Analysis of Second Graders’ Counting an Irregular Arrangement of ThreeDigit Objects
장혜원 Chang Hyewon
36(4) 469486, 2022
장혜원 Chang Hyewon
DOI: JANT Vol.36(No.4) 469486, 2022
Counting occupies a fundamental and important position in mathematical learning due to its relation to number concepts and numeral operations. In particular, counting up to large numbers is an essential learning element in that it is structural counting that includes the understanding of place values as well as the onetoone correspondence and cardinal principles required by counting when introducing number concepts in the early stages of number learning. This study aims to derive didactical implications by investigating the possibility of and the strategies for counting large numbers that is expected to have no students’ experience because it is not composed of current textbook activities. To do this, 89 secondgrade elementary school students who learned the threedigit numbers and experienced groupcounting and skipcounting as textbook activities were provided with questions asking how many penguins were in a picture where 260 penguins were irregularly arranged and how to count. As a result of analyzing students’ responses in terms of the correct answer rate, the strategy used, and their cognitive characteristics, the incorrect answer rate was very high, and the use of decimal principles, groupcounting, counting by one, and partial sum strategies were confirmed. Based on these analysis results, several didactical implications were derived, including the need to include counting up to large numbers as textbook activities.

Exploration of Teacher Questions and Discourse Types in Chinese Mathematics Classrooms
Liu Wenting
36(4) 487509, 2022
Liu Wenting
DOI: JANT Vol.36(No.4) 487509, 2022
The purpose of this study is to analyze classroom discourse in the math classroom of middle school in China, which has a unique math classroom background of entrance examination for high school. To this end, this study analyzed teacher question statistics and episodes by teacher question type as starting speech in mathematics classroom discourse, and five IRF subtypes were especially identified by class discourse structure analysis. The data were analyzed focusing on a total of 15 transcripts of math classes recorded by three math teachers at H School in Guiyang, Guizhou Province, China, and written interviews of teachers. According to the results of this study, an average of 20 teacher questions were observed for each class, and the teacher question type was classified into confirmation question (understanding confirmation question, explanation request question, and double check question) and information question (information presentation question). In addition, according to classroom discourse analysis, the IRF discourse structure was divided into fragmentary evaluation, evaluation+reason, evidence of explanation, evaluation+student response restatement, guidance on other thoughts or solutions, and student answer correction or teacher opinion presentation.

CARE Modelbased Math Learning Coaching Model Development Study
김정현 Kim Jung Hyun , 고호경 Ko Ho Kyoung
36(4) 511533, 2022
김정현 Kim Jung Hyun , 고호경 Ko Ho Kyoung
DOI: JANT Vol.36(No.4) 511533, 2022
The purpose of this study is to develop a learning coaching model suitable for the mathematics subject by reflecting the characteristics of the mathematics subject and the mathematics teaching/learning process in the CARE learning coaching model that supports students' selfdirected learning. The mathematics learning coaching model developed in this study is a ‘step’ and ‘element’ to apply coaching, and a ‘strategy’ for carrying out it. Mathematics learning coaching model evaluated rapport, trust, state management, and math pretest as elements of 'creating a comfortable atmosphere', and problem recognition, hypercognition, restructuring, initiative, and math learning ability as elements of 'improving perception'. Selfefficacy, learning readiness, confirmation (feedback) as elements of the 'reawakening of learning immersion' stage, voluntary motivation and success experiences as elements of the 'empowerment' stage, and various math learning strategies to perform each element presented. The math learning coaching model can be used to help math teachers motivate students to learn and help students solve their own problems.

Analysis on Statistical Problem Solving Process of Preservice Mathematics Teachers: Focus on the Result Interpretation Stage
김소형 Kim Sohyung , 한선영 Han Sunyoung
36(4) 535558, 2022
김소형 Kim Sohyung , 한선영 Han Sunyoung
DOI: JANT Vol.36(No.4) 535558, 2022
In the current society, where statistical literacy is recognized as an important ability, statistical education utilizing the statistical problem solving, a series of processes for performing statistics, is required. The result interpretation stage is especially important because many forms of statistics we encounter in our daily lives are the information from the analysis results. In this study, data on private education were provided to preservice mathematics teachers, and a project was carried out in which they could experience a statistical problem solving process using the population mean estimation. Therefore, this study analyzed the characteristics shown by preservice mathematics teachers during the result interpretation stage. First, many preservice mathematics teachers interpreted results based on the data, but the inference was found to be a level of 2 which is not reasonable. Second, preservice mathematics teachers in this study made various kinds of decisions related to public education, such as improving classes and afterschool classes. In addition, the preservice mathematics teachers in this study seem to have made decisions based on statistical analysis results, but they made general decisions that teachers could make, rather than specifically. Third, the preservice mathematics teachers of this study were reflective about the question formulation stage, organizing & reducing data stage, and the result interpretation stage, but no one was reflective about the result interpretation stage.

A Comparative Analysis of Economic Terms & Function Notations and Function Graphs in High School < Mathematics for Economics >, < Economics > Textbooks
이경원 Lee Kyungwon , 권오남 Kwon Oh Nam
36(4) 559587, 2022
이경원 Lee Kyungwon , 권오남 Kwon Oh Nam
DOI: JANT Vol.36(No.4) 559587, 2022
The purpose of this study is to derive implications for the development of the next curriculum and textbooks by comparing and analyzing the textbooks of the 2015 revised high school mathematics curriculum < Mathematics for Economics > and social studies curriculum < Economics >. In the < Mathematics for Economics > textbooks, economic terms and function notations should be introduced. Additionally, the use of graphs for economicrelated functions is different from the use of graphs in mathematics in the < Mathematics for Economics > textbooks. For these reasons, the usage of economic terms, function notations, and function graphs covered in the < Mathematics for Economics > textbooks were compared and analyzed with the usage in the < Economics > textbooks. In the < Mathematics for Economics > textbooks, economic terms that are highly related to mathematics are defined and presented. Contrary to the conventions of mathematics and economics, the function notations in the < Mathematics for Economics > textbooks were used inconsistently because uppercase and lowercase letters were mixed in the function notations. Function graphs in the < Mathematics for Economics > textbooks had differences in the range of values represented by the variables regarding axes and scaling. The < Mathematics for Economics > textbooks did not provide a mathematical interpretation of the translation or slope. In the course of < Mathematics for Economics >, it is necessary to specify considerations for teaching and learning, and assessment in the curriculum to promote students' understanding of mathematics and economics. The descriptions in the curriculum document and textbooks of < Mathematics for Economics > should be supplemented to provide learning opportunities for mathematical interpretation of economicsrelated contents.

A Comparative Analysis of pi in Elementary School Mathematics Textbooks
최은아 Choi Eunah , 강향임 Kang Hyangim
36(4) 589610, 2022
최은아 Choi Eunah , 강향임 Kang Hyangim
DOI: JANT Vol.36(No.4) 589610, 2022
This study aimed to derive pedagogical implications by comparing and analyzing how the concept of pi is taught in 10 different elementary mathematics textbooks, which are scheduled to be applied from 2023. We developed a textbook analysis framework by previous studies on the concept of pi and the teaching of pi, