• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.57-68
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• 2005

무한, 극한, 연속, 미분가능과 같은 중요한 수학적 개념을 이해하는 것은 대학수학 교양과정의 미분적분학 수강생들에게 필수적이다. 이들 개념의 이해 수준을 부록1, 2, 3을 통해 알아보고 평가를 분석한다. 평가결과는 이해도가 낮은 학생들을 위한 새로운 교수법이 필요성을 알게 하고 수학적 기본개념의 이해를 증진시키는데 정의의 정확한 이해를 돕고 구체적인 예제를 제시하는 교수법 개발에 수학교수의 노력을 필요로 한다.

• 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.

• Communications of Mathematical Education
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• v.15
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• pp.77-86
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• 2003

초등학교 영재들은 여러 사설 교육기관이나 국립기관 그리고 개인 교습을 통하여 많은 양의 선수학습을 행하고 있다. 이들 중 일부는 방법과 이유를 아는 관계 이해를 하기보다는, 주어진 규칙을 적용하여 정답을 찾아내는 도구적 이해를 하고 있다. 그들은 수학을 능동적이기보다는 수동적인 입장에서 받아들이기에 새로운 수학적 지식을 창출하지 못하는 성향을 강하게 보이고 있다. 이에 본 연구자는 이러한 문제의 해결을 위해 초등학교 영재들이 가지고 있는 수학적 스키마와 선생님들이 가르치는 스키마 사이의 간격에 초점을 맞추어 연구하였다. 대전에 있는 영재교육기관에 등록된 초등학교 3학년 영재들을 대상으로 하여 연구한 결과, 스키마와 스키마 사이의 간격이 멀수록 학생들이 방법과 이유를 아는 관계적 이해를 하기보다는 주어진 규칙을 적용하여 정답을 찾아내는 도구적 이해를 하고, 그 간격을 줄일수록 수학에 흥미를 느끼고 고학년의 수학내용까지도 스스로 파악하고 이해하려는 성향이 나타난다는 사실을 발견하게 되었다. 그 간격이 적을수록 학생들은 교사로부터 학습받은 내용을 자신의 지식으로 재구성하여 새로운 문제에 적용을 쉽게 하였다. 본 발표에서는, 학생들의 수학적 스키마와 선생님들이 가르치는 스키마 사이의 간격을 줄이는 것이 학생들이 수학을 관계적 이해를 하는데 큰 도움을 줄 수 잇음을 보이려고 한다.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.499-521
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• 2013

This paper analyzed the relationship between middle school students' belief about understanding with regard to mathematical concepts, procedures, and applications of the procedures. In order to gain our purpose, the academic achievement results of midterm examination of 139 middle school students and the surveys about their beliefs about understanding, mathematical concepts, and mathematical procedures were collected. And the cross analysis and the frequency analysis of SPSS were conducted. The research results showed that students' belief about understanding are irrelevant to their academic achievements. And the percentage of the students who believe that they understand was almost the same with the percentage of the students who understand the procedures. But there were differences between the percentage of the students who believe that they understand and the percentage of the students who understand the concepts. Through these, it is conformed. Students' belief about understanding does not mean they understand mathematical concepts. They just can solve mathematical problems through mechanical procedures.

• 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.24 no.2
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• pp.365-384
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• 2010

This paper is an analysis study where we surveyed how well pre-service teachers understand the mathematical concepts taught in elementary school. We analyzed the results focusing on the following: First, what are the pre-service teachers' understandings of the equal sign and variables? Secondly, how exact are their understandings of other elementary school mathematical concepts? The survey was done on the students in Teachers College of Jeju National University. We hope that the results of this study will help the improvement of mathematical education for elementary pre-service teachers.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.247-268
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• 2009

The purpose of this study was to examine the mathematical components of word problems and the structure of the components, to examine the characteristics of the understanding of mathematics high achievers about word problems, and ultimately to devise a teaching method geared toward facilitating learner understanding of the word problems. Given the findings of the study, the following conclusion was reached: First, word problems could be categorized according to their mathematical components, namely the mathematical structure of multiple variables provided to learners for their problem solving. And learner's reaction might hinge on the type of word problems. Second, the mathematics high achievers relied on diverse strategies to understand the mathematical components of word problems to solve the problems. The use of diverse strategies made it possible for them to succeed in problem solving. Third, identifying the characteristics of the understanding of the mathematics high achievers about word problems made it possible to layout successful lesson plans that stressed understanding of the mathematical structure of word problems. And the teaching plans enabled the learners to get a better understanding of the given word problems.

• 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.

• School Mathematics
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• v.5 no.2
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• pp.223-240
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• 2003

The purpose of this study was to investigate the preservice elementary teachers' knowledge of division through open-ended problems focused on the following perspectives in understanding division : connectedness between procedural and conceptual knowledge as well as the knowledge of units. Results indicates that the preservice elementary teachers showed low level of understanding of division such as the making word problem including division of fractions and the identification of the units in division operation.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.123-141
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• 2003

This study investigated the understanding level and the using level of mathematical language for middle school students in terms of Freudenthal' language levels. It was proved that the understanding level task developed by current study for geometric concept had reliability and validity, and that there was the hierarchy of levels on which students understanded mathematical language. The level that students used in explaining mathematical concepts was not interrelated to the understanding level, and was different from answering the right answer according to the sorts of tasks. And, the level of mathematical language that was understood easily as students' thought, was the third level of the understanding levels. Mathematics teachers should consider the students' understanding level and using level, and give students the tasks which students could use their mathematical language confidently.