• School Mathematics
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• v.11 no.4
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• pp.643-664
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• 2009

This study was aimed to understand the problems that students experience during the self--directed study of a mathematics digital textbook and to find the implications for the design of digital textbook. For this study, we analyzed the process of self-directed learning on 'division of fractions with same denominator' using digital textbook by eight 6th graders. Students asked to use think aloud method while they study the unit. Their learning process was videotaped and analyzed by researchers after the experiment. After the self-directed learning, students filled out a test items and participated interview with a researcher. The result showed that students experienced several misconceptions and errors while using a digital textbook. The types of misconceptions and errors were cataegorized as "misconceptions and errors caused by a mathematics textbook" and "misconceptions and errors caused by a digital textbook". Especially, students showed several important misconceptions and errors because of the design factors. This implies we need to consider the causes of misconceptions for the design of a digital textbook.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.83-105
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• 2021

In this paper, we analyzed the misconceptions and errors incurred during factorization learning. We also examined whether online individualization classes had a positive effect on students' mathematical achievement. The experiment was conducted for 4 weeks (16 times in total) on middle school juniors in rural areas of Gyeonggi Province, where the influence of private extra education was small. In the class, the 'Google Classroom' was used as a LMS, the video lecture was uploaded to YouTube, and the teacher interacted with the students through "Zoom" and "Facetalk". In the online class situation, students' assignments and test answers were checked in real time through 'Google Classroom', and immediate feedback was provided to the experimental class group's students. However, for the control group students, feedback was provided only to those who desired. A total of 7 achievement evaluations were conducted in the order of pre-test, formative evaluation (5 times), and post-test to confirm the change in students' ability improvement and achievement. Through the formative evaluation analysis, it was possible to grasp the types of errors and misconceptions that occured during the factorization process. Students' errors were divided into four types: theorem or definition distortion error, functional errors such as calculation, operation, and manipulation, errors that do not verify the solution, and no response. As a result of ANCOVA, the two groups did not show any difference from the 1st to 4th formative assessment. However, the 5th formative assessment and post-test showed statistically significant differences, confirming that online individualization classes contributed to improvemed achievement.

• Journal of the Korean Chemical Society
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• v.50 no.6
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• pp.486-493
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• 2006

study investigated the relationship between conceptual understanding and mapping errors induced in learning chemistry concept with two analogies presented in current science textbooks. Each of the two groups from 7th graders (N=260) in three middle schools studied with one of the analogies, and then a conception test and a mapping test were administered. Analyses of the results indicated that students conceptual understanding has a significant relationship with their understanding about the mapping. The scores of the conception test and the mapping test for the unshared attributes were lower than those for the shared attributes. Five types of mapping errors were also identified: overmapping, mismapping, failure to map, rash mapping, and artificial mapping. Many representative misconceptions were found to be associated with their mapping errors. Educational implications are discussed.

• School Mathematics
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• v.5 no.2
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• pp.209-221
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• 2003

This study focuses on the necessity of developing the material for teachers who are involved in diagnosing and prescribing students' mathematical errors. And it also intends to stimulate the related research of this area. For this, it tries to suggest the fundamental components-(1)types and frequencies of errors, (2) diagnostic test kit, (3)causes of errors, (4)ideas for prevention, (5)ideas for correction, (6)practice for settlement, and (7) performance test kit and frame of the teaching guide book for the teachers according to the general procedure of diagnosis and prescription. Finally it provides the concrete research areas for the future study.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.379-388
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• 2005

일차변환은 선형대수에서 가장 중요한 개념 중 하나이다. 그럼에도 많은 학생들에게서 나타나는 이 개념에 대한 오류는 무엇이며 또 어디에 근거하는가? 이 논문은 효과적인 선형대수 교수학습 연구의 일부로, 주어진 여러 함수 중에서 일차변환인 것을 찾는 과정 중에 나타난 학생들의 오류와 그 근거를 알아보았다. 본 연구 결과는 선형대수 학습에 어려움을 겪는 학생들에게 보다 효율적인 교수디자인 설계를 위한 기초 자료의 의미를 갖는다.

