• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.189-200
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• 2000

The purpose of this thesis is that the students understand the sentence stated math problems closely related to the real life and adapted the right solving strategies try to find the solution to a problem. The following research problem were proposed. 1. How repeated thinking lessons develop the understanding of problems and influence the usage of correct problem solving strategies and extensions of problem solving. 2. There are how much differences of achievement for each type of sentence stated problems by using comparative analysis of upper class, intermediate class, and lower class for each level between the experimental and comparative classes. In order to conduct this research the classes were divided into three different level - upper class, intermediate class and lower class. Each level include an experimental class and a comparative class. The two classes (experimental class and comparative class) of the same level were tested on the basis of class division record with the experimental class repeated learning papers for two weeks were used to guide the fixed thinking algorism for each sentence stated math problems. Eight common problems were chosen from a variety of textbooks : number calculation problems, velocity-distance-time problems, the density of a mixture, benefit problems, distribution problems, problems about working, ratio problems, the length of a figure problems. After conducting this research experiment The differences in achievement level between the experimental class and comparative class, were compared and analyzed through achievement tests made from the achievement test papers with seven problems, which were worth seventy points (total score). The conclusions of this thesis are as follows: Firstly, leaning activities through the usage of repeated learning papers for each level class produce an even development of achievement level especially in the case of the upper class learners, they have particular differences (between experimental class and comparative class) compared to the intermediate level and lower classes. Secondly, according to the analysis about achievement development each problems, learners easily accept the strategies of solution through the formula setting up to the problem of velocity -distance-time, and to the density of the mixture they adapted the picture drawing strategies interestingly, However each situation requires a variety of appropriate solution strategies. Teachers will have to employ other interesting solution strategies which relate to real life.

• The Mathematical Education
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• v.62 no.3
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• pp.381-400
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• 2023

As the era of solving various and complex problems in the real world using artificial intelligence and big data appears, problem-solving competencies that can solve realistic problems through a mathematical approach are required. In fact, the 2015 revised mathematics curriculum and the 2022 revised mathematics curriculum emphasize mathematical modeling as an activity and competency to solve real-world problems. However, the real-world problems presented in domestic and international textbooks have a high proportion of artificial problems that rarely occur in real-world. Accordingly, domestic and international countries are paying attention to the reality of mathematical modeling tasks and suggesting the need for authentic tasks that reflect students' daily lives. However, not only did previous studies focus on theoretical proposals for reality, but studies analyzing teachers' perceptions of reality and their competency to reflect reality in the task are insufficient. Accordingly, this study aims to analyze in-service mathematics teachers' perception of reality among the characteristics of tasks for mathematical modeling and the in-service mathematics teachers' competency for designing the mathematical modeling tasks. First of all, five criteria for satisfying the reality were established by analyzing literatures. Afterward, teacher training was conducted under the theme of mathematical modeling. Pre- and post-surveys for 41 in-service mathematics teachers who participated in the teacher training was conducted to confirm changes in perception of reality. The pre- and post- surveys provided a task that did not reflect reality, and in-service mathematics teachers determined whether the task given in surveys reflected reality and selected one reason for the judgment among five criteria for reality. Afterwards, frequency analysis was conducted by coding the results of the survey answered by in-service mathematics teachers in the pre- and post- survey, and frequencies were compared to confirm in-service mathematics teachers' perception changes on reality. In addition, the mathematical modeling tasks designed by in-service teachers were evaluated with the criteria for reality to confirm the teachers' competency for designing mathematical modeling tasks reflecting the reality. As a result, it was shown that in-service mathematics teachers changed from insufficient perception that only considers fragmentary criterion for reality to perceptions that consider all the five criteria of reality. In particular, as a result of analyzing the basis for judgment among in-service mathematics teachers whose judgment on reality was reversed in the pre- and post-survey, changes in the perception of in-service mathematics teachers was confirmed, who did not consider certain criteria as a criterion for reality in the pre-survey, but considered them as a criterion for reality in the post-survey. In addition, as a result of evaluating the tasks designed by in-service mathematics teachers for mathematical modeling, in-service mathematics teachers showed the competency to reflect reality in their tasks. However, among the five criteria for reality, the criterion for "situations that can occur in students' daily lives," "need to solve the task," and "require conclusions in a real-world situation" were relatively less reflected. In addition, it was found that the proportion of teachers with low task development competencies was higher in the teacher group who could not make the right judgment than in the teacher group who could make the right judgment on the reality of the task. Based on the results of these studies, this study provides implications for teacher education to enable mathematics teachers to apply mathematical modeling lesson in their classes.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.1-27
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• 2010

This study intends to provide implications about sluggish use of calculators in our case by analyzing the math textbook of U.S. Macmillan/McGraw-Hill along with the tendency of paying more attention to math class using technologies. From the results of analysis, this textbook deals with various methods over around 3.3% of all pages, using calculators across all grades from 1st to 6th grade. In particular, it offers guidance into three types such as 'Choose a Computation Method', 'You can also use a calculator.', and 'TECHNOLOGY LINK', while particularly it is impressive in the perspective of using calculators as one of calculation strategies. And case studies of usage in textbooks describe 8 different perspectives as an example-represent; solve problems or equations; develope or demonstrate conceptual understanding; analyze; compute or estimate; describe, explain or justify; choose appropriate calculation method; determine a calculated answer's reasonableness. Reflecting on the fact that we still use calculators in a passive way, there are considerable implications to us.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.545-567
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• 2023

