• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

• The Mathematical Education
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• v.48 no.3
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• pp.303-328
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• 2009

In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations -especially verval, visual and symbolic representations- and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the $0{\sim}2$ vervalism level, but in the third class, about 65% of students are in the $6{\sim}7$ level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in II items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.05a
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• pp.108-111
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• 2014

In this paper, we tried to identify implications of selecting gifted of information science & followed educational system via analyzing each of student's characteristics in each subjects they study within Science Education Institute for the Gifted. A study of the existing institutions do not have experience of the gifted students based on assessment through observation of the 1-year science, mathematics and information science education in the List of attribute analysis. Learners of Information Science became with analysis that Attitude Category was superior in mathematics to the subject of science and Problem Solving Category regardless of the subjects showed similar. As to, Attitude Category, Problem Solving Category and Mathematics Cognition Category was analyzed to be closed and we could confirm through the qualitative observation record. On this, the researcher concluded that the mathematics could know the effect fitness by a learner rather than the subject of science as to an attitude and problem resolution area.

• The Mathematical Education
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• v.60 no.3
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• pp.363-386
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• 2021

To learn statistics meaningfully, we must provide an opportunity to experience the process of solving statistical problems with actual data. In particular, exploration questions at the problem setting stage are important for students to successfully guide them from the beginning to the conclusion of the statistical problem solving process. Therefore, in this study, a mixed research method was carried out for the exploration questions of pre-service mathematics teachers during the problem setting stage. As a result, some pre-service mathematics teachers categorized incorrect statistical questions because they did not clearly define the meaning or variables of the questions in the process of categorizing them from possible questions. In addition, questions that cannot be solved statistically were categorized due to misconceptions about statistical knowledge. Second, only 50% of the pre-service mathematics teachers met all 6 conditions suitable for solving statistical problems, while there maining they met only a few conditions. Therefore, the conclusion of this study is as follows. First of all, they should be given the opportunity to experience all the statistical problem solving processes through teacher education because they do not have enough experience in statistical problem solving. Secondly, since the problem setting stage is very important in the statistical problem solving process, a series of subdivided processes are also required in the problem setting stage.

• Journal of the Korean School Mathematics Society
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• v.25 no.1
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• pp.61-77
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• 2022

This study looked at the deviation of each textbook, focusing on the detailed learning content related to the quadratic curve properties contained in high school geometry textbooks. Rather than criticizing the diversity of content elements covered in high school geometry textbooks and suggesting alternatives, it focused on analyzing the actual conditions of content element diversity. The curriculum specifies that the practical application of the quadratic curve should be emphasized so that student could recognize the usefulness and value. However, as a result of the analysis, it was confirmed that the purpose of the curriculum and the structure of the textbook did not match somewhat, the deviation of content elements for each textbook was quite large. In terms of acknowledging the diversity of teaching and learning, the diversity of each textbook on the methods of the introduction and the natures related to the quadratic curve can be fully recognized. But in our educational reality, which is aiming for the university entrance examination system through national evaluation such as CSAT, the results are too sensitive in society as a whole, so the diversity of expressions in mathematics textbooks is sometimes interpreted as a disadvantage of evaluation. It is time to reconsider the composition of textbooks that recognizes the diversity of content elements in textbook teaching and learning and at the same time reflects the aspect of equality in evaluation.

• Journal of the Korean Chemical Society
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• v.68 no.1
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• pp.40-53
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• 2024

The study investigates the number and proportion of questions in each area by examining Chemistry I questions from the College Scholastic Ability Test from 2019 to 2022. The analysis was conducted using a three-dimensional framework that included key concepts in chemistry, behavioral domains in chemistry, and behavioral domains in mathematics. The results indicated that Chemistry I questions on the College Scholastic Ability Test had a relatively even distribution of questions across core individual topics, but highly difficult questions were predominantly biased toward stoichiometry. In terms of the behavioral domains in chemistry, there was a remarkably low proportion of questions related to problem recognition and hypothesis establishment, as well as designing research and implementing research. Conversely, highly difficult questions were more inclined towards drawing conclusions and evaluations. Regarding behavioral domains in mathematics, there was a limited number of questions addressing heuristic reasoning and deductive reasoning. On the other hand, high-difficulty questions favored internal problem-solving ability. Additionally, certain key concepts in chemistry and behavioral domains in chemistry exhibited a strong correlation with specific behavioral domains in mathematics. This characteristic was particularly evident in questions that encompassed higher-dimensional behavioral domains in mathematics, which students tend to find challenging.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.177-197
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• 2007

