방정숙 Pang Jeongsuk , 이수진 Lee Soojin , 강은진 Kang Eunjeen , 김리나 Kim Leena

DOI: JANT Vol.62(No.2) 175-194, 2023

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Despite the importance of pattern learning for elementary school students, few studies have investigated in detail the understanding of patterns of lower-grade students. This study aimed to analyze the understanding of patterns of second-grade elementary school students. Since the patterns in the second grade are taught through the unit called Finding Rules, students’ understanding of patterns was compared and contrasted before and after they learned the unit. To this end, a written instrument to measure students’ understanding of patterns was developed on the basis of previous studies on pattern learning for lower-grade students. A total of 189 students were analyzed. As a result of the study, the overall correct answer rates in the post-test were higher in most items than those in the pre-test, illustrating the positive effect of the specific unit. However, students found it difficult to find rules in which two components would change simultaneously either in geometric or numeric patterns, find patterns that would be similar in structure, represent geometric patterns into numeric patterns, find empty terms in increasing patterns, and reason the specific terms in patterns that can be differently interpreted. Based on these research results, this study sheds light on students’ understanding of patterns and suggests implications to improve their understanding.

송효섭 Song Hyo Seob , 정희선 Jung Hee Sun

DOI: JANT Vol.62(No.2) 195-209, 2023

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This study examined the effect and structural relationship of math teachers' teaching ability and class activity types on learners' value perception, confidence, and interest of mathematics at the student level and teacher level. To this end, data from 2nd graders of korea middle school in TIMSS 2019 were applied to the multilevel structural equation model. As a result of the analysis, the teaching ability of math teachers had a positive effect on value perception, confidence, and interest of mathematics at the student level and teacher level. Also, math value perception and math confidence had a positive effect on math interest. and it was confirmed that the teaching ability of math teachers indirectly had a positive effect on math interest by mediating math value perception and math confidence. In addition, the math class activity of applying what was learned to problems had a positive effect on math value perception, but it had a negative effect on math interest. and the class activity of the same ability group had a positive effect on math confidence and math interest. This study presents meaningful implications for math classes in the school field through a multilevel analysis of the student level and the teacher level.

권오남 Kwon Oh Nam , 권민성 Kwon Minsung , Lim Brian S. , 문진 Mun Jin , 정원 Jung Won , 조항윤 Cho Hangyun , 이경원 Lee Kyungwon

DOI: JANT Vol.62(No.2) 211-236, 2023

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The purpose of this study is to derive implications of preservice mathematics teacher education in Korea by analyzing the case of edTPA used in the preservice teacher training process in the United States. Recently, there has been a growing interest in promoting professional competencies considering not only the cognitive dimension related to knowledge development of preservice mathematics teachers but also the situational dimension considering reality in the classroom. The edTPA in the United States is a performance-based assessment based on lessons conducted by preservice teachers at school. This study analyzes the professional competencies required of preservice mathematics teachers by analyzing handbooks that described the case of edTPA in which preservice mathematics teachers in the United States participate. The edTPA includes planning, instruction, and assessment tasks, and continuous tasks are performed in connection with classes. Thus, the analysis is conducted on the points of linkage between the description of evaluation items and criteria in the planning, instruction, and assessment tasks, as well as the professional competencies required from that linkage. As a result of analyzing the edTPA handbooks, the professional competencies required of preservice mathematics teachers in the edTPA assessment were the competency to focus on and implement specific mathematics lessons, the competency to reflectively understand the implementation and assessment of specific mathematics lessons, and the competency to make a progressive determination of students’ achievement related to their learning and their uses of language and representations. The results of this analysis can be used as constructs for competencies that can be assessed in the preservice in the organization of the preservice mathematics teacher curriculum and practice training semester system in Korea.

