• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.91-111
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• 2007

This study investigated how high school students predict the rule, the sum of sequence for the concept of sequence, for the given patterns based on inductive approach using computers that provide dynamic functions and materials that are visual. Students for themselves were able to induce the formula without using the given formula in the textbook. Furthermore, this study examined how these technology and materials affect students' understanding of the concept of actual infinity for those who have the concept of the potential infinity which is the misconception of infinity in a infinity series. This study shows that students made a progress from the concept of potential infinity to that of actual infinity with technology and materials used I this study. Students also became interested in the use of computer and the visualized materials, further there was a change in their attitude toward mathematics.

• Journal of the Korean Chemical Society
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• v.55 no.6
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• pp.1030-1041
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• 2011

We investigated the understanding of pre-service science teacher about the chemistry concept of middle school curriculum using some items in National Assessment of Educational Achievement and analyzed the result according to background variables of pre-service science teacher. The result was that there were some pre-service science teachers who select incorrect answer at all items, pre-service science teachers don't fully understand the concept needed to solve item. And the percentage of correct answer at some items was low regardless of selection of chemistry as an elective subject at CSAT(College Scholastic Ability Test). We found some facts through the depth interviews to find the cause of the result. First, the misconception acquired in middle school days is tend not to change until college student. Second, the formation of misconception is affected by the study habit with which solve problem by simple calculation and memory without essential understanding. Third, the study habit with which solve problem by simple calculation and memory without essential understanding could not replace misconceptions acquired in middle school days with scientific concept regardless of selection of chemistry as an elective subject at CSAT.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.239-266
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• 2004

This article presents new perspectives for analysing and diagnosing students' mathematical errors on the basis of Pascaul-Leone's neo-Piagetian theory. Although Pascaul-Leone's theory is a cognitive developmental theory, its psychological mechanism gives us new insights on mathematical errors. We analyze mathematical errors in the domain of proof problem solving comparing Pascaul-Leone's psychological mechanism with mathematical errors and diagnose misleading factors using Schoenfeld's levels of analysis and structure and fuzzy cognitive map(FCM). FCM can present with cause and effect among preconceptions or misconceptions that students have about prerequisite proof knowledge and problem solving. Conclusions could be summarized as follows: 1) Students' mathematical errors on proof problem solving and LC learning structures have the same nature. 2) Structures in items of students' mathematical errors and misleading factor structures in cognitive tasks affect mental processes with the same activation mechanism. 3) LC learning structures were activated preferentially in knowledge structures by F operator. With the same activation mechanism, the process students' mathematical errors were activated firstly among conceptions could be explained.

• Communications of Mathematical Education
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• v.13 no.2
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• pp.563-589
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• 2002

