• School Mathematics
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• v.17 no.3
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• pp.391-405
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• 2015

This study was aimed to investigate how students' relational thinking about equations could be formed by exploring web-based balance. The researchers developed 3 groups of 4 typed 12 equation problems of (a+b+c = d+ _ ) to test 24 4th graders. Pretest and post-test were conducted using Eye-tracker for investigating their eye movements. The researchers interviewed students who were not having distinct strategies to look into their cognitive process. As a result, we can conclude web-based balance helped students to get the concept of the equal sign and to form the relational thinking by the process of comparing both sides, right and left on the basis of fulcrum on balance.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.321-340
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• 2009

The purpose of this study was to analyze how lower graders in elementary school might respond to 4 different problem types in the context of measuring length: unit-length comparison, units and unit counting, unit-length expectation, and length comparison. A total of 375 students(185 second graders and 190 third graders) were surveyed and analyzed. The results showed that students were good at 'unit-length comparison' and 'units and unit counting', whereas they were not as to 'length comparison', This paper includes detailed analysis of students' responses as to both correct answer and incorrect one in conjunction with their typical answers and reasoning behind the answers. This paper suggests that teachers be sensitive to the certain level of reasoning tied to each type of problems and attend to students' difficulties in comparing length.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.1-16
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• 2013

The primary purpose of this study is to survey multiplicative thinking levels and its characteristics of third graders in elementary school and to analyze how to use it when they solve the proportional problems. As results, the transition thinking ranked the highest among the four kinds of thinking levels when the $3^{rd}$ graders solved the multiplication problems. It means that the largest numbers of students still can not distinguish the additive and multiplicative situations completely and remain in the transition thinking, which thinks both additively and multiplicatively. In addition, the performance of solving proportional problems was distinguished from the levels of thinking. Through this study, we can give some implications of the importance of multiplicative thinking and instructional methods related to multiplication.

• School Mathematics
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• v.10 no.3
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• pp.423-441
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• 2008

The purpose of this study was to examine the Pedagogical Content Knowledge(PCK) of teachers and their educational practice in the category of plane figure, to make a comparative analysis of their PCK and educational practice, and to discuss the relationship between their PCK and the characteristics of their instruction. Instruction of four selected elementary school teachers was analyzed to find out their educational practice. In conclusion, the characteristics of the PCK and actual instruction of the teachers could be listed as below: First, as a result of comparing their PCK and educational practice on plane figure by applying selected analysis criteria, there was a close correlation between their PCK and actual instruction. Second, the teachers had various levels of PCK on different areas. Especially, there was a large disparity in mathematical content knowledge and knowledge of teaching methods. Third, the teachers who had plenty of PCK were more excellent in textbook reconstructing, and those who fell behind in terms of PCK were more reliant on textbooks as if the textbooks had been the Bible.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.471-485
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• 2007

In this study, a 27 class hour prescribed program for the fourth grade students is to be developed and applied by extracting the contents associated with basic operations studied prior to the fourth grade level of mixed calculations. After analyzing the results of the research, the following conclusions are obtained. First, the prescribed program for mixed calculations brought about the improvement in the mixed calculation problem solving ability of the students. Second, applying the prescribed program for mixed calculation resulted in an increase in students' interest and concentration on problem solving. In synthesis of the above conclusions, the development and application of the prescribed program for mixed calculation improved the students' concentration on the problem and the students' problem solving ability.

• Education of Primary School Mathematics
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• v.2 no.1
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• pp.53-64
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• 1998

Two different CAI programs have been developed to study the affect of CAI element for the types of learners'performance; (i) one is the 'CAI program 1' including the open questions for the fourth grade (the fourth period of the 'Time and Angle' in chapter 3 of the first term) of the mathematics class in the elementary school, and (il) the other is 'CAI program 2' for the existing methods. The fourth grade of Andong Songhyun elementary school has been chosen as the study subjects (243 learners), and the t-test and learners'interview have also been used to analysis the results of CAI programs. The CAI programs have only been used as the control variable. The developed CAI programs have been applied two different learners'groups to investigate the degree of performance among the superior, average, and inferior learners. For the superior group (p＜.0023) at the t＜3.2268 level and for the average group (p＜.0706) at the t＜1.8211 level the learner' group using CAI program 1 shows the higher performance compared with the learners' group using the CAI program 2, whereas fur the inferior group (p＜.8073) at the t＜.2458 level two programs did not show any difference. The learners interviews show that the superior and average groups have an interest for the open problems, whereas the inferior group do not shows an interest for the open problems. Thus, the CAI programs including the open questions (open fields, open evaluation) will be helped to the learners' group with the individual differences. Furthermore, it is expected that the CAI programs including the open questions as the mathematics and the program model of CAI can be used to develope the CAI program in future.

