Study on the Mathematics Teaching and Learning Artificial Intelligence Platform Analysis
박혜연 Park Hye Yeon , 손복은 Son Bok Eun , 고호경 Ko Ho Kyoung
36(1) 121, 2022
박혜연 Park Hye Yeon , 손복은 Son Bok Eun , 고호경 Ko Ho Kyoung
DOI: JANT Vol.36(No.1) 121, 2022
The purpose of this study is to analyze the current situation of EduTech, which is proposed as a way to build a flexible learning environment regardless of time and place according to the use of digital technology in mathematics subjects. The process of designing classes to use the EduTech platform, which is still in the development introduction stage, in public education is still difficult, and research to observe its effects and characteristics is also in its early stages. However, in the stage of preparing for future education, it is a meaningful process to grasp the current situation and point out the direction in preparation for the future in which EduTech will be actively applied to education. Accordingly, the current situation and utilization trends of EduTech at home and abroad were confirmed, and the functions and roles of EduTech platforms used in mathematics were analyzed. As a result of the analysis, the EduTech platform was pursuing learners' selfdirected learning by constructing its functions so that they could be useful for individual learning of learners in hierarchical mathematics education. In addition, we have confirmed that the platform is evolving to be useful for teachers' work reduction, suitable activities, and evaluations learning management. Therefore, it is necessary to implement instructional design and individual customized learning support measures for students that can efficiently utilize these platforms in the future.

Understanding the Proof of Inverse Square Law of Newton’s Principia from a Heuristic Point of View
강정기 Kang Jeong Gi
36(1) 2338, 2022
강정기 Kang Jeong Gi
DOI: JANT Vol.36(No.1) 2338, 2022
The study provided a perspective on which readers can see Newton’s proof heuristically in order to overcome the difficulty of proof showing 'QT^{2}/QR converges to the latus rectum of ellipse’ in the proof of the inverse square law of Newton's Principia. The heuristic perspective is as follows: The starting point of the proof is the belief that if we transform the denominators and numerators of QT^{2}/QR into expression with respect to segments related to diameter and conjugate diameter, we may obtain some constant, the desired value, by their relationship PV × VG/QV^{2}/PC^{2}/CD^{2} in Apollonius’ Conic sections. The heuristic perspective proposed in this study is meaningful because it can help readers understand Newton's proof more easily by presenting the direction of transformation of QT^{2}/QR.

A Case Study on the Relationship between Indefinite Integral and Definite Integral according to the AiC Perspective
박민규 Park Minkyu , 이경화 Lee Kyeonghwa
36(1) 3957, 2022
박민규 Park Minkyu , 이경화 Lee Kyeonghwa
DOI: JANT Vol.36(No.1) 3957, 2022
This study aims to design an integral instruction method that follows the Abstraction in Context (AiC) framework proposed by Hershkowitz, Schwarz, and Dreyfus to help students in acquiring indepth understanding of the relationship between indefinite integrals and definite integrals and to analyze how the students’ understanding improved as a result. To this end, we implemented lessons according to the integral instruction method designed for eight 11th grade students in a science high school. We recorded and analyzed data from graded student worksheets and transcripts of classroom recordings. Results show that students comprehend three knowledge elements regarding relationship between indefinite integral and definite integral: the instantaneous rate of change of accumulation function, the calculation of a definite integral through an indefinite integral, and The determination of indefinite integral by the accumulation function. The findings suggest that the AiC framework is useful for designing didactical activities for conceptual learning, and the accumulation function can serve as a basis for teaching the three knowledge elements regarding relationship between indefinite integral and definite integral.