• Journal of the Korean School Mathematics Society
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• v.13 no.1
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• pp.23-43
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• 2010

This study is to investigate how much highschool students, who have learned functional concepts included in the Middle school math curriculum, understand chapters of the function, to analyze the types of errors which they made in solving the mathematical problems and to look for the proper instructional program to prevent or minimize those ones. On the basis of the result of the above examination, it suggests a classification model for teaching-learning methods and teaching material development The result of this study is as follows. First, Students didn't fully understand the fundamental concept of function and they had tendency to approach the mathematical problems relying on their memory. Second, students got accustomed to conventional math problems too much, so they couldn't distinguish new types of mathematical problems from them sometimes and did faulty reasoning in the problem solving process. Finally, it was very common for students to make errors on calculation and to make technical errors in recognizing mathematical symbols in the problem solving process. When students fully understood the mathematical concepts including a definition of function and learned procedural knowledge of them by themselves, they did not repeat the same errors. Also, explaining the functional concept with a graph related to the function did facilitate their understanding,

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.101-113
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• 2003

The purpose of this study is to analyze students misunderstood types relate to trigonometric function and to devise its teaching method using GSP. To do this, we performed several steps as followings: First, we performed questionnaire survey to 70 students belong to second year at high school to find students comprehension degree about radian angle representation and trigonometric function graph. Second, we devised the teaching-learning materials relate to trigonometric function graph using GSP. And then, we used them in the class of 35 students who are at the time to learn trigonometric function in the first year at high school. Third, we conducted Questionnaire survey to students studied through teaching and learning materials using GSP. As a result of doing the survey, we found that general students were interested in the class using GSP and they could also operate computer without difficulty.

• Journal of the Korean Chemical Society
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• v.43 no.3
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• pp.328-339
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• 1999

This study was to clarify the problems of questionnaires related to misconception researches of middle school chemistry and to prepare a ground for the correct misconception research for students. For these purposes, the questionnaires of the misconception researches related to chemistry in middle school were analyzed, and the mistakes of the questions which were used in 7th grade students were found, based on a definition of misconceptions in this study. Also, the errors in contents of the questionnaires were indicated. The results of the analysis revealed that most of the 7th grade students did not have misconceptions contrary to some of the previous researches conclusions. They only had no conceptions related to the contents. In order to support this analysis, two different questionnaire sets (questionnaire set A and B) for 182 7th grade students were used. After obtaining similar results to those of the previous researches by the questionnaire set A, the students' thoughts were examined by the questionnaire set B. From the results of this study, the correct answer rates of subjective questions were very low compared with those of objective questions in the questionnaire set A for 7th grade students. It was hard to find consistency among the results of the researches using the questionnaire set A. And many contents of the questions consisted of the questionnaire est A were not consisted with a definition of misconceptions. There were errors in the contents of the questions, too. The students classified as the havingscience-concepts group and the having-misconceptions group by the questionnaire set A were classified as the having-no-concepts group by the questionnaire set B.

• Communications of Mathematical Education
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• v.12
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• pp.103-124
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• 2001

수학은 계통성이 강한 학문이다. 이러한 수학의 특성은 학습의 결손이 있거나 학습속도가 느린 학생들에게 수학을 학습하는 데 어려움의 근원이 된다. 특히 중학교 수학에서는 처음으로 형식적인 수학이 도입되기 때문에, 중학교 1학년에서 수학을 제대로 이해하지 못할 경우 그 학생은 수학 장애아, 수학부진아로 전락할 가능성이 있다. 그러나 학교에서의 개별지도는 어려운 실정이다. 따라서 수학 부진아를 선정하여 수학학습에서의 어려움을 진단하고, 학생의 오개념과 오류를 분석한 후, 그 학생에게 맞는 학습전략을 선택하여 처방 지도하고자 한다. 이를 통해 학생의 이해와 사고과정을 알아보고 태도변화를 고찰하는 것을 목적으로 한다.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.709-730
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• 2010

The inverse function of a one-to-one correspondence is explained with a graph, a numerical formula or other useful expressions. The purpose of this paper is to know how low achieving students understand the learning contents needed reversible thinking about irrational functions. Low achieving students in this study took paper-pencil test and their written answers were collected. They made various mistakes in solving problems. Their error types were grouped into several classes and identified in this analysis. Most students did not connected concepts that they learned in the lower achieving students to think in reverse order in case of and to visualize concepts of functions. This paper implies that it is very important to take into account students' accommodation and reversible thinking activity.