• Education of Primary School Mathematics
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• v.26 no.4
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• pp.349-368
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• 2023

The purpose of this study is to explore ways for students to connect conceptual and procedural knowledge in mathematical modeling lessons. Accordingly, we selected the greatest common divisor among the learning contents in which elementary school students have difficulties connecting conceptual and procedural knowledge. A mathematical modeling lesson was designed and implemented to solve problems related to the greatest common divisor while connecting conceptual and procedural knowledge. As a result of the analysis, it was found that the mathematical modeling lesson had positive effects on students solving problems by connecting conceptual and procedural knowledge. In addition, through actual class application, a teaching and learning plan was derived to meaningfully connect conceptual and procedural knowledge in mathematical modeling lessons.

• Journal of Gifted/Talented Education
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• v.22 no.3
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• pp.619-637
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• 2012

The purpose of this study is to develop a new program for elementary math-gifted students by using 'Girih Tililng' and apply it to the elementary students to improve their math-ability. Girih Tililng is well known for 'the secrets of mathematics hidden in Mosque decoration' with lots of recent attention from the world. The process of this study is as follows; (1) Reference research has been done for various tiling theories and the theories have been utilized for making this study applicable. (2) The characteristic features of Mosque tiles and their basic structures have been analyzed. After logical examination of the patterns, their mathematic attributes have been found out. (3) After development of Girih tiling program, the program has been applied to math-gifted students and the program has been modified and complemented. This program which has been developed for math-gifted students is called 'Exploring the Secrets of Girih Hidden in Mosque Patterns'. The program was based on the Renzulli's three-part in-depth learning. The first part of the in-depth learning activity, as a research stage, is designed to examine Islamic patterns in various ways and get the gifted students to understand and have them motivated to learn the concept of the tiling, understanding the characteristics of Islamic patterns, investigating Islamic design, and experiencing the Girih tiles. The second part of the in-depth learning activity, as a discovery stage, is focused on investigating the mathematical features of the Girih tile, comparing Girih tiled patterns with non-Girih tiled ones, investigating the mathematical characteristics of the five Girih tiles, and filling out the blank of Islamic patterns. The third part of the in-depth learning activity, as an inquiry or a creative stage, is planned to show the students' mathematical creativity by thinking over different types of Girih tiling, making the students' own tile patterns, presenting artifacts and reflecting over production process. This program was applied to 6 students who were enrolled in an unified(math and science) gifted class of D elementary school in Daejeon. After analyzing the results produced by its application, the program was modified and complemented repeatedly. It is expected that this program and its materials used in this study will guide a direction of how to develop methodical materials for math-gifted education in elementary schools. This program is originally developed for gifted education in elementary schools, but for further study, it is hoped that this study and the program will be also utilized in the field of math-gifted or unified gifted education in secondary schools in connection with 'Penrose Tiling' or material of 'quasi-crystal'.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.359-388
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• 2012

The study aims to extract the framework of sub-factors of spatial sense, to develop test instruments based on the framework to investigate the actual spatial sense ability of fourth to sixth graders in elementary school and to analyze the results. According to the framework of sub-factors of spatial sense of the study, spatial sense has two factors of spatial visualization and spatial orientation. Spatial visualization is divided into mental rotation, mental transformation and figure-ground perception while spatial orientation is categorized into direction sense, distance sense, and location sense. Based on the framework, the test instrument for spatial sense ability was developed and the test was conducted to 430 fourth to sixth students in five elementary schools in capital areas. The following conclusions were drawn from the results obtained in the study. Firstly, the higher school year gets, the more spatial sense grows. However, spatial visualization is developed much more than spatial orientation and their order is reversed with higher graders. Secondly, the most insufficient abilities among fourth to sixth elementary school students' spatial sense were mental transformation of spatial visualization and location sense of spatial orientation. Thirdly, the reasons of differences in sub-factors of spatial sense and graders seem to be from effects of students' learning experiences of spatial sense of mathematics curriculum and the complexities of test items.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.309-341
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• 2017

