• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.1-19
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• 2015

This paper aims to explore what we can improve in the curriculum, teaching-learning, and evaluation on the bases of the analyses of multiple-choice items set in National Assessment of Educational Achievement. For this goal, by using the distribution curves of the responses percentages, we will grasp the features of educational achievement which appear to students through an in-depth analysis about not only item itself but also the contents included in particular distracters. These analyses provide more information than the descriptive statistical values such as the mean of correct answer percentage and the discrimination of whole group and the mean of responses percentages of replies of subgroups. Because the distribution curves of the responses percentages reveal the transition from the lowest to the highest educational achievement very well. From these analyses we acquire the implications about the concept of prime factor or prime factorization, ratio(proportion) such as velocity, linear function, volume of cone, properties of solid figure, and probabilities of empty event and total event.

• The Mathematical Education
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• v.59 no.2
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• pp.131-146
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• 2020

Regarding the formula for measuring the area of a circle, the Archimedes' constant is generally written in front of the square of radius length, but there were a few cases where the Archimedes' constant was written after that in Germany and France. In this study, two things are studied: First, how many students are writing the Archimedes' constant after that? Second, what do the students think about the written order of characters in the formula for measuring the area of a circle? In the online survey of 201 people aged 14 to 21 in Korea, there was a perception of more than 86% that both are possible or only after that are possible. In this study, it is suggested that there is a difference between the general written order of characters and the natural perception of students formed through school education. In addition, students aged 14 to 16 thought more that the Archimedes' constant should be written after that, and after that age, there was a greater perception that both are possible without confusion of meaning. It can be seen that the change in students' perception has emerged through school education on natural mathematical written order of characters after middle school courses. From this point of view, the most common perception can be that if there is no confusion in meaning, then both expressions are possible.

• Research in Mathematical Education
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• v.13 no.2
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• pp.151-170
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• 2009

This study reports a research which was conducted on how frequently and where the students use the unit circle method while dealing with trigonometric functions in solving the trigonometry questions. Moreover, the reasons behind the choice of the methods, which could be the unit circle method, the ratio method, or the use of trigonometric identities, are also investigated to get an insight about their understanding. In this study, the relationship between the students' choices of methods in solving questions is examined in terms of instrumental or relational understanding. This is a multi-method research which involves a range of research strategies. The research techniques used in this study are test, verbal protocol (think aloud), and interview. The test has been applied to ten tenth grade students of a public school to get students' solution processes on the paper. Later on, verbal protocol has been performed with three students of these ten who were of the upper, middle and lower sets in terms of their performance in the test. The aim was to get much deeper data on the students' thinking and reasoning. Finally, interview questions have been asked both these three students and other three from the initial ten students to question the reasons behind their answers to the trigonometry questions. Findings in general suggest that students voluntarily choose to learn instrumentally whose reasons include teachers' and students' preference for the easier option and the anxiety resulting from the external exam pressure.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.297-312
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• 2006

As research on the instruction method of the concept of irrational numbers, this thesis is theoretically based on the Freudenthal's Mathematising Instruction Theory and a conducted case study in order to find an introduction method of irrational numbers. The purpose of this research is to provide practical information about the instruction method ?f irrational numbers. For this, research questions have been chosen as follows: 1. What is the introducing method of irrational numbers based on the Freudenthal's Mathematising Instruction Theory? 2 What are the Characteristics of the teaming process shown in class using introducing instruction of irrational numbers based on the Freudenthal's Mathematising Instruction? For questions 1 and 2, we conducted literature review and case study respectively For the case study, we, as participant observers, videotaped and transcribed the course of classes, collected data such as reports of students' learning activities, information gathered through interviews, and field notes. The result was analyzed from three viewpoints such as the characteristics of problems, the application of mathematical means, and the development levels of irrational numbers concept.

• Journal of Educational Research in Mathematics
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• v.27 no.2
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• pp.171-189
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• 2017

By designing and applying the lesson helping to discover the power laws, we tried to investigate the characteristics on the class. To do this, we designed a discovery lesson on the power laws and applied to 54 8th grade students. As results, we could observe the overproduction of monotonous laws, tendency to vary the type of development and increase error to students without prior learning experience, and various errors. All participants failed to express the generalization of $a^m{\div}a^n$ and some participants expressed an incomplete generalization using variables partially for the base or power. We could also observe an error of limited generality or a representation error which did not use the equal sign or variables. In the survey of students, there were two contradictory positions to appeal to the enjoyment of the creation and to talk about the difficulty of creation. Based on such results, we discussed the pedagogical implications relating to the discovery of power laws.