고학년으로 갈수록 지필 환경에만 머무르는 현실 속에서 생활 및 예술 작품 등에서 수학적 원리와 개념을 발견하도록 하는 테셀레이션 수업은 학생들의 흥미와 호기심을 유발하고 수학의 아름다움을 느끼게 하는 것 이상으로 기하학적 사고의 기초를 학습하는데 도움을 줄 수 있다. 이에 본 연구는 4학년까지 적용되고 있는 7차 교육과정을 중심으로 새롭게 등장하고 있는 테셀레이션에 대한 이해 및 교수 학습 자료가 체계적으로 정비되어 있지 못한 현실적인 문제의 해결 방안으로서 테셀레이션을 활용한 수학 학습의 내용을 분석하여 교사들에게는 테셀레이션의 이해 및 교수 학습 자료로서 , 학생들에게는 수학의 기하적 개념들을 쉽고 재미있게 학습할 수 있는 학습도구로서 활용할 수 있도록 하는 것을 목적으로 테셀레이션을 구현할 수 있는 컴퓨터 소프트웨어를 활용하여 테셀레이션 교수 학습 자료를 개발하였고 이를 위해 다음과 같은 연구 내용을 설정하였다. 가. 테셀레이션의 정의와 예 그리고 종류를 알아보고 테셀레이션 속의 수학적 개념을 활용방법과 함께 제시한다. 나. 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 테셀레이션을 적용할 수 있는 내용영역을 분석하고 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한다. 다. 제작된 테셀레이션 교수 학습 자료의 효과적 활용을 위한 활용 방안을 탐색한다. 라. 제작된 테셀레이션 교수 학습 자료의 활용 효과를 알아보기 위해 적용 실험을 하고 이에 대한 학생들의 반응을 분석하여 학습의 효과를 밝힌다. 제작된 테셀레이션 교수 학습 자료의 적용 실험을 위하여 광주대성초등학교 6학년 한 반을 선정하였고 약 4주에 걸쳐 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료를 투입하여 4번의 활동수업을 실시하였다. 수업 후 작성된 학습지와 소감문 및 연구자에 의해 관찰된 수업내용을 바탕으로 다음과 같은 연구 결과를 얻을 수 있었다. 첫째, 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한 결과 지필적 환경에서 제한적이었던 탐구하고 조작해보는 활동을 할 수 있는 역동적인 수학 실험실 환경이 제공됨으로써 도구적 이해가 아닌 관계적 이해를 하는 것을 확인할 수 있었다. 수학적 개념을 암기하는 것에서 벗어나 자연스런 조작을 통해 학생들이 개념을 이해하고 탐구하는 과정 속에서 학생들은 수학을 공부한다기 보다는 수학 속에서 재미있게 놀이한다는 생각을 가지고 수업에 참여하였고 배우는 즐거움을 알고 자신감을 가지며 더 나아가 창의적인 생각을 하도록 하는 기회를 줄 수 있었다. 둘째, 테셀레이션은 우리 생활 속에서 쉽게 발견할 수 있는 것으로 수학이 단순히 책에서만 한정되지 않고 다양한 분야 즉 디자인, 생활 속에서의 벽지문양과 포장지, 예술작품 등에 활용되고 있음을 체험함으로써 수학이 실생활에 광범위하게 활용되고 있음을 알게 하였다. 역으로 생활 속에서의 테셀레이션을 통해 수학적 개념을 찾는 과정을 통해 수학이 아름다우면서도 실용적이라는 생각을 심어줄 수 있었다. 셋째, 테셀매니아, GSP, 캐브리, 거북기하 등 평소 수업에서는 활용도가 적은 컴퓨터 소프트웨어를 활용함으로써 컴퓨터 소프트웨어 자체에서 오는 호기심뿐만이 아니라 직접 조작하여 테셀레이션 작품과 개념을 익히고 새로운 작품과 학습을 해 내는 과정을 통해 자신감과 성취감 등에 있어 큰 변화가 있음을 발견할 수 있었다. 컴퓨터 기능이 미숙한 학생의 경우 처음에는 당황해 하고 어려워하는 부분도 있었으나 조작할 시간적 여유를 주고 교사와 우수한 학생들이 도우미로서 역할을 잘해내어 나중에는 큰 어려움 없이 마칠 수 있었다. 테셀레이션이라는 용어가 아직은 생소한 현장에서 교수 학습 자료가 부족하고 그에 따른 이해도 부족한 현실 속에서 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료가 교수 학습 현장에 투입되어 유용하게 사용될 수 있는지 그 가능성을 조사한 것을 목적으로 한 본 연구의 결과로서 테셀레이션이라는 주제는 도형 영역과 규칙성과 함수 영역에서 평면 도형의 각과 모양 등의 성질을 탐구하게 하고, 대칭변환의 개념을 효율적으로 학습하게 할 수 있고, 반복되는 모양에서 규칙성을 발견하고 부분과 전체를 파악하여 패턴을 인지할 수 있게 하며 제작하고 분석하는 과정을 통해 여러 가지 수학적 개념과 수학적 창의성, 수학적인 아름다움을 느끼게 할 수 있음을 발견할 수 있었다. 또한 테셀레이션은 수학적 개념은 물론 수학과 미술, 수학과 일상 생활과의 연결성을 논의하고 확인하는 데 흥미로운 주제가 될 수 있다. 초등학교 교육과정에서 새롭게 도입되고 있는 테셀레이션을 활용하여 지도하기 위한 교수 학습 자료로 유용하게 사용될 수 있고 앞으로는 테셀레이션과 관련된 내용이 직접적으로 교육과정 내에서 다루어지고, 또한 테셀레이션을 적용한 수업이 학생들의 기하학적 사고 및 수학적 태도에 미치는 영향과 관련한 연구가 뒤따라야 할 것으로 본다.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.727-745
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• 2017