A Case Study of Lesson Design Based on Mathematical Modeling of PreService Mathematics Teachers
최희선 Choi Heesun
36(1) 5972, 2022
최희선 Choi Heesun
DOI: JANT Vol.36(No.1) 5972, 2022
The purpose of this study is to understand the characteristics of the mathematical modeling tasks and lesson designs developed by preservice teachers based on the inherent awareness of mathematical modeling, considering the importance of creating a task to perform mathematical modeling activity and designing a lesson. As a result, the mathematical modeling tasks developed by preservice teachers mainly presents an appropriate amount of information using real life contexts for the purpose of learning using concepts, and it showed a tendency to develop to the level of cognitive demand that required procedures with connections to understanding, meaning, or concepts. And most of the developed modeling taskbased lessons showed a tendency to design warmup activity, modeleliciting activity, and modelexploration activity. This result is due to the lack of experience of preservice teachers in creating mathematical modeling tasks. Therefore, it is necessary to continuously provide opportunities for preservice teachers to learn concepts or create mathematical modeling tasks intended for exploration according to various mathematical contents, thereby actively cultivating their ability to create modeling tasks in the course of training preservice teachers. Furthermore, it is necessary to strengthen the expertise in mathematical modeling teaching and learning by providing opportunities to actually perform the mathematical modelingbased classes designed by preservice teachers and to experience the process of reflecting on the lessons.

A Study on Textbooks and Languages Used in College Mathematics Education
이상구 Lee Sanggu , 유주연 Yoo Jooyeon , 함윤미 Ham Yoonmee
36(1) 7388, 2022
이상구 Lee Sanggu , 유주연 Yoo Jooyeon , 함윤미 Ham Yoonmee
DOI: JANT Vol.36(No.1) 7388, 2022
Mathematics is a way of thinking. To do mathematics means to think mathematically. In other words, mathematics education and mathematics literacy are related. In elementary and secondary school mathematics education in many countries, teaching of mathematics using textbooks is conducted mostly in their native language. So mathematics education takes place while reading, writing, listening, and speaking mathematics.
Analysis of mathematics textbooks for the lower grades of undergraduate mathematics shows that most advanced countries in mathematics use excellent undergraduate mathematics textbooks written in their native language. However, the ratio of using imported textbooks from foreign countries is particularly high in the case of textbooks for mathematics majors at Korean universities. In this article, the effect of language used in university mathematics education is analized. In particular, the importance of highquality leadingedge university mathematics textbooks in native language is introduced by analyzing the case of Bourbaki in France and ‘War of language’ at the Israel Institute of Technology.
The innovation of French university mathematics education in the 20th century began with Bourbaki's 'Fundamentals of Mathematics', a French textbook written in his native language. Israel's Technion and the Hebrew University of Jerusalem continue to teach all subjects in their mother tongue. This has led to produce many Nobel Prize and Fields medal winners in these two countries. This study shows that textbooks and languages used in university mathematics education has affected mathematical literacy.

A Study of the Questions Presented in Chapters of Number and Operation Area in Elementary School Mathematics Textbooks
도주원 Do Joowon
36(1) 89105, 2022
도주원 Do Joowon
DOI: JANT Vol.36(No.1) 89105, 2022
In this research, in order to obtain teaching/learning implications for effective use of questions when teaching number and operation area, the types of questions presented in chapters of number and operation area of 2015 revised elementary math textbooks and the function of questions were compared and analyzed by grade cluster. As a result of this research, the types of questions presented in chapters of number and operation area showed a high percentage of occurrences in the order of reasoning questions, factual questions, and open questions not calling for reasoning in common by grade cluster. And reasoning questions were predominant in all grade clusters. In addition, in all grade clasters, the proportion of questions acting as a function to help guess, invention, and solving problems and questions acting as a function to help mathematical reasoning were relatively high. As such, it can be inferred that the types and functions of the questions presented in chapters of number and operation area are related to the characteristics of the learning content by grade cluster. This research will be able to contribute to the preparation of advanced teaching/learning plans by providing reference materials in the questions when teaching number and operation area.

