• Communications of Mathematical Education
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• v.22 no.3
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• pp.311-335
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• 2008

The importance of students' precise understanding of mathematical definitions, formulas, and theorems can not be underestimated. In this survey research, we attempted to evaluate students' understanding of the concepts of five topics -limit, continuity and intermediate theorem, derivative, application of derivative and integral. On the basis of the research result, this paper suggests that we need to 1) be more inventive and speculative in making test problems, 2) explain the examples and counter-examples more concretely, 3) stress and repeat the basic concepts on the stage of introducing new concepts, 4) develop more effective problems for the measure of students' understanding of mathematical concepts, 5) use developed problems in actual teaching.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.219-236
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• 2023

This study examined the relationship between preservice teachers' mathematical understanding and problem posing in fractions multiplication and division. To this purpose, 41 preservice teachers performed visual representation and problem posing tasks for fraction multiplication and division, measured their mathematical understanding and problem posing ability, and examined the relationship between mathematical understanding and problem posing ability using cross-tabulation analysis. As a result, most of the preservice teachers showed conceptual understanding of fraction multiplication and division, and five types of difficulties appeared. In problem posing, most of the preservice teachers failed to pose a math problem that could be solved, and four types of difficulties appeared. As a result of cross-tabulation analysis, the degree of mathematical understanding was related to the ability to pose problems. Based on these results, implications for preservice teachers' mathematical understanding and problem posing were suggested.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.511-533
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• 2012

In order to determine whether there is a significant correlation between relational understanding and creative math. problem finding ability, this study performed relational understanding and problem finding ability tests on a sample of 186 8th grade middle school students. According to the study results, we found a very significant positive correlation between relational understanding and the creativity of the mathematising ability and the combining ability of mathematical concepts in the problem finding ability. Although there was no statistically significant correlation between relational understanding and the extension ability of mathematical facts, the results from analyzing the students response rate and actual scores in each test showed that students with high relational understanding scores also had high response rate and high scores in analogical reasoning and inductive reasoning. Through this study, therefore, relational understanding is found to have a positive impact on the creative mathematics problem finding ability.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.45-55
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• 2005

대학수학 1학년 과정(미분적분학)에서 정리, 정의 등 개념의 이해를 도와주기 위해 학생들이 갖는 어려움을 그들이 자주 겪는 실수를 통해 찾아내어 분석하고 올바른 이해의 길로 안내한다. 실수를 탓하기보다 학생의 편에 서서 이해하고 도움을 주도록 한다. 흔히 부딪칠 수 있는 예제 문제를 풀어보게 하고 공통으로 저지르는 실수를 제시하여 개념의 이해나 문제풀이를 바르게 하도록 이끌어 준다.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.129-144
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• 2009

The purpose of the study was to investigate the effects of the use of RNP curriculum based on Lesh translation model on third grade students' understandings of fraction concepts and problem solving ability. Students' conceptual understandings of fractions and problem solving ability were improved by the use of the curriculum. Various manipulative experiences and translation processes between and among representations facilitated students' conceptual understandings of fractions and contributed to the development of problem solving strategies. Expecially, in problem situations including fraction ordering which was not covered during the study, mental images of fractions constructed by the experiences with manipulatives played a central role as a problem solving strategy.

• Proceedings of the Korea Information Processing Society Conference
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• 2023.11a
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• pp.23-26
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• 2023

본 논문에서는 서술형 수학 문제 풀이 모델의 숫자 대소관계 파악을 위한 명시적 자질추출방식 Explicit Feature Extraction(EFE) Reasoner 모델을 제안한다. 서술형 수학 문제는 자연현상이나 일상에서 벌어지는 사건을 수학적으로 기술한 문제이다. 서술형 수학 문제 풀이를 위해서는 인공지능 모델이 문장에 함축된 논리를 파악하여 수식 또는 답을 도출해야 한다. 때문에 서술형 수학 문제 데이터셋은 인공지능 모델의 언어 이해 및 추론 능력을 평가하는 지표로 활용되고 있다. 기존 연구에서는 문제를 이해할 때 숫자의 대소관계를 파악하지 않고 문제에 등장하는 변수의 논리적인 관계만을 사용하여 수식을 도출한다는 한계점이 존재했다. 본 논문에서는 자연어 이해계열 모델 중 SVAMP 데이터셋에서 가장 높은 성능을 내고 있는 Deductive-Reasoner 모델에 숫자의 대소관계를 파악할 수 있는 방법론인 EFE 를 적용했을 때 RoBERTa-base 에서 1.1%, RoBERTa-large 에서 2.8%의 성능 향상을 얻었다. 이 결과를 통해 자연어 이해 모델이 숫자의 대소관계를 이해하는 것이 정답률 향상에 기여할 수 있음을 확인한다.

