• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.885-905
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• 2010

This study questions that mathematical evaluations strive to memorize fragmentary knowledge and have an objective test. To solve these problems on mathematical education We did descriptive test. Through the descriptive test, students think and express their ideas freely using mathematical terms. We want to know if that procedure is correct or not, and, if they understand what was being presented. We studied this because We want to analyze where and what kinds of faults they committed, and be able to correct an error so as to establish a correct mathematical concept. The result from this study can be summarized as the following; First, the mistakes students make when solving the descriptive tests can be divided into six things: error of question understanding, error of concept principle, error of data using, error of solving procedure, error of recording procedure, and solving procedure omissions. Second, students had difficulty with the part of the descriptive test that used logical thinking defined by mathematical terms. Third, errors pattern varied as did students' ability level. For high level students, there were a lot of cases of the solving procedure being correct, but simple calculations were not correct. There were also some mistakes due to some students' lack of concept understanding. For middle level students, they couldn't understand questions well, and they analyzed questions arbitrarily. They also have a tendency to solve questions using a wrong strategy with data that only they can understand. Low level students generally had difficulty understanding questions. Even when they understood questions, they couldn't derive the answers because they have a shortage of related knowledge as well as low enthusiasm on the subject.

• Journal of Educational Research in Mathematics
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• v.23 no.3
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• pp.389-406
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• 2013

The purpose of this study is to analyze eighth grade students' errors in the constructed-response items to improve teaching and learning of mathematics in schools. By analyzing 99 students' responses to nine constructed-response items, we found several types of students' errors in their responses to the assessment items involving with mathematical reasoning and representations, problems within realistic contexts, and mathematical connections. Not only a single error but also multiple errors (a combination of two or more types of errors) were discovered. In particular, high achieving students showed more simple errors than multiple errors while low achieving students had more multiple errors in various kinds.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.797-820
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• 2013

This study intended on analyzing the error patterns of mathematic problem posing sentences by the 100 elementary pre-teachers and discussing about the solutions. The results showed that the problem posing sentences have five error patterns: phonological error patterns, word error patterns, sentence error patterns, meaning error patterns, and notation error patterns. Divided into fourteen specific error patterns, they are as in the following. 1) Phonological error patterns are consisted of the 'ㄹ' addition error pattern and the abbreviated word error pattern. 2) Words error patterns are divided with the inappropriate usage of word error pattern and the inadequate abbreviation error pattern, which are formulized four subgroups such as the case maker, ending of the word, inappropriate usage of word, and inadequate abbreviation of article or word error pattern in detail. 3) Sentence error patterns are assumed four kinds of forms: the reference, ellipsis of sentence component, word order, and incomplete sentence error pattern. 4) Meaning error patterns are composed the logical contradiction and the ambiguous meaning. 5) Notation error patterns are formed four patterns as the spacing, punctuation, orthography of Hangul, and spelling rules of foreign words in Korean. Furthermore, the solutions for these error patterns were discussed: First, it has to be perceived the differences between spoken and written language. Second, it has to be rejected the spoken expressions in written contexts. Third, it should be focused on the learning of the basic sentence patterns during the class. Forth, it is suggested that the word meaning should have the logical development perception based on what it means. Finally, it is proposed that the system of spelling of Korean has to be learned. In addition to these suggestions, a new understanding is necessary regarding writing education for college students.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.699-718
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• 2012

The purpose of mathematics eduction is to develop the ability of thinking mathematically. It informs method to solve problem through mathematical thinking that teach mathematical ability. Errors in the problem solving can be thought as those in the mathematical thinking. Therefore analysis and classification of mathematics errors is important to teach mathematics. This study researches the preceding studies on mathematics errors and presents the characteristic of them with analyzed models. The results achieved by analysis of the process of problem solving are as follows : ▸ Students feel much harder to solve words problems rather than multiple-choice problems. ▸ The length of sentence make some differences of understanding of the words problems. Students easy to understand short sentence problems than long sentence problems. ▸ If students feel difficulties on the pre-learned mathematical content, they feel the same difficulties on the words problems based on the pre-learned mathematics content.

