마민영 Ma Minyoung

DOI: JANT Vol.37(No.4) 569-590, 2023

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The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

김정현 Kim Jeonghyeon , 고상숙 Choi-koh Sangsook

DOI: JANT Vol.37(No.4) 591-614, 2023

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For a long time, mathematics education institutions such as NCTM(National Council of Teachers of Mathematics) have emphasized the essential role of writing, and recent surveys by the Ministry of Education report a decline in foundational academic skills in the post-COVID19 period. The purpose of this study is to redefine the significance of mathematics writing in mathematics education, focusing on competencies highlighted in the field, particularly in the areas of problem-solving, communication, and reasoning. The research findings indicate that writing in problem-solving enhances cognitive organization, fostering the ability to grasp concepts and methods. Writing in communication builds confidence through the meta-cognitive process, and writing in inference allows self-awareness of step-by-step identification of areas lacking understanding. Particularly in the future society where artificial intelligence(AI) is utilized, changes in the learning environment necessitate research for the establishment of authenticity judgment through writing and the cultivation of a proper writing culture.

조미경 Cho Mi Kyung

DOI: JANT Vol.37(No.4) 615-633, 2023

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This study analyzed Korean studies up to August 2023 to suggest the direction of future research on basic academic abilities in mathematics. For this purpose, frequency analysis and LDA-based topic modeling were conducted on the Korean abstracts of 197 domestic studies. The results showed that, first, 'academic achievement', 'impact', 'effect', and 'factors' were all ranked at the top of the TFs and TF-IDFs. Second, as a result of LDA-based topic modeling, five topics were identified: causes of basic academic abilities deficiency, learning status of math underachievers, teacher expertise in teaching math underachievers, supporting programs for math underachievers, and results of National Assessment of Educational Achievement. As a direction for future research, this study suggests focusing on the growth of math underachievers, systematizing the programs provided to students who need learning support in mathematics, and developing teacher expertise in teaching math underachievers.

김상미 Kim Sangmee

DOI: JANT Vol.37(No.4) 635-652, 2023

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This study conducts a comprehensive analysis of the curricular progression of the concepts and learning sequences of ‘lines’, specifically, ‘line segments’, ‘straight lines’, and ‘rays’, at the elementary school level. By examining mathematics curricula and textbooks, spanning from 2^nd to 7th and 2007, 2009, 2015, and up to 2022 revised version, the study investigates the timing and methods of introducing these essential geometric concepts. It also explores the sequential delivery of instruction and the key focal points of pedagogy. Through the analysis of shifts in the timing and definitions, it becomes evident that these concepts of lines have predominantly been integrated as integral components of two-dimensional plane figures. This includes their role in defining the sides of polygons and the angles formed by lines. This perspective underscores the importance of providing ample opportunities for students to explore these basic geometric entities. Furthermore, the definitions of line segments, straight lines, and rays, their interrelations with points, and the relationships established between different types of lines significantly influence the development of these core concepts. Lastly, the study emphasizes the significance of introducing fundamental mathematical concepts, such as the notion of straight lines as the shortest distance in line segments and the concept of lines extending infinitely (infiniteness) in straight lines and rays. These ideas serve as foundational elements of mathematical thinking, emphasizing the necessity for students to grasp concretely these concepts through visualization and experiences in their daily surroundings. This progression aligns with a shift towards the comprehension of Euclidean geometry. This research suggests a comprehensive reassessment of how line concepts are introduced and taught, with a particular focus on connecting real-life exploratory experiences to the foundational principles of geometry, thereby enhancing the quality of mathematics education.

한인기 Han Inki , 허은숙 Huh Eunsook , 서은희 Seo Eunhee

DOI: JANT Vol.37(No.4) 653-674, 2023

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The development of mathematical problem solving ability and the making(transforming) mathematical problems are consistently emphasized in the mathematics curriculum. However, research on the problem making methods or the analysis of the characteristics of problem making methods itself is not yet active in mathematics education in Korea. In this study, we concretize the method of deductive problem making(DPM) in a different direction from the what-if-not method proposed by Brown & Walter, and present the characteristics and phases of this method. Since in DPM the components of the problem solving process of the initial problem are changed and problems are made by going backwards from the phases of problem solving procedure, so the problem solving process precedes the formulating problem. The DPM is related to the verifying and expanding the results of problem solving in the reflection phase of problem solving. And when a teacher wants to transform or expand an initial problem for practice problems or tests, etc., DPM can be used.

권미선 Kwon Misun

DOI: JANT Vol.37(No.4) 675-695, 2023

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To learn mathematics effectively, understanding vocabulary is essential. Accordingly, as a way to present vocabulary for mathematics education, high-frequency vocabulary was extracted from the 2009 revised 1st and 2nd grade mathematics textbooks and the 2015 revised 1st and 2nd grade mathematics textbooks. At this time, mathematics textbooks were analyzed by grade and semester, and vocabulary with a common frequency of 5 or more was extracted. In order to use it effectively in school settings, common vocabulary for each grade and intensive vocabulary for each semester were presented. As a result of the study, 61 vocabulary words for first grade education and 121 vocabulary words for second grade education were selected. As a result of analysis by vocabulary level, various levels of vocabulary from grades 1 to 5 were used. As a result of analysis by vocabulary type, the proportion of academic words increased similarly, but the proportion of technical words was found to be highest in the first semester of the second year. Based on these results, the extracted vocabulary for mathematics education is used as a resource for vocabulary instruction for students' mathematics education in each grade to help students learn mathematics.

방정숙 Pang Jeongsuk , 김리나 Kim Leena

DOI: JANT Vol.37(No.4) 697-715, 2023

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The purpose of this study is to investigate the overall understanding of patterns by second- and third-grade elementary school students. For this purpose, 12 classes per grade were selected from 10 schools, and a 46-item test was administered to 216 second graders and 223 third graders. The results of the study showed that in most cases, there was no statistically significant difference in the understanding of patterns between second- and third-graders. The exception occurred regarding the 10 items of identifying the structure of a pattern: Second-graders did better than third-graders regarding 8 items, whereas vice versa regarding 2 items. The items that both second- and third-graders struggled with included finding multiple components of a given pattern, comparing the structures between patterns, and guessing a particular term in an open pattern. Based on these findings, this paper discusses second- and third- graders' understanding of patterns and suggestions for further instruction.

김윤하 Kim Yunha , 장혜원 Chang Hyewon

DOI: JANT Vol.37(No.4) 717-736, 2023

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The purpose of this study is to develop a statistical program using data and artificial intelligence prediction models and apply it to one class in the sixth grade of elementary school to see if it is effective in improving students' statistical literacy. Based on the analysis of problems in today's elementary school statistical education, a total of 15 sessions of the program was developed to encourage elementary students to experience the entire process of statistical problem solving and to make correct predictions by incorporating data, the core in the era of the Fourth Industrial Revolution into AI education. The biggest features of this program are the recognition of the importance of data, which are the key elements of artificial intelligence education, and the collection and analysis activities that take into account context using real-life data provided by public data platforms. In addition, since it consists of activities to predict the future based on data by using engineering tools such as entry and easy statistics, and creating an artificial intelligence prediction model, it is composed of a program focused on the ability to develop communication skills, information processing capabilities, and critical thinking skills. As a result of applying this program, not only did the program positively affect the statistical literacy of elementary school students, but we also observed students' interest, critical inquiry, and mathematical communication in the entire process of statistical problem solving.