• Journal of Elementary Mathematics Education in Korea
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• v.3 no.1
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• pp.41-59
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• 1999

We believe that there can be a mutually supportive relationship between emphasizing problem solving and emphasizing understanding in mathematics instruction, when teachers teach via problem solving, as well as about it and for it they provide their student with a powerful and important means of developing their own understanding. As students' understanding of mathematics becomes deeper and richer, their ability to use mathematics to solve problem increases.

• School Mathematics
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• v.7 no.2
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• pp.123-137
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• 2005

Elementary combinatorial problem may be classified into three different combinatorial models(selection, distribution, partition). The main goal of this research is to determine the effect of type of combinatorial operation and implicit combinatorial model on problem difficulty. We also classified errors in the understanding combinatorial problem into error of order, repetition, permutation with repetition, confusing the type of object and cell, partition. The analysis of variance of answers from 339 students showed the influence of the implicit combinatorial model and types of combinatorial operations. As a result of clinical interviews, we particularly noticed that some students were not able to transfer the definition of combinatorial operation when changing the problem to a different combinatorial model. Moreover, we have analysed textbooks, and we have found that the exercises in these textbooks don't have various types of problems. Therefore when organizing the teaching , it is necessary to pose various types of problems and to emphasize the transition of combinatorial problem into the different models.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.429-459
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• 2009

The purpose of this study was to help the students deepen their mathematical understanding and practitioner improve her mathematics lessons. The teacher-researcher developed mathematical situation based problem solving instruction model which was modified from PBL(Problem Based Learning instruction model). Three lessons were performed in the cycle of reflection, plan, and action. As a result of performance, reflective knowledges were noted as followed points; students' mathematical understanding, mathematical situation based problem solving instruction model, improvement of mathematics teachers.

• Proceedings of the Korean Society for the Gifted Conference
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• 2003.05a
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• pp.139-139
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• 2003

오늘날 세계는 일반국민과 과학기술의 상호관계에 대해 두 가지 큰 논쟁에 빠져있다. 하나는 국민의 과학기술에 대한 공동체 유대감을 어떻게 형성하느냐하는 것과, 또 다른 하나는 과학기술에 대한 일반국민의 이해 수준을 어떻게 측정하느냐에 대한 것이다. 다시 말해서 이제 과학계는 금연캠페인이나 환경캠페인의 성공처럼, 과학기술 지식을 활용하는 데 국민의 참여를 불러오도록 적극적으로 나서야 하며, 그것을 통해 과학기술에 대한 국민의 이해를 높일 수 있다는 주장이다. 즉 일반국민의 과학기술에 대한 공동체 유대감을 높이는 길은 그들의 관심에 근거할 때 가능하며, 그런 과정에서 과학기술에 대한 이해도 높아진다. 예컨대, 지금 우리 국민의 최대 관심사는 급성호흡기장애로 죽음까지 불러오는‘사스 (SARS)’확산과 북한의‘핵무기’소유이다. 그렇다면, 과학기술계와 국가가 전적으로 나서서 그 문제들을 해결하는 모습을 보일 때, 과학기술에 대한 국민의 공동체 유대감이 형성될 수 있고, 나아가 병리학과 핵물리학 자체에 대한 일반국민의 이해도 증진될 수 있다. 본 연구는 이러한 맥락에서, 과학영재 학생들의 과학기술에 대한 이해도를 알아보기 위해 요즈음 국제 사회적으로 커다란 이슈가 되고 있는 북한 핵문제에 대해 과학영재들은 어떤 생각을 갖고 있으며, 어느 정도 이해하고 있는지를 설문조사 하였으며, 이를 남학생과 여학생을 구분하여 분석하였다. 설문에 응답한 학생들은 모두 85명으로 공주대학교 과학영재교육원 영재교육 프로그램에 참여하고 있다.