A Study on the Development of FeedbackBased Instructional Materials for ProcessFocused Assessment Classes in High School Mathematics Classes
이동근 Lee Dong Gun , 한창훈 Han Chang Hun
36(1) 107138, 2022
이동근 Lee Dong Gun , 한창훈 Han Chang Hun
DOI: JANT Vol.36(No.1) 107138, 2022
This study is a study that developed class materials that can apply ProcessFocused Assessment to classes by paying attention to feedback using teacher learning community programs centered on teachers belonging to the same school in the field. In particular, this study was conducted with the aim of developing class materials applicable to actual classes. At this time, We thought about how to provide appropriate feedback when applying coursebased evaluation in school field classes. It was conducted according to the procedure of data development research by Lee & Ahn(2021).
As for the procedure of data development itself, an evaluation plan was established by establishing a strategy to reconstruct achievement standards and confirm understanding based on curriculum analysis. Next, an evaluation task, a scoring standard table, and a preliminary feedback preparation table were developed. In addition, based on these development materials, a learning guidance plan that can predict scenes when applying actual classes was developed as a result.
This study has value as a practical study that can contribute to providing a link between theory and field schools. It is also meaningful in that it considered how the teacher would grasp when to provide feedback in performing rocessFocused Assessment. Likewise, in providing feedback by teachers, it is meaningful in that it reflects in the data development how to prepare in advance and take classes according to the characteristics of the subject. Finally, it seems that the possibility of field application can be improved in that the results of the 4th class developed in this study are presented in a form applicable to the class directly in the field.

An Analysis of Differentiated Teaching Materials in the Russian Mathematics Textbooks
한인기 Han Inki
36(1) 139170, 2022
한인기 Han Inki
DOI: JANT Vol.36(No.1) 139170, 2022
In relation to differentiated mathematics education, Russia has a longer experience in research and practice than Korea. The mathematics curriculum for 1011 grades currently in use in Russia is a levelspecific curriculum and consists of a basic level and an advanced level. And in Russia mathematics textbooks for 1011 grades are also textbooks for each level. In this study, we analyzed basic level textbook and advanced level textbook written by the same author group among the textbooks ‘Algebra and Introduction of Mathematical Analysis’ of the 10th grade in Russia.
To analyze the main learning contents and textbook descriptions that were added in advanced level the ‘real numbers’ and ‘complex numbers’ sections were studied. The main contents of basic and advanced level textbooks for ‘functions’, ‘trigonometric functions’, ‘trigonometric equations’, ‘conversions of trigonometric expressions’, and ‘derivatives’, which are included in both basic and advanced textbooks were compared and analyzed, and the descriptive characteristics of the definitions and theorems presented in the two levels of textbooks were also compared and analyzed.
From the results of this study, it is expected that various information on the contents of various level textbooks of mathematics, the differences between textbooks for each level, and strategies for the composition of textbooks for various level can be accumulated.

An Analysis of Descriptions about the History of Mathematics in the 2015 Mathematics Textbooks and Teacher Guides for Elementary School Level
박민구 Park Mingu
36(1) 171199, 2022
박민구 Park Mingu
DOI: JANT Vol.36(No.1) 171199, 2022
In this study, we review contents to supplement the descriptions of the history of mathematics in the 2015 mathematics textbooks and teacher guides for the elementary school level and offer our opinion on them. For this purpose, we conducted a literature review on 24 types of 2015 mathematics textbooks and teacher guides for the elementary school level. The results of this study are as follows: A total of 10 topics were found whose contents were supplemented with descriptions. They were the “Arithmetic of the Ancient Egyptians,” the “A'hmosè Papyrus in Mathematics Textbooks of the Ancient Egyptians,” “The Old Akkadian Square Band in Mesopotamia,” “The Relationship of the Old Babylonians in Mesopotamia with the Angle,” “The Pi of the Ancient Egyptians and the Old Babylonians,” “The Square Roots 2 of the Ancient Egyptians and the Old Babylonians,” “The Relationship of the Islamites with the Decimal Fraction,” “Two Arguments for the Roots of the Golden Ratio,” “The Relationship of Archimedes with the Exhaustion Method,” and “The Design of Flats.” Then, their specific supplements were suggested. It is expected that this will overcome the perspective of the history of the Axial Age and acknowledge and accept the perspective evidencing the transfer of mathematical culture from Ancient Egypt and Old Babylonia to Ancient Greece and Hellenism, and then through Central Asia to Europe.
