Exploring the Conceptual Elements and Meaning of Metaaffect in Mathematics Learning
손복은 Son Bok Eun , 고호경 Ko Ho Kyoung
35(4) 359376, 2021
손복은 Son Bok Eun , 고호경 Ko Ho Kyoung
DOI: JANT Vol.35(No.4) 359376, 2021
In this study, in accordance with the research trend that the learner’s emotions expressed positively or negatively in mathematics learning or the learner's beliefs and attitudes toward mathematics learning affect the results of mathematics learning, the learner's emotions and affective factors are analyzed in the learner's own learning. A power that can be adjusted according to a goal or purpose is needed, and I tried to explain this power through metaaffect. To this end, the meaning of the definitional and conceptual factors of metaaffect was explored based on prior studies. Affective factors of metaaffect were viewed as emotions, attitudes, and beliefs, and conceptual factors of metaaffect were viewed as awareness, evaluating, controlling, utilization, and monitoring, and the meaning of each conceptual factor was also defined. In this study, the conceptual factors and meanings of metaaffect in terms of using them to help in learning mathematics by controlling them, beyond the identification or examination of the characteristics of the affective factors, which are meaningfully dealt with in the field of mathematics education.

Exploring Central Beliefs through Noticing Analysis of Mathematics Teachers
강성권 Kang Sung Kwon , 홍진곤 Hong Jinkon
35(4) 377411, 2021
강성권 Kang Sung Kwon , 홍진곤 Hong Jinkon
DOI: JANT Vol.35(No.4) 377411, 2021
This study aims to explore central and peripheral beliefs of mathematics teachers in the context of teaching and learning. For this purpose, this study analyzed teacher noticing of 8 mathematics teachers who are inservice in terms of mathematical beliefs using videoclips of math lessons. When the teachers in the videoclips seemed to have a teaching and learning problem, teachers who adopt noticing critized the classroom situation by reflecting his or her own mathematical beliefs and suggested alternatives. In addition, through noticing analysis, teachers' mathematical beliefs reflected in specific topics such as student participation in teaching and learning were compared to reveal their individual central and peripheral beliefs. Through these research results, this study proposed a model that extracts the central and peripheral beliefs of math teachers from the constraints of the teaching and learning context using noticing analysis. Additionally, it was possible to observe the teacher decisionmaking and expertise of mathematics teachers.

The Empty Set as a Mathematical Object
유미영 Ryou Miyeong , 최영기 Choi Younggi
35(4) 413423, 2021
유미영 Ryou Miyeong , 최영기 Choi Younggi
DOI: JANT Vol.35(No.4) 413423, 2021
This study investigated the empty set which is one of the mathematical objects. We inquired some misconceptions about empty set and the background of imposing empty set. Also we studied historical background of the introduction of empty set and the axiomatic system of Set theory. We investigated the nature of mathematical object through studying empty set, pure conceptual entity. In this study we study about the existence of empty set by investigating Alian Badiou’s ontology known as based on the axiomatic set theory. we attempted to explain the relation between simultaneous equations and sets. Thus we pondered the meaning of the existence of empty set. Finally we commented about the thoughts of sets from a different standpoint and presented the meaning of axiomatic and philosophical aspect of mathematics.

A Case Study on Teaching the Sum of the Interior Angles of a Triangle Using Measurement Errors
오영열 Oh Youngyoul , 박주경 Park Jukyung
35(4) 425444, 2021
오영열 Oh Youngyoul , 박주경 Park Jukyung
DOI: JANT Vol.35(No.4) 425444, 2021
In this study, under the assumption that the goal pursued in measurement area can be reached through the composition of the measurement activity considering the mathematical process, the method of summing the interior angles of a triangle using the measurement error was applied to the 4th grade class of the elementary school. Results of the study, first, students were able to recognize the possibility of measurement error by learning the sum of the interior angles of a triangle using the measurement error. Second, the discussion process based on the measurement error became the basis for students to attempt mathematical justification. Third, the manipulation activity using the semicircle was recognized as a natural and intuitive way of mathematical justification by the students and led to generalization. Fourth, the method of guiding the sum of the interior angles of a triangle using the measurement error contributed to the development of students’ mathematical communication skills and positive attitudes toward mathematics.

An Analysis of 'Related Learning Elements' Reflected in < Artificial Intelligence Mathematics > Textbooks
권오남 Kwon Oh Nam , 이경원 Lee Kyungwon , 오세준 Oh Se Jun , 박정숙 Park Jung Sook
35(4) 445473, 2021
권오남 Kwon Oh Nam , 이경원 Lee Kyungwon , 오세준 Oh Se Jun , 박정숙 Park Jung Sook
DOI: JANT Vol.35(No.4) 445473, 2021
The purpose of this study is to derive implications for the design of the next curriculum by analyzing the < Artificial Intelligence Mathematics > textbooks designed as a new subject in the 2015 revised curriculum. In the mathematics curriculum documents of < Artificial Intelligence Mathematics >, ‘related learning elements’ are presented instead of ‘learning elements’. 'Related learning elements' are defined as mathematical concepts or principles that can be used in the context of artificial intelligence, but there are no specific restrictions on the amount and scope of dealing with 'related learning elements'. Accordingly, the aspects of ‘related learning elements’ reflected in the < Artificial Intelligence Mathematics > textbooks were analyzed focusing on the textbook format, the amount and scope of contents, and the ways of using technological tools. There were differences in the format of describing 'related learning elements' in the textbook by textbook and the amount and scope of handling mathematics concepts. Although similar technological tools were dealt with in each textbook so that ‘related learning elements’ could be used in the context of artificial intelligence, the focus was on computations and interpretation of results. In order to fully reflect the intention of the curriculum in textbooks, a systematic discussion on 'related learning elements' will be necessary. Additionally, in order for students to experience the use of mathematics in artificial intelligence, substantialized activities that can set and solve problems using technological tools should be included in textbooks.