• Education of Primary School Mathematics
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• v.22 no.4
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• pp.281-294
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• 2019

The purpose of this study is to analyze errors and treatment behavior during the course of mathematics learning of academic achievement by applying reflective activities in the second semester of the third year of elementary school. The study participants are students from two classes, 21 from the third-grade S elementary school in Seoul and 20 from the comparative class. In the case of the experiment group, the multiplication unit was reconstructed into a mathematics class that applied reflective activities. They were pre-post-test to examine the changes in students' mathematics performance, and mathematical communication was recorded and analyzed for the focus group to analyze the patterns of learners' error handling in the reflective activities. In addition, they recorded and analyzed students' activities and conversations for error type and error handling. As a result of the study, the student's mathematics achievement was increased using reflective activities. When learning double digit multiplication, the error types varied. It was also confirmed that the reflective activities helped learners reflect on the multiplication algorithm and analyze the error-ridden calculations to reflect on and deal with their errors.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• School Mathematics
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• v.16 no.1
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• pp.57-81
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• 2014

This study was to investigate how the underachievers of mathematics in a non-leveling excellent high school would overcome the errors through the lessons based on the inductive thinking model in the equation of a circle. The results showed that when there were many stages to solve the problem, the students gave it up or forgot the stage they reached. In this case, if they had a revisit-opportunity to review their thinking process by planning ahead the stage to solve the problem and recording it, the omission error of the solving process and the error of wrong conclusions would be dramatically decreased. Moreover, they understood the mathematical concept, principle, and formula and remembered the learning contents extremely well through thinking by themselves in exploration-based activities and by using visualization for the problem and could solve the problem through these pictures besides algebraic expressions.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.355-376
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• 2010

This research was about analyzing students' major error types in the field of elementary 1st grade mathematics numbers and operations, and formulating and applying effective teaching methods to find out their effects. Among the errors the students were making, it was found that in the field of numbers there was more than 50% chance of making calculation mistakes in 50 rounds of rational counting. Also, in the field of operations, it was discovered that most of students' mistakes had to do with subtraction. The results from the classification of the 4 types of error showed that most errors were made from having inaccurate concept of knowledge and definition. Thus, it can be concluded that when elementary 1st grade teachers teach students mathematics, it is most important that they put best effort into firmly establishing the students fundamental concept, definition, facts, and functions. For that matter, students were interviewed one by one, and by implementing learning method using some concrete materials as tools, students were able to fix their own errors. More importantly, students were able to gain interest and become more willing to participate by joining in this program, which led to more effective guidance.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.223-237
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• 2004

본 연구는 중학교 1학년을 대상으로 일차방정식의 풀이 과정에서 나타나는 오류를 분석하고 그래핑 계산기를 활용하여 오류의 교정 과정을 제시하였다. 오류의 유형을 개념적 이해 미흡 오류, 등식의 성질에 대한 오류, 이항에 대한 오류, 계산 착오로 인한 오류, 기호화에 의한 오류로 분류하였으며, 이 중에서 등식의 성질에 대한 오류와 개념적 이해 미흡으로 인한 오류를 많이 범하고 있었다. 학생들이 TI-92를 활용하여 일차방정식의 해를 구할 때, Home Mode에서 Solve 기능을 이용하여 단순히 결과만을 보는 것 보다 Symbolic Math Guide를 이용하여 풀이 과정을 선택하여 대수적 알고리즘을 형성하면서 해를 구하는 것을 선호하였다. 그리고 학생들의 정의적 및 기능적 측면을 고려해야 할 필요성을 느끼게 되었다.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.461-488
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• 2005

This article presents new perspectives for classification of students' mathematical errors on the basis of experiential structuralism. Experiential structuralism's mechanism gives us new insights on mathematical errors. The hard core of mechanism is consist of 6 autonomous capacity spheres that are responsible for the representation and processing of different reality domains. There are specific forces that are responsible for this organization of mind. There are expressed in terms of a set of five organizational principles. Classification of mathematical errors is ascribed by the theory to the interaction between the 6 autonomous capacity spheres. Different types of classification require different autonomous capacity spheres. We can classify mathematical errors in the domain of linear function problem solving comparing cognitive psychological mechanism of experiential structuralism.