• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권2호
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• pp.125-133
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• 2005

This paper investigates student conceptual understanding and application on algebra using problem-based curricula. Seven principles which National Research Council announced were considered because these seven principles all involved in the development of a deep conceptual understanding. A problem-based curriculum itself provides a significant contribution to improving student learning. A problem-based curriculum encourages students to obtain a more conceptual understanding in algebra. From the results the national curriculum developers in Korea consider the problem-based curriculum.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제26권4호
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• pp.219-236
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• 2023

본 연구는 분수의 곱셈과 나눗셈에서 예비교사의 수학적 이해와 문제 만들기 사이의 관련성을 탐색하였다. 이를 위해여 41명의 예비교사들을 대상으로 분수의 곱셈과 나눗셈에 대한 시각적 표현과 문제 만들기 과제를 수행하고 수학적 이해 정도와 문제 만들기 능력을 측정하였으며, 수학적 이해 정도와 문제 만들기 능력 사이의 관련성을 교차분석을 통해 알아보았다. 그 결과, 예비교사들의 대부분은 분수의 곱셈과 나눗셈의 개념적 이해를 나타냈으며, 다섯 가지 유형의 어려움이 나타났다. 문제 만들기에서는 대부분의 예비교사들이 풀 수 있는 수학 문제를 만들지 못했으며 이 과정에서 네 가지 유형의 어려움이 나타났다. 또한 교차분석 결과, 수학적 이해 정도는 문제 만들기 능력과 연관이 있었다. 이러한 결과를 바탕으로 예비교사의 수학적 이해와 문제 만들기에 대한 시사점을 제시하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제48권3호
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.

• 한국학교수학회논문집
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• 제15권3호
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• pp.511-533
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• 2012

본 연구는 관계적 이해와 창의적 수학 문제발견능력이 유의한 상관관계가 있는지를 알아보기 위하여 중학교 2학년 학생 186명을 대상으로 관계적 이해 검사와 문제발견능력 검사를 실시하였다. 이를 위해 문제발견능력을 수학화 능력, 수학적 개념 결합능력, 수학적 사실 확장능력의 세 가지 하위요소로 분류하여 관계적 이해와의 상관관계를 분석하였다. 연구 결과에 따르면, 관계적 이해는 문제발견능력의 수학화 능력과 수학적 개념 결합능력의 창의성과는 매우 유의미한 정적 상관관계가 있음을 알 수 있었다. 또한 비록 관계적 이해와 수학적 사실 확장능력과는 통계적으로 유의미한 상관관계를 얻지는 못했으나, 학생들의 검사에 따른 응답율과 점수를 분석한 결과 관계적 이해수준이 높은 학생들의 유추능력과 귀납추리능력에서 높은 응답율과 점수를 얻었다. 따라서 본 연구를 통하여 수학에 대한 관계적 이해가 창의적 수학 문제발견능력에 긍정적인 영향을 미치는 것을 알 수 있었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제51권2호
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• pp.95-114
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• 2012

This study examines the use of ill-structured problem to help the 4th graders' problem solving and reasoning. It appears that children with good understanding of problem situation tend to accept the situation as itself rather than just as texts and produce various results with extraction of meaningful variables from situation. In addition, children with better understanding of problem situation show AR (algorithmic reasoning) and CR (creative reasoning) while children with poor understanding of problem situation show just AR (algorithmic reasoning) on their reasoning type.

• 한국과학교육학회지
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• 제17권1호
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• pp.11-19
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• 1997

Students' protocols obtained from think-aloud interviews were analyzed in the aspects of the success at first two problem-solving stages (understanding and planning), the time to complete a problem, the time at each problem-solving stage, the number of transition, and the transition rate. These were compared in the aspects of the context of problem, the success in solving problem, students' logical reasoning ability, spatial ability, and learning approach. The results were as follows:1. Students tended to spend more time in everyday contexts than in scientific contexts, especially at the stages of understanding and reviewing. The transition rate during solving a problem in everyday contexts was greater than that in scientific contexts. 2. Unsuccessful students spent more time at the stage of understanding, but successful students spent more time at the stage of planning. 3. Students' logical reasoning ability, as measured with the Group Assessment of Logical Thinking, was significantly correlated with the success in solving problem. Concrete-operational students spent more time in completing a problem, especially understanding the problem. 4. Students' spatial ability, as measured with the Purdue Visualization of Rotations Test and the Find A Shape Puzzle, was significantly correlated with their abilities to understand a problem and to plan for its solution. 5. Students' learning approach, as measured with the Questionnaire on Approaches to Learning and Studying, was not significantly correlated with the success in solving problem. However, the students in deep approach had more transitions and greater transition rates than the students in surface approach.