A Study on the Development of PersonBased Class Materials in Subject < Mathematics Project Inquiry Subject >
이동근 Lee Dong Gun
35(4) 475504, 2021
이동근 Lee Dong Gun
DOI: JANT Vol.35(No.4) 475504, 2021
This study is a study that developed class materials that can be applied directly to classes by field teachers in consideration of '< Mathematics Project Inquiry Subject > research on the development is valuable as a field support study.', 'In material development, organizing data centering on the knowledge composition and inquiry activities of characters related to the mathematics concept can help develop class materials', and 'The fact that the development of subject data for < Mathematics Project Inquiry Subject > has been insufficient'.
To this end, this study went through the procedure of ‘establishing a data development plan, data development, verifying field teachers on development data, verifying subject experts on development data, and developing final data reflecting verification opinions.’ Therefore, based on the 1st 50 minutes reflecting the task exploration model, it was possible to develop class materials for the 3rd time. In this study, development data were presented with a 17week curriculum plan, a class guidance plan that presents teacherstudent interaction, and a task development form that students fill out and submit in class.
This study was developed with the developed data in mind to be applied to actual classes. Therefore, a followup study is needed to apply the developed data to actual classes and analyze the results.

Comparative Research on Teaching Method for Multiplication by 2Digit Numbers in Elementary Mathematics Textbooks of Korea, Japan, Singapore, and USA
최은아 Choi Eunah , 정연준 Joung Younjoon
35(4) 505525, 2021
최은아 Choi Eunah , 정연준 Joung Younjoon
DOI: JANT Vol.35(No.4) 505525, 2021
In this study, we investigated how multiplication by 2digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the ‘×tens’ teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

Examining Mathematics Teachers’ Intentions regarding Formative Assessment
이다은 Lee Daeun , 김구연 Kim Gooyeon
35(4) 527546, 2021
이다은 Lee Daeun , 김구연 Kim Gooyeon
DOI: JANT Vol.35(No.4) 527546, 2021
The purpose of this study is to reveal what mathematics teachers focus on and how they assess students’ thinking during lessons enacted. For this purpose, we googled and searched internet sites to collect formative assessment materials for the year 2014 to 2019. The formative assessment tasks data were analyzed according to the levels cognitive demand levels and tasks suggested in textbooks in terms of degrees to which how they are related. The data analysis suggested as follows: a) most of the formative assessment tasks were at the lowlevel, in particular, PNC level tasks that require applying particular procedures without connections to concepts and meaning underlying the procedures, b) the assessment tasks appeared to be very similar to the tasks suggested in the secondary mathematics textbooks, and c) it seemed that 3 types of formative assessment, observation notes, selfassessment, and peerassessment were dominantly utilized during mathematics lessons and these different types of formative assessment were employed apparently to find out whether students participated actively in class and in group activity, not how they go through understanding or thinking processes.

An Analysis of the Capacity Concept in Elementary School Mathematics: Focused on the Textbooks and Teacher Understanding
김정원 Kim Jeongwon , 방정숙 Pang Jeongsuk
35(4) 547573, 2021
김정원 Kim Jeongwon , 방정숙 Pang Jeongsuk
DOI: JANT Vol.35(No.4) 547573, 2021
Capacity is a concept that has been covered in elementary mathematics textbooks but its meaning has not been accurately defined in the textbooks. Two units, liter (L) and milliliter (mL), are introduced as the units of capacity in the textbooks, but they are the units of volume according to the International System of Unit. These stimulated us to analyze what capacity is, and how the capacity is related to the concept of volume. This study scrutinized how the different elementary mathematics textbooks that were developed from the first national curriculum to the most recently revised curriculum introduced the capacity and explained the relationship between capacity and volume. This study also examined the understanding of capacity by elementary school teachers using a questionnaire. The results of this study showed that the concept of capacity has been mostly introduced in the third grade in common but that there were differences among textbooks in terms of how they presented and used the concept of capacity as well as whether they described its definition or relationship with the concept of volume. Regarding the results of teachers’ understanding, most teachers could explain the capacity as either “the size of the inner space of the container” or “the amount that can be contained” but some of them provided only superficial or inappropriate feedback for the students with the common misunderstandings of capacity. Based on these results, this paper presents implications for textbook developers and teachers to better address the concept of capacity.
