• School Mathematics
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• v.18 no.2
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• pp.277-300
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• 2016

In school mathematics, the definition and concept of a differentiation has been dealt with as a formula. Because of this reason, the learners' fundamental knowledge of the concept is insufficient, and furthermore the learners are familiar with solving routine, typical problems than doing non-routine, unfamiliar problems. Preceding studies have been more focused on dealing with the issues of learner's fallacy, textbook construction, teaching methodology rather than conducting the more concrete and efficient research through experiment-based lessons. Considering that most studies have been conducted in such a way so far, this study was to create a lesson plan including teaching resources to guide the understanding of differential coefficients and derivatives. Particularly, on the basis of the theory of Historical Genetic Process Principle, this study was to accomplish the its goal while utilizing a technological device such as GeoGebra. The experiment-based lessons were done and analyzed with 68 first graders in S high school located in G city, using Posttest Only Control Group Design. The methods of the examination consisted of 'learning comprehension' and 'learning satisfaction' using 'SPSS 21.0 Ver' to analyze students' post examination. Ultimately, this study was to suggest teaching methods to increase the understanding of the definition of differentials.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1950-1951
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• 2011

본 논문에서는 요구되는 성능을 만족시키는 최적 Fuzzy PI 제어의 정압제어로의 효율적인 적용 및 성능 향상을 위하여 유전자 알고리즘(GA: Genetic Algorithm)을 이용한 제어 설계 방법을 제시 한다. PID제어기는 이해가 쉽고 구조가 간단하여, 실제 구현이 용이하여 공정 산업분야에서 가장 널리 사용되고 있는 제어기 이다. 따라서 단일 입 출력 선형 시스템 에서는 우수한 성능을 보이나 동적 시스템, 고차 시스템 및 수학적 모델 선정이 어려운 시스템에서는 비효율 적이다. 반면, Fuzzy 제어기는 인간의 지식과 경험을 이용한 지적 제어방식으로 IF-THEN형식의 규칙으로부터 제어 입력을 결정하는 병렬형 제어기이다. 이는 과도상태에서 큰 오버슈트 없이 설정치에 도달하게 하는 속응성과 강인성이 좋은 제어기법으로 비선형성이 강하고 불확실하며 복잡한 시스템을 쉽게 제어 할 수 있다는 장점을 지닌다.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.101-116
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• 2005

The purpose of this study is to survey mathematics teacher's cognition of proof along with their proof forms of expression and proof ability, and to explore the relationship between their proof scheme and teaching practice. This study shows that mathematics teachers tend to regard proof as a deduction from assumption to conclusion and that they prefer formal proof with mathematical symbols. Mathematics teachers also recognize that prof is an important area in school mathematics but they reveal poor understanding of teaching methods of proof. Teachers tend to depend on the proof style employed in mathematics textbooks. This study demonstrates that a proof scheme is a major factor of determining the teaching method of proof.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.241-262
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• 2010

This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.

• School Mathematics
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• v.14 no.4
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• pp.469-493
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• 2012

The purpose of this study is find the relation between students' concept and types of proof construction. For this, four undergraduate students majored in mathematics education were evaluated to examine how they understand mathematical concepts and apply their concepts to their proving. Investigating students' proof with their concepts would be important to find implications for how students have to understand formal concepts to success in proving. The participants' proof productions were classified into syntactic proof productions and semantic proof productions. By comparing syntactic provers and semantic provers, we could reveal that the approaches to find idea for proof were different for two groups. The syntactic provers utilized procedural knowledges which had been accumulated from their proving experiences. On the other hand, the semantic provers made use of their concept images to understand why the given statements were true and to get a key idea for proof during this process. The distinctions of approaches to proving between two groups were related to students' concepts. Both two types of provers had accurate formal concepts. But the syntactic provers also knew how they applied formal concepts in proving. On the other hand, the semantic provers had concept images which contained the details and meaning of formal concept well. So they were able to use their concept images to get an idea of proving and to express their idea in formal mathematical language. This study leads us to two suggestions for helping students prove. First, undergraduate students should develop their concept images which contain meanings and details of formal concepts in order to produce a meaningful proof. Second, formal concepts with procedural knowledge could be essential to develop informal reasoning into mathematical proof.