• Education of Primary School Mathematics
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• v.10 no.2
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• pp.125-139
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• 2007

The purpose of this study seeks entry into a method to make the use of educational aids popular. To achieve it, it is observed that instructions applying worksheets to make an activation of use of educational aids have influences on mathematical achievement and mathematical disposition and attitude. All variables exception with the frequence of use of educational aids are controlled in both experimental group and comparative group. According to the result, there is no significant difference of mathematical achievement in pre t-test between two groups, while experimental group get 10 points higher than comparative group in average (t=0.519, p<0.01). On the other hand, within intra-experimental group the influences of use of educational aids on mathematical achievement is positive without the achievement levels of students. The difference dependent on the levels of student is sought by ANCOVA using prescores as a covariance, and it appears in the significance level of 5%(F=4.885, p<0.05), and the effect is more in the lower level of students than in the middle and high level.

• School Mathematics
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• v.5 no.3
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• pp.361-384
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• 2003

The purpose of this study was to investigate students' problem solving process based on the model of IDEAL if they learn to solve word problems of simultaneous linear equations through structure-representation instruction. The problem solving model of IDEAL is followed by stages; identifying problems(I), defining problems(D), exploring alternative approaches(E), acting on a plan(A). 160 second-grade students of middle schools participated in a study was classified into those of (a) a control group receiving no explicit instruction of structure-representation in word problem solving, and (b) a group receiving structure-representation instruction followed by IDEAL. As a result of this study, a structure-representation instruction improved word-problem solving performance and the students taught by the structure-representation approach discriminate more sharply equivalent problem, isomorphic problem and similar problem than the students of a control group. Also, students of the group instructed by structure-representation approach have less errors in understanding contexts and using data, in transferring mathematical symbol from internal learning relation of word problem and in setting up an equation than the students of a control group. Especially, this study shows that the model of direct transformation and the model of structure-schema in students' problem solving process of I and D stages.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.39-69
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• 2004

This paper investigates the teaching and learning of Linear function relating functional contexts and suggests the improved methods of representation-shift through this analysis. The methods emphasize the link between students' preacquired knowledge of mathematical representations and the way of using those. This methods are explanatory teaching, teaching and teaming based on modelling perspectives or tasks (interpretation, prediction, translation and scaling). We categorize the 8th grade middle school students' errors on the linear function relating real contexts and make a comparative study of the error-remedial effects and the teaching and teaming methods. We present the results of a study in which representation-shift methods based on modelling perspectives and tasks are more effective in terms of flexible connection of representations and error remediation. Also, We describe how students used modelling perspective-taking to explain and justify their conceptual models, to assess the quality of their models and to make connection to other mathematical representation during the problem solving focusing on the students' self-diagnosis.

• Communications of Mathematical Education
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• v.34 no.2
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• pp.41-68
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• 2020

The purpose of this study is to analyze the cognition of per-service teachers, who experienced a teacher education process for developing their discursive competency, about relations between class plan and class practice as well as discursive competency required in class process. For this purpose, 15 pre-service teachers participated in the course of mathematics teaching theory for developing discursive competency and their final projects including the process of analysing their own teaching discourse after actually teaching middle or high school students were collected as data and analyzed. Results show that they realized that there were differences between class plan and class practice after having experienced unexpected teaching and learning situations, recognized the importance of discursive competency learned from the course, and reflected on their discursive competency in conjunction with their classes. These results imply that the course contributed to pre-service teachers' cognitions of the existential possibility of discursive competency. which helps to develop a teaching method combining teachers' knowledge and practice, the importance of discursive competency, and the need for developing it. The course also provided practical ideas about a teacher education program to develop prospective teachers' discursive competency

• The Journal of Korean Association of Computer Education
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• v.16 no.6
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• pp.55-70
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• 2013

This study tried to redesign a robot curriculum and proposed it for the purpose of enhancing, supporting sustainable development of robot in educations. For doing so, this study referred relevant existing literacy contents at robot literacy educations, and defined a robot literacy education. In addition, this study presented elements of robot literacy by dividing them into five kinds. In relation with the scope of robot literacy education suggested here, this study proposed basic robot area, measurement and observation along with robots based on three elements of robotics, movement and expression made by robots, my own robot design, and comprehensive activity area. Regarding to development stages of robot literacy, the study applied the classical model of curriculum development by Tyler (1949), and intended to secure validity and reliability on the curriculum composition, and then developed a curriculum after analyzing mathematics and science curriculums in existing elementary, middle schools accordingly.