjects were interviewed formally before and after conducting the experiment and interviewed informally two times, and the recordings were audio-typed.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.1-17
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• 2014

Recently a student's mathematical thinking and problem-solving skills are emphasized. Nevertheless, the students solved the problem associated with a given type of problem solving using mechanical algorithms. With this algorithm, It's hard to achieve the goal that are recently emphasized. Furthermore It may be formed error or misconception. However, consistent errors have positive aspects to identify of the current cognitive state of the learner and to provide information about the cause of the error. Thus, this study tried to analyze the error happening in the process of solving gearwheel-involved problem and to propose the correct teaching method. The result of student's error analysis, the student tends to solve the gear-wheel problem with proportional expression only. And the student did not check for the proportional expression whether they are right or wrong. This may be occurred by textbook and curriculum which suggests only best possible conditioned problems. This paper close with implications on the discussion and revision of the concepts presented in the curriculum and sequence related to the gearwheel-involved problem as well as methodological suggested of textbook.

• 대한공업교육학회지
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• v.36 no.1
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• pp.1-22
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• 2011

The purpose of this study was to develop and apply activity-centered STEM education program of electricity and electronics technology are in middle schools. The program was developed on the emphasis of problem solving in real world in relation to knowledge, attitude, and skill of Science, Technology, Engineering, and Mathematics. Basically the activity-centered STEM education program was developed through three steps of preparation, development and improvement. In the preparation stage the fellowing was included: (1) need analysis of student, educator, society (2) selection of integration type (3) analyzing subject matter of electricity, electronics area (4) establishing criteria for selecting activity tasks. In the development stage the fellowing was conducted: (1) selection of activity tasks (2) setting up educational goals (3) analyzing activity and clarifing the detailed activity (4) selecting program content, (5) organization of instructional content (6) statement of instructional objectives (7) structuring STEM education program In the improvement stage the fellowing was consisted of: (1) verification of validity by experts (2) execution of pilot test and field test by students and correction of program. The results of the applied the Activity-Based STEM Education Program to 'Afterschool' activities of S middle school were as follow: First, student' satisfaction level was high. Second, student' achievement in the cognitive domain, and affective domain was positive change. Third, student' problem solving ability was positive effect.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.235-257
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• 2010

Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.

• Journal of Gifted/Talented Education
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• v.13 no.4
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• pp.65-94
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• 2003

The purpose of this study is to acquire the information on the current situation of students' selection process in order to renovate the system of picking up the students. As a first step of the study, we examined the validity of the factors of the single-out system such as qualification and the process for the application and the standards and proceeding of the selection. Then we analysed the result of the entrance examination of Hansung Science Highschool in 2002. The analysis was on the correlation between the result of entrance examination and the achievement in the school and the decision of the course after graduation. To know on the achievement of the students, we investigated the records of regular tests and asked the teachers' opinion in math and science classes. As a result, we gained the following points: First, the present single-out system has a danger of excluding students who are much talented in science and math field because it is based on students' achievements in middle schools; Second, the new selection system should consider the character and attitude of the applicants in addition to their knowledge; Third, the continuous observation of the teacher in middle school should be an important factor of the picking up system; Fourth, more questions requiring divergent thinking ability and inquiry skill should be developed as selective examination question. Also examination questions should cover the various contents from mathematics to science, and do not affect pre-learning; Finally, the system of present letting all students stand in one line should be changed into that of letting students in various lines. We can consider using multi-step selection system.