• 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 School Mathematics Society
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• v.21 no.4
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• pp.419-443
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• 2018

The purpose of this study was to analyze the problem solving strategies of ordinary students, gifted students, pre-service teachers, and in-service teachers with the 'chicken and pig problem,' which has multiple strategies to obtain the solution. For this study, 98 students in the 6th grade elementary schools, 96 gifted students in a gifted institution, 72 pre-service teachers, and 60 in-service teachers were selected. The researcher presented the "chicken and pig" problem and requested them the solution strategies as many as possible for 30 minutes in a free atmosphere. As a result of the study, the gifted students used relatively various and efficient strategies compared to the ordinary students, and there was a difference in the most used strategies among the groups. In addition, the percentage of respondents who suggested four or more strategies was 1% for the ordinary students, 54% for the gifted students, 42% for the pre-service teachers, and 43% for the in-service teachers. As suggestions, the researcher asserted that various kinds of high-quality mathematical problems and solving experiences should be provided to students and teachers and have students develop multi-strategy problems. As a follow-up study, the researcher suggested that multi-strategy mathematical problems should be applied to classroom teaching in a collaborative learning environment and reflected them in teacher training program.

• Education of Primary School Mathematics
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• v.25 no.2
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• pp.143-160
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• 2022

This study was conducted to discuss educational implications by analyzing the types of mathematical thinking that appeared in challenge math in 5th and 6th grade math teacher's guidebooks. To this end, mathematical thinking types that can be evaluated and nurtured based on teaching and learning contents were organized, a framework for analyzing mathematical thinking was devised, and mathematical thinking appearing in Challenge Math in the 5th and 6th grade math teachers' guidebooks was analyzed. As a result of the analysis, first, 'challenge mathematics' in the 5th and 6th grades of elementary school in Korea consists of various problems that can guide various mathematical thinking at the stage of planning and implementation. However, it is feared that only the intended mathematical thinking will be expressed due to detailed auxiliary questions, and it is unclear whether it can cause mathematical thinking on its own. Second, it is difficult to induce various mathematical thinking at that stage because the questionnaire of the teacher's guidebooks understanding stage and the questionnaire of the reflection stage are presented very typically. Third, the teacher's guidebooks lacks an explicit explanation of mathematical thinking, and it will be necessary to supplement the explicit explanation of mathematical thinking in the future teacher's guidebooks.

• Education of Primary School Mathematics
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• v.26 no.3
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• pp.181-197
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• 2023

The importance of reasoning processes based on fractional concepts and number senses, rather than a formalized procedural method using common denominators, has been noted in a number of studies in relation to compare the magnitudes of unlike fractions. In this study, a unlike fraction magnitudes comparison test was conducted on fourth-grade elementary school students who did not learn equivalent fractions and common denominators to analyze the reasoning perspectives of the correct and wrong answers for each of the eight problem types. As a result of the analysis, even students before learning equivalent fractions and reduction to common denominators were able to compare the unlike fractions through reasoning based on fractional sense. The perspective chosen by the most students for the comparison of the magnitudes of unlike fractions is the 'part-whole perspective', which shows that reasoning when comparing the magnitudes of fractions depends heavily on the concept of fractions itself. In addition, it was found that students who lack a conceptual understanding of fractions led to difficulties in having quantitative sense of fraction, making it difficult to compare and infer the magnitudes of unlike fractions. Based on the results of the study, some didactical implications were derived for reasoning guidance based on the concept of fractions and the sense of numbers without reduction to common denominators when comparing the magnitudes of unlike fraction.

• Journal of The Korean Association For Science Education
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• v.25 no.7
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• pp.746-753
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• 2005

In order to be efficient teachers should understand the current level of leaners through diagnostic evaluation. However, it is arduous to administer a diagnostic examination in every class because of various limitations. This study examined, the major issues arising from the development of a new science diagnostic evaluation system by incorporating the using knowledge state analysis method. The proposed evaluation system was based on the knowledge state analysis method. Knowledge state analysis is a method where by a distinguished collection of knowledge uses the theory of knowledge space. The theory of knowledge space is very advantageous when analyzing knowledge in strong hierarchies like mathematics and science. It helps teaching plan through methodically analyzing a hierarchy viewpoint for students' knowledge structure. The theory can also enhance objective validity as well as support a considerable amount of data fast by using the computer. In addition, student understanding is improved through individualistic feedback. In this study, an evaluation instrument was developed that measured student learning outcome, which is unattainable from the existing method. The instrument was administered to pre-service physics teachers, and the results of student evaluation was analyzed using the theory of knowledge space. Following this, a revised diagnostic evaluation system for facilitating student individualized learning was constructed.