This study investigated the Aristotle's continuity and the historical development of continuity of function to explore the differences between the concepts of mathematics and students' thinking about continuity of functions. Aristotle, who sought the essence of continuity, characterized continuity as an 'indivisible unit as a whole.' Before the nineteenth century, mathematicians considered the continuity of functions based on space, and after the arithmetization of nineteenth century modern ${\epsilon}-{\delta}$ definition appeared. Some scholars thought the process was revolutionary. Students tended to think of the continuity of functions similar to that of Aristotle and mathematicians before the arithmetization, and it is inappropriate to regard students' conceptions simply as errors. This study on the continuity of functions examined that some conceptions which have been perceived as misconceptions of students could be viewed as paradigmatic thoughts rather than as errors.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.311-331
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• 2016

The purpose of this study was to analyze mathematical errors and the effects of reflective problem posing activities on students' mathematical problem solving abilities and attitudes toward mathematics. We chose two 5th grade groups (experimental and control groups) to conduct this research. From the results of this study, we obtained the following conclusions. First, reflective problem posing activities are effective in improving students' problem solving abilities. Students could use extended capability of selecting a condition to address the problem to others in the activities. Second, reflective problem posing activities can improve students' mathematical willpower and promotes reflective thinking. Reflective problem posing activities were conducted before and after the six areas of mathematics. Also, we examined students' mathematical attitudes of both the experimental group and the control group about self-confidence, flexibility, willpower, curiosity, mathematical reflection, and mathematical value. In the reflective problem posing group, students showed self check on their problems solving activities and participated in mathematical discussions to communicate with others while participating mathematical problem posing activities. We suggested that reflective problem posing activities should be included in the development of mathematics curriculum and textbooks.

• Journal of the Korean School Mathematics Society
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• v.9 no.3
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• pp.309-316
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• 2006

This study examined the ambiguous using the terminology of statistics at mathematics textbook of highschool in Korea and proposed the correct using of sampling error and sampling distribution of sample mean with consistency. And this paper proposed that the concept of error have to teach in context of sampling action in school mathematics.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.467-490
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• 2013

Correlation is a basic statistical concept which is necessary for understanding the relationship between two variables when they change values. In the middle school curriculum of Korea, only informal definition of correlation is taught with two-way data representations such as scatter plots and contingency tables. In this study, we investigated Korean high school students' understanding of correlation using a test consisting of 35 items about interpretation of scatter plot, contingency table, and text in realistic situation. 216 students from a high school in Seoul took the test for 20 minutes. From the results, we could observe the following: First, students did not have right criteria for determining the strength of correlation presented in scatter plots. Most of students could determine if there is correlation/no correlation and if the correlation is positive/negative by seeing the data presented in scatter plots. However, they did not judge by the closeness to the regression line but rather judged by the closeness between data points. Second, when statements about comparing the strength of correlation in the context of real life situation were given in text, the students had difficulty in understanding the distribution-related characteristic of the bi-variate data. Students had difficulty in figuring out the local distribution characteristic of data, which cannot be guessed merely based on the expression 'The correlation is strong' without statistical knowledge of correlation. Third, a large number of students could not judge the association between two variabels using conditional proportions when qualitative data are given in 2-by-2 tables. They made judgement by the absolute cell count and when the marginal sum of two categories are different for explanatory variable they thought the association could not be determined. From these results, we concluded that educational measures are required in order to remove such misconceptions and to improve understanding of correlation. Considering that the current mathematics curriculum does not cover the concept of correlation, we need to improve the curriculum as well.

• The Mathematical Education
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• v.63 no.1
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• pp.1-18
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• 2024

This study aims to analyze low-performing high school students' difficulties in constructed response (CR) mathematics assessments and explore ways to use writing activities to support student learning. The participants took CR assessments, engaged in guided writing activities across 15 lessons, and provided responses to our interviews. The study identified 20 types of student difficulties, which were sorted into two main categories: "mathematical difficulties" and "CR difficulties." The difficult nature of mathematics as a school subject included a lack of understanding of mathematical concepts, students' difficulty with mathematical symbols and notations, and struggles with word problems. Challenges specific to CR assessments included students' difficulties arising from the testing conditions unlike those of multiple-choice items, and included issues related to constructing appropriate responses and psychological barriers. To address these challenges in CR assessments, the study conducted guided writing activities as an intervention, through which six themes were identified: (1) internalization of mathematical concepts, (2) mathematical thinking through relational understanding, (3) diverse problem-solving methods, (4) use of mathematical symbols, (5) reflective thinking, and (6) strategies to overcome psychological barriers.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.417-444
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• 2008

Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.