• School Mathematics
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• v.10 no.2
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• pp.155-179
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• 2008

Multiplication problems for the 7th curriculum focus on functional realms featuring the memorization and application of the multiplication table, exposing learners only to additive thinking characterized by simple counting and drawing. A diversity of research has yet to be conducted for the transition to multiplicative thinking that highlights the capability to solve problems by using multiplication and division in the expanded number scope like 'prime numbers', 'fractional numbers', and 'ratio/rates' and to describe accurately how they solved. This research was designed to develop and utilize teaching-learning materials for the transition of fifth graders' additive thinking to advanced multiplicative one and to analyze the application results in order to identify validity in material development. The following conclusions were made. First, the development and application of teaching-learning materials for multiplicative thinking cultivation facilitated the transition from additive thinking featuring simple counting and drawing to multiplicative thinking characterized by multiplication and accurate description in a more complicated and expanded number scope. Second, the development of materials featuring 'basic'-'intermediate'-'in-depth' courses by activity enabled learners to benefit from learning by level and expansion in number scope. Third, the use of topics and materials closely connected to daily lives stimulated learners' curiosity, helping them concentrate more on given problems. Fourth, communication between teachers and students or among learners themselves was promoted by continuously encouraging them to explain and by reviewing their documents identifying rules or patterns.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.225-243
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• 2013

This study was to analyze the effects of basic computational abilities using G-learning contents, which was developed for mathematically slow learners. The participant students were 146 mathematically slow learners in grade 3-6 in Seoul. The researchers analyzed the difference between pre and post test scores to check their effectiveness. Also, teachers and parents as well as students responded survey items to check dispositions and satisfactions towards the program. The research results showed that the application of the G-learning contents on basic computation areas was effective to develop students' basic computational skills. In addition, students also showed that they were satisfied studying basic computations with the G-learning contents. They had increased beliefs about and decreased difficulties in mathematics. Parents and teachers also had satisfactions in using the G-learning programs in spite of some negative effects such as errors in the contents, use of computers, and concentration on the game itself. For the improvement of G-learning contents, we need to keep studying on G-learning contents with wide range of areas and long term studies.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.215-241
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• 2017

This study analyzed teachers' Pedagogical Content Knowledge (PCK) regarding the pedagogical aspect of the instruction of ratio and rate in order to look into teachers' problems during the process of teaching ratio and rate. This study aims to clarify problems in teachers' PCK and promote the consideration of the materialization of an effective and practical class in teaching ratio and rate by identifying the improvements based on problems indicated in PCK. We subdivided teachers' PCK into four areas: mathematical content knowledge, teaching method and evaluation knowledge, understanding knowledge about students' learning, and class situation knowledge. The conclusion of this study based on analysis of the results is as follows. First, in the 'mathematical content knowledge' aspect of PCK, teachers need to understand the concept of ratio from the perspective of multiplicative comparison of two quantities, and the concept of rate based on understanding of two quantities that are related proportionally. Also, teachers need to introduce ratio and rate by providing students with real-life context, differentiate ratios from fractions, and teach the usefulness of percentage in real life. Second, in the 'teaching method and evaluation knowledge' aspect of PCK, teachers need to establish teaching goals about the students' comprehension of the concept of ratio and rate and need to operate performance evaluation of the students' understanding of ratio and rate. Also, teachers need to improve their teaching methods such as discovery learning, research study and activity oriented methods. Third, in the 'understanding knowledge about students' learning' aspect of PCK, teachers need to diversify their teaching methods for correcting errors by suggesting activities to explore students' own errors rather than using explanation oriented correction. Also, teachers need to reflect students' affective aspects in mathematics class. Fourth, in the 'class situation knowledge' aspect of PCK, teachers need to supplement textbook activities with independent consciousness and need to diversify the form of class groups according to the character of the activities.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.59-74
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• 2019

According to previous studies, it shows that the metacognitive ability that makes the positive element of the problem solver positively affects the problem-solving process of mathematics. In order to accurately grasp causality, this study investigates the specific characteristics of the meta-affect factor in the process of problem-solving. To do this, we analyzed the types and frequency of data collected from collaborative problem-solving situations composed of 4th~6th grade mathematically gifted children in small group of two. As a result, it can be seen that the type of meta-affect in the problem-solving process of mathematically gifted children is related to the correctness rate of the problem. First, regardless of the success or failure of the problem-solving, the meta-affect appeared relatively frequently in the meta-affect types in which the cognitive factors related to the context of problem-solving appeared first, and acted as the meta-functional type of the evaluation and attitude. Especially, in the case of successful problem-solving of mathematically gifted children, meta-affect showed a very active function as meta-functional type of evaluation.