• Journal of Gifted/Talented Education
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• v.16 no.2
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• pp.167-191
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• 2006

The purpose of this study was to explore logical thinking abilities and metacognitive characteristics by student's giftedness and grade level. Furthermore, this study sought to present the practical basis for the promotion of students' abilities in self-driven learning as well as cognition. Average-ability students(n=199), economically disadvantage gifted students(n=133), and gifted students(n=111), who were sampled by two-step sampling procedures, responded the logical thinking ability test(Cho et al, 2006) and the questionnaire asking self-perception for 'metacognitive knowledge' and 'metacognitive control' abilities(Cho & Han, 2004). As the results, average-ability students showed less logical thinking abilities(in language, mathematics, and space) than gifted students. The logical thinking abilities had affected by giftedness, grade level and these interaction. And gifted students showed higher metacognitive control abilities in planning, monitoring, priority, and strategies of learning than average-ability students. However, there were no significant differences in metacognitive knowledge and metacognitive control abilities between economically disadvantaged gifted students and gifted students.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Communications of Mathematical Education
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• v.36 no.2
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• pp.253-286
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• 2022

This study is a study in which four teachers from the same school who participated in a teacher learning community program at the school field developed interdisciplinary linkage and convergence data using Plato as a collaborative circle in ethics and mathematics subjects. In particular, this study aimed to develop practical and shareable lesson materials. The data development procedure was developed according to the following four procedures. 'Development of data development plan, data development, verification of development data, and development of final data that reflects the verification opinions' At this time, in the data development stage, a theme-based design model was applied and developed. In addition, the development data were verified by conducting CVR verification for field teachers to focus on the validity and class applicability, and the final data were presented after the development data being revised to reflect the verification results. This study not only introduced the developed data, but also described the procedure of the data development process and the trial and error and concerns of the developers in the process to provide information on the nature of basic research to other field researchers who attempt data development.

• Journal of The Korean Association For Science Education
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• v.43 no.4
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• pp.403-414
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• 2023

In this study, we examined the adaptive practices of science teachers in their classrooms and their perspectives on the distinguishing features of these practices within science subjects. Our analysis comprised 339 cases from 128 middle and high school science teachers nationwide, and 199 cases on the characteristics of adaptive practices in science disciplines. The primary findings were as follows: First, the most significant characteristic of adaptive practice in science disciplines pertained to experimental procedures. Within the 'suggestion of additional materials/activities' category, the most frequently cited adaptive practice, teachers incorporated demonstrations to either facilitate student comprehension or enhance motivation. Additionally, 'experimental equipment manipulation or presentation of inquiry skills' emerged as the second most common adaptive practice related to experiments. Notably, over 50% of teacher responses regarding the characteristics of adaptive practices in science pertained to experiment guidance. Second, many adaptive practices involving difficulties experienced by students in learning situations were presented, particularly in areas such as numeracy and literacy. Many cases were related to the basic ability of mathematics used as a tool in science learning and understanding scientific terms in Chinese characters. Third, beyond 'experiment guidance', the characteristic adaptive practices of science subjects were related to 'connections between scientific theory and the real world', 'misconception guidance in science', 'cultivation of scientific thinking', and 'convergence approaches'. Fourth, the cases of adaptive practice presented by the science teachers differed by school level and major; therefore, it is necessary to consider school level or major in future research related to adaptive practice. Fifth, most of the adaptive action items with a small number of cases were adaptive actions executed from a macroscopic perspective, so it is necessary to pay attention to related professionalism. Finally, based on the results of this study, the implications for science education were discussed.