This study discussed the climbing learning method which studied and practiced by Professor Saito Noboru. This is the learning method which is devised to know not only the relationship of the learning factors but the systemic or structural connection of whole studying contents- affects children's math learning ability through practical class to both the lower and the higher grades. To achieve the purpose of this study, these following issues were set; A. Develop the teaching and learning course of mathematics by applying the climbing learning method. B. Execute the mathematics lesson according to the climbing learning method and analyze the learning achievement. C. Analyze the difference between application of the climbing learning method and that of the learning method by student's level in mathematics. D. Analyze what the climbing learning method gives a shift of the recognition of learning mathematics. In order to accomplish these study issues, we analyzed the text book of math not only for children but also for teachers and developed the teaching and learning course applied the climbing learning method with advice of experts. It was chosen two different homogeneous groups each, third year for lower grade group and fifth year for higher grade group. It was done the experimental group lesson applying the climbing learning method and general lesson for the control group. After then, t-test against independent samples was done depending on the result of the student's assessment(T1, T2). These two groups' students were divided into smaller groups based on result of achievement level regardless of gender. These subgroups were confirmed the difference of learning ability between upper and lower level group. As regarding the result making out grades of faith and attitude for math, t-test was used on independent sample. At the same time, experimental groups were tested using learning attitude with the learning structure chart. Through this study the following results are obtained and the conclusion was drawn. Firstly, although applying the climbing learning method to the lesson does not have significant effect to the lower grade of elementary school student's achievement it has significant influence on the higher grade student's achievement. Second, as a result of analyzing the difference between the climbing learning method and the learning method by student's level in mathematics, it is of no beneficial effect to the lower grade both upper level and lower level. However, it has appreciable effect to the higher grade classes both upper level and low level. Especially, upper level students have higher effect than low level students. Third, climbing learning method does not affect to the faith and attitude of the lower grade students positively, but it has affirmative effect to the higher grade students'. As a result of the survey of the experimental groups which were applied to the climbing loaming method, the lesson by using the learning structure chart proved to be helpful to the both the lower and higher grade. The best advantage of using the learning structure chart, children say, is easily understood whole contents of studying and is useful for review. Furthermore, using the learning structure chart is more efficient compared with previous learning method and is given the successful result to self-directed learning. In conclusion, keeping up with the current of the thought of education, we suggest a scheme as a new teaching method from the constructive learning method which emphasize the self-directed learning.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.459-476
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• 2010

The purpose of this study is to suggest a new direction in using LOGO as a gifted education program and to seek an effective approach for LOGO teaching and learning, by analyzing the strategic thinking of mathematically gifted elementary students. This research is exploratory and inquisitive qualitative inquiry, involving observations and analyses of the LOGO Project learning process. Four elementary students were selected and over 12 periods utilizing LOGO programming, data were collected, including screen captures from real learning situations, audio recordings, observation data from lessons involving experiments, and interviews with students. The findings from this research are as follows: First, in LOGO Project Learning, the mathematically gifted elementary students were found to utilize such strategic ways of thinking as inferential thinking in use of prior knowledge and thinking procedures, generalization in use of variables, integrated thinking in use of the integration of various commands, critical thinking involving evaluation of prior commands for problem-solving, progressive thinking involving understanding, and applying the current situation with new viewpoints, and flexible thinking involving the devising of various problem solving skills. Second, the students' debugging in LOGO programming included comparing and constrasting grammatical information of commands, graphic and procedures according to programming types and students' abilities, analytical thinking by breaking down procedures, geometry-analysis reasoning involving analyzing diagrams with errors, visualizing diagrams drawn following procedures, and the empirical reasoning on the relationships between the whole and specifics. In conclusion, the LOGO Project Learning was found to be a program for gifted students set apart from other programs, and an effective way to promote gifted students' higher-level thinking abilities.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.351-370
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• 2013

The purpose of this study is to analyze the modes of visualization which appears in the process of thinking that mathematically gifted 6th grade students get to understand components of the three-dimensional shapes on the duality of regular polyhedrons, find the duality relation between the relations of such components, and further explore on whether such duality relation comes into existence in other regular polyhedrons. The results identified in this study are as follows: First, as components required for the process of exploring the duality relation of polyhedrons, there exist primary elements such as the number of faces, the number of vertexes, and the number of edges, and secondary elements such as the number of vertexes gathered at the same face and the number of faces gathered at the same vertex. Second, when exploring the duality relation of regular polyhedrons, mathematically gifted students solved the problems by using various modes of spatial visualization. They tried mainly to use visual distinction, dimension conversion, figure-background perception, position perception, ability to create a new thing, pattern transformation, and rearrangement. In this study, by investigating students' reactions which can appear in the process of exploring geometry problems and analyzing such reactions in conjunction with modes of visualization, modes of spatial visualization which are frequently used by a majority of students have been investigated and reactions relating to spatial visualization that a few students creatively used have been examined. Through such various reactions, the students' thinking in exploring three dimensional shapes could be understood.

• 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.