• 한국초등과학교육학회지:초등과학교육
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• 제30권2호
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• pp.213-231
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• 2011

The purpose of this study was to investigate knowledge types which the elementary science gifted students would use when solving a science problem, and to examine characteristics and types that were shown in the science problem solving process. For this study, 39 fifth graders and 38 sixth graders from Institute of Education for the Gifted Science Class were sampled in one National University of Education. The results of this study were as follows. First, for science problem solving, the elementary science gifted students used procedural knowledge and declarative knowledge at the same time, and procedural knowledge was more frequently used than declarative knowledge. Second, as for the characteristics in the understanding step of solving science problems, students tend to exactly figure out questions' given conditions and what to seek. In planning and solving stage, most of them used 3~4 different problem solving methods and strategies for solving. In evaluating stage, they mostly re-examined problem solving process for once or twice. Also, they did not correct the answer and had high confidence in their answers. Third, good solvers had used more complete or partially applied procedural knowledge and proper declarative knowledge than poor solvers. In the problem solving process, good solvers had more accurate problem-understanding and successful problem solving strategies. From characteristics shown in the good solvers' problem solving process, it is confirmed that the education program for science gifted students needs both studying on process of acquiring declarative knowledge and studying procedural knowledge for interpreting new situation, solving problem and deducting. In addition, in problem-understanding stage, it is required to develop divided and gradual programs for interpreting and symbolizing the problem, and for increasing the understanding.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권2호
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• 한국학교수학회논문집
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• 제5권1호
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• pp.13-19
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• 2002

In this experiment we emphasized the cooperative small group learning and the members of my group worked together to succeed and communicate their mathematics ideas freely. The researcher(teacher) became an observer and facilitator of small group interaction, paying attention to the ongoing learning process, Sometimes the researcher suggested some investigation approach(or discovery)being written by computer software or papers. In this experiment we provided 6 activities as follows : (1) changing the conditions in given problem. (2) operating the meaningful heuristics with the problem sets. (3) creating the problem situations related to understanding (4) creating the Modeling situations. (5) creating the problem related to combinatorial thinking in real world. (6) posing some real problem from real world. we could observed several conjectures First, Attitude and chility to interpret the problem setting is highly important to pose the problem effectively. Second, Generating the understanding can be a great tool to pose the problem effectively. Third, Sometimes inquiry approach represented by software or programmed book could be some motivation to enhance the posing activities. Forth, The various posing activities relate to one concept could give the students some opportunity to be adaptable and flexible in the their approach to unfamiliar problem sets.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제26권2호
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• pp.83-97
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• 2023

명사화는 문법적 은유 중 하나로, 수식으로 변환해야 하는 대상의 수학화를 용이하게 한다는 장점과 함께 복잡하고 압축된 문장 구성으로 인해 문장 이해를 어렵게 할 가능성이 있다는 단점이 있다. 이러한 명사화가 실제 학생들의 문장제 해결 과정에 어떠한 영향을 미치는지 파악하기 위하여 초등학교 3학년을 대상으로 명사화 여부에 따른 사칙연산 문장제 8개를 제공하여 검사를 실시하였다. 분석 결과, 문장제의 명사화 여부는 문제 이해 및 수식화 가능 여부에 의미 있는 영향을 미치지 못하였다. 그러나, 검사에 참여한 학생에게 명사화에 대한 사전 경험이 없음에도 불구하고 문제 이해 단계에서 명사화 또는 탈명사화가 나타나는 것을 확인하였으며, 명사화의 유형 변화가 발생하는 경우 성공 비율이 높게 나타나는 등 수식화 단계를 용이하게 하였다. 이를 통하여 명사화가 문장제의 문제 이해 및 수식화 단계에서 교수학적 전략으로 활용될 수 있으며 문장제의 학습에서 더 깊이 있는 이해를 유도할 수 있을 것으로 기대할 수 있다.