• The Mathematical Education
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• v.43 no.2
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• pp.139-149
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• 2004

This study was initiated by the idea to help students to be more ideally educated following the 7th curriculum that seeks the proactive students along with creativity for the 21st century. Mind-map was the main tool throughout the study and this was performed to find answers for the following questions : 1) to examine how students' drawing a mind-map affects their mathematical tendency or emotional aspects (motivation for study, interest, etc); 2) to investigate the types and characteristics of mind-maps that students draw; 3) to analyze advantages and obstacles that they experience during the process of drawing a mind-map and provide some suggestions for overcoming them. The research shows that students were highly motivated by the drawing a mind-map. There are types of mind-maps: tree shape and radial shape, and each shape has its own advantages. But the more important factor for being a good mind-map is where and how each concept is located and connected. Although it is true that drawing a mind-map helped students to see the bigger structure of what they learned, but there are several hardships taken care of. The study suggests to extend the experiment to various levels of students and diverse contents.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.85-104
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• 2019

The purpose of this study is to analyze the tasks developed through task development activities with emphasis on mathematical connectivity, and to provide implications for teacher education to enhance teacher's competence. For this purpose, I analyzed the task developed by 52 pre-teachers through the activities. As a result, they combined mathematics with 'other subjects', 'mathematics', 'phenomenon', 'technology' and 'real life'. And they also made various internal connections of 'Different representation', 'Part-whole relationship', 'Implication', 'Procedure', and 'Instruction-oriented connection'. From the point of view of teacher knowledge, the study revealed that CCK and SCK were positive in terms of 'logical' and 'expression', and KCT as 'strategic' was meaningful but disappointing in diversity; however in terms of 'level', the KCS was limited due to tasks that did not meet the level of students. As such, this analysis reveals that teachers continue to struggle with understanding students' level, but exhibit little difficulty with 'logic', 'expression' and 'strategy. This being the case, teacher education needs to place additional emphasis in understanding students' levels and planning corresponding activities.

• Journal of the Korean School Mathematics Society
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• v.19 no.4
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• pp.441-457
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• 2016

The purpose of this study is to analyze Korean students' mathematics achievement characteristics and draw implications for better math education in schools through comparing the results of three east Asian top level countries, Korea, Singapore, and Japan in PISA 2012 results. As a results, the rate of correct answers of Korea students was relatively low compared with those of Singapore, but relatively higher than Japan. From the results of effect size, similar results from t-test was discovered. As shown in analysis according to sub-elements in math assessment framework, the Korean students had low effect size in every sub-elements than Singapore. and they had high effect size at most of sub-elements than Japan, except "personal" context. In top performing level(above level 5), the Korean students had high effect size at "quantities" in mathematical contents, and "employ" in mathematical processes compared with Singapore. And they had row effect size at 6 sub-elements compared with Japan.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.257-275
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• 2021

This study investigated the prospective teacher's noticing of students' mathematical thinking from the perspective of how the prospective teacher pays attention to, interprets, and responds to the student's responses related to variables. The prospective teachers were asked to infer the students' thinking from the variables related to the tasks and suggest feedback accordingly. An analysis of the responses of 26 prospective teachers showed that it was not easy for prospective teachers to pay attention to the misconception of variables and that some of them did not make proper interpretations. Most prospective teachers who did not attend and interpret were found to have failed to provide an appropriate response due to a lack of overall understanding of variables. even though prospective teachers who did proper attend and interpret were found to have failed to respond appropriately due to a lack of empirical knowledge, even with proper attention and interpretation.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.433-452
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• 2009

This study investigated the teaching strategies of two exemplary American teachers regarding word problems and their impact on students' ability to both understanding and solving word problems. The teachers commonly explained the background details of the background of the word problems. The explanation motivated the students' mathematical problem solving, helped students understand the word problems clearly, and helped students use various solving strategies. Emphasizing communication, the teachers also provided comfortable atmosphere for students to discuss mathematical ideas with another. The teachers' continuous questions became the energy for students to plan various problem solving strategies and reflect the solutions. Also, this research suggested a complementary model for Polya's problem solving strategies.