This study investigates effective ChatGPT prompts for solving mathematical problems, focusing on the chapters of quadratic equations and quadratic functions. A structured prompt was designed, following a sequence of 'Role-Rule-Example Solution-Problem-Process'. In this study, an artificial intelligence model combining GPT-4, Wolfram plugin, and Advanced Data Analysis was utilized. Wolfram was used as the primary tool for calculations to reduce computational errors. When using the structured prompt, the accuracy rate for problems from nine high school mathematics textbooks on quadratic equations and quadratic functions was 91%, showing higher performance compared to zero-shot prompts. This confirmed the effectiveness of the structured prompts in solving mathematical problems. The structured prompts designed in this study can contribute to the development of intelligent information systems for personalized and customized education.

• Education of Primary School Mathematics
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• v.19 no.2
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• pp.127-142
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• 2016

The purpose of this study was to examine the students' problem solving ability according to numeric expression and the semantic types of addition and subtraction word problems. For this, a research was to analyze the addition and subtraction calculation ability, word problem solving ability of the selected $2^{nd}$ grade(118) and 3rd grade(109) students. We got the conclusion as follows: When the students took the survey to assess their ability to solve the numerical expression and the word problems, the correct answer rates of the result unknown problems was larger than those of the change unknown problems or the start unknown problems. the correct answer rates of the change add-into situation was larger than those of the part-part-whole situation in the result unknown addition word problems: they often presented in text books. And, in the cases of the result unknown subtraction word problems that often presented in text books, the correct answer rates of the change take-away situation was the largest. It seemed probably because the students frequently experienced similar situations in the textbooks. We know that the formal calculation ability of the students was a precondition for successful word problem solving, but that it was not a sufficient condition for that.

• The Mathematical Education
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• v.63 no.1
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• pp.63-83
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• 2024

The purpose of this study is to analyze the mathematical connection components of the tasks included in the trigonometric ratio unit of 3rd grade middle school textbook based on the 2015 revised mathematics curriculum and investigate teachers' perceptions and practical measures regarding these components. To this end, we analyzed the characteristics of mathematical connection tasks included in the trigonometric ratio units in nine types of 3rd grade middle school mathematics textbooks, and we conducted a questionnaire survey and interviews with one in-service math teachers in pre interview and with two in-service math teachers in this interview to investigate their perceptions and practical measures. As a result of the study, the number of tasks with external connection in the trigonometric ratio unit were less than those of internal connection. In addition, in terms of teachers' perceptions and practical measures, the perspective of analyzing tasks with mathematical connections varied depending on the teacher's perspective, and the practical measures varied accordingly. These findings are significant in that they reveal the relationship between mathematical tasks, teacher perceptions and measures to foster effectively students' mathematical connections.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.445-459
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• 2018

The purpose of this study is to provide a method to help elementary school students learn ratio-related concepts effectively through visual representations. This study was conducted to identify the differences in the composition of ratio-related concepts between Korean and Singaporean textbooks, reconstruct a unit of proportional expressions and distributions by using visual representations and confirm the differences in performance between an experimental and a comparison group of 6th grade students. While the experimental group mathematics lessons is from the reconstructed textbook, the comparison group lessons is from an existing textbook that does not include any reconstructive representations. A t-test of mean was applied to determine the differences between the experimental and comparison group. Analysis revealed significant differences in the mean between the experimental group and the comparison group, and the intermediate level group showed more improvement compared to the higher and lower level groups. An implication of this study is that the application of visual representations can assist students' understanding of ratio-related concepts.

• Journal of Korean Society of Forest Science
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• v.110 no.4
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• pp.689-710
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• 2021

The purpose of this study was to analyze contents of the elementary school textbooks on 'Forest Education' based on the 2015 revised curriculum. This study is designed to determine the status of forest educationrelated content in the curriculum. Thetypesofforesteducationintextbooksweredividedintoanalysis. In addition, the standards of achievement of the curriculum were analyzed into the areas of forest education curriculum to determine the similarities between the curriculum and the achievement of forest education. This study shows that, first, the field of knowledge in forest education was included in all subjects and grades except mathematics. It noted that the curriculum includes areas of knowledge that directly convey knowledge related to forest education. This showed that the forest education knowledge area is linked to various courses. Second, the types of forest education included in the curriculum appeared differently depending on age. In the lower grades, there was the most information on the tools and sensibilities of forest education, and in the higher grades, the more knowledge and value-related areas were addressed. As the school year increases, so do forest education levels. Third, when analyzing the achievement criteria in the curriculum, the curriculum achievement criteria included key points in forest education. Thus, this study confirmed the link between the curriculum and forest education.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.131-155
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• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.