김원 Kim Won

DOI: JANT Vol.62(No.2) 237-255, 2023

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The objective of this study is to explore the meaning generated through discourse in three different types of 1st-grade middle school textbooks in Korea and CMP textbook in the United States, specifically focusing on histograms. Through a discursive perspective, the study aims to analyze the characteristics of questioning within the stages of statistical problem-solving found in histogram tasks. The findings highlight several significant points. Firstly, variations exist in the definitions of histograms between Korean and US CMP textbooks. Secondly, diverse discursive structures contribute to the interpretation and understanding of histograms in textbooks. Thirdly, limitations are observed in the stages of statistical problem-solving reflected in histogram tasks. Lastly, distinctions are identified in the types of questioning employed in histogram tasks between Korean and US CMP textbooks. Building on these insights, the study suggests concrete ideas for enhancing the process of defining histograms and refining the questioning in histogram tasks.

오영석 Oh Young-seok , 김동중 Kim Dong-joong

DOI: JANT Vol.62(No.2) 257-268, 2023

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The purpose of the study is to analyze the characteristics of open-ended tasks in terms of cognitive demands. For this purpose, we analyzed characteristics of open-ended tasks presented in the sequence units of three high school mathematics textbooks. The results of the study have revealed that low cognitive demand levels of open-ended tasks had characteristics including procedures within previous tasks or within those tasks. On the other hand, high cognitive demand levels of open-ended tasks had characteristics of actively exploring new conditions to gain access to what is being sought, requesting a basis for judgement, linking various representations to the concepts of sequences, or requiring a variety of answers. These results are significant in that they not only specified the characteristics of open-ended tasks with high cognitive demands in terms of the intended curriculum, but also provided a direction for the development of open-ended taks with high congitive demands.

안은경 Ahn Eunkyung , 고호경 Ko Ho Kyoung

DOI: JANT Vol.62(No.2) 269-287, 2023

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Matrix theory is widely used not only in mathematics, natural sciences, and engineering, but also in social sciences and artificial intelligence. In the 2009 revised mathematics curriculum, matrices were removed from high school math education to reduce the burden on students, but in anticipation of the age of artificial intelligence, they will be reintegrated into the 2022 revised education curriculum. Therefore, there is a need to analyze the matrix content covered in other countries to suggest a meaningful direction for matrix education and to derive implications for textbook composition. In this study, we analyzed the German mathematics curriculum and standard education curriculum, as well as the matrix units in the German Hesse state mathematics curriculum and textbook, and identified the characteristics of their content elements and development methods. As a result of our analysis, it was found that the German textbooks cover matrices in three categories: matrices for solving linear equations, matrices for explaining linear transformations, and matrices for explaining transition processes. It was also found that the emphasis was on mathematical reasoning and modeling when learning matrices. Based on these findings, we suggest that if matrices are to be reintegrated into school mathematics, the curriculum should focus on deep conceptual understanding, mathematical reasoning, and mathematical modeling in textbook composition.

이정화 Lee Junghwa , 한채린 Han Chaereen , 임웅 Lim Woong

DOI: JANT Vol.62(No.2) 289-302, 2023

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In today’s digital information society, student knowledge and skills to analyze big data and make informed decisions have become an important goal of school mathematics. Integrating big data statistical projects with digital technologies in high school < Artificial Intelligence > mathematics courses has the potential to provide students with a learning experience of high impact that can develop these essential skills. This paper proposes a set of guidelines for designing effective big data statistical project-based tasks and evaluates the tasks in the artificial intelligence mathematics textbook against these criteria. The proposed guidelines recommend that projects should: (1) align knowledge and skills with the national school mathematics curriculum; (2) use preprocessed massive datasets; (3) employ data scientists' problem-solving methods; (4) encourage decision-making; (5) leverage technological tools; and (6) promote collaborative learning. The findings indicate that few textbooks fully align with these guidelines, with most failing to incorporate elements corresponding to Guideline 2 in their project tasks. In addition, most tasks in the textbooks overlook or omit data preprocessing, either by using smaller datasets or by using big data without any form of preprocessing. This can potentially result in misconceptions among students regarding the nature of big data. Furthermore, this paper discusses the relevant mathematical knowledge and skills necessary for artificial intelligence, as well as the potential benefits and pedagogical considerations associated with integrating technology into big data tasks. This research sheds light on teaching mathematical concepts with machine learning algorithms and the effective use of technology tools in big data education.