This study aims to investigate an approach to teach percentages in elementary mathematics class by analyzing calculating strategies with percentage the students use to solve the percentage tasks and their percentages of correct answers, as well as types of errors with percentages the students make. For this research 182 sixth graders were examined. The instrument test consists of various task types in reference to the previous study; the percentages tasks are divided into algebraic-geometric, part whole-comparison-change and find part-find whole-find percentage tasks. According to the analysis of this study, percentages of correct answers of students with percentage tasks were lower than we expected, approximately 50%. Comparing the percentages of correct answers according to the task types, the part-whole tasks are higher than the comparison and change tasks, the geometric tasks are approximately equal to the algebraic tasks, and the find percentage tasks are higher than the find whole and find part tasks. As to the strategies that students employed, the percentage of using the formal strategy is not much higher than that of using the informal strategy, even after learning the formal strategy. As an insightful approach for teaching percentages, based on the study results, it is suggested to reinforce the meaning of percentage, include various types of the comparison and change tasks, emphasize the informal strategy explicitly using models prior to the formal strategy, and understand the relations among part, whole and percentage throughly in various percentage situations before calculating.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.391-421
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• 2015

The scientific technology developed rapidly and the internet became more popular, also, the world became interactive with one another and the word 'Global' became popular and built a new paradigm. As the development of the society, the ideal criteria for the competent student changed. Consequently, the attention for the globalized education increased. From the points of view of mathematical education, it became a important task to be prepared for international competitiveness for korean talented students. For theses reasons, this article analyzes the characteristics of IBDP and its textbook, which is an international official curriculum and one of the actualizing method for internalization Korean high school curriculum and text book, specifically, focusing on algebra part. Especially, Korean curriculum textbooks and the Mathematical Higher Level textbooks of IBDP was compared and analyzed. As a result, the depth and range of the content, standard level of the question, methods being used to explain the concept, type of questions as well as teaching - learning method were analyzed and in each chapter of the algebra we give meaningful result and proposed discussion.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.657-673
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• 2015

In this study, we are interested in the teachers' MCK about '$N{\div}0$' and MPCK in relation to the proper ways to teach it. Even though '$N{\div}0$' is not on the current curriculum and textbooks of elementary school mathematics, a few students sometimes ask a question about it because the division of the form '$a{\div}b$' is dealt in whole number including 0. Teacher's obvious understanding and appropriate guidance based on students' levels can avoid students' error and have positive effects on their subsequent learning. Therefore, we developed an interview form to investigate teachers' MCK about '$N{\div}0$' and MPCK of the proper ways to teach it and carried out individual interviews with 30 elementary school teachers. The results of the analysis of these interviews reveal that some teachers do not have proper MCK about '$N{\div}0$' and many of them have no idea on how to teach their students who are asking about '$N{\div}0$'. Based on our discussion of the results, we suggest some didactical implications.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.247-265
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• 2009

In the 21C information-based society, there is an increasing demand for emphasizing communication in mathematics education. Therefore the purpose of this study was to research how properties of communication among small group members varied by mathematical problem types. 8 fourth-graders with different academic achievements in a classroom were divided into two heterogenous small groups, four children in each group, in order to carry out a descriptive and interpretive case study. 4 types of problems were developed in the concepts and the operations of fractions and decimals. Each group solved four types of problems five times, the process of which was recorded and copied by a camcorder for analysis, among with personal and group activity journals and the researcher's observations. The following results have been drawn from this study. First, students showed simple mathematical communication in conceptual or procedural problems which require the low level of cognitive demand. However, they made high participation in mathematical communication for atypical problems. Second, even participation by group members was found for all of types of problems. However, there was active communication in the form of error revision and complementation in atypical problems. Third, natural or receptive agreement types with the mathematical agreement process were mainly found for conceptual or procedural problems. But there were various types of agreement, including receptive, disputable, and refined agreement in atypical problems.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.545-562
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• 2009

Calculus is used in various parts of human life and the basis of social science such as economics and public administration. Yet that is still considered important in the field of science and technology only, and there have been a lot of disputes on that phenomenon. Fortunately, calculus is going to be taught as part of the academic high school second-year mathematics curriculum in and after 2010. Students who face calculus for the first time should be helped not to lose interest in differentiation learning, not to be apprehensive of it nor to avoid it. The purpose of this study was to examine the types of errors made by students in the course of solving differentiation problems in an effort to lay the foundation for differentiation education. A pilot test was conducted after generalized differentiation problems to which students were usually exposed were selected, and experts were asked to review the pilot test. And then a finalized test was implemented to make an error analysis according to an error type analysis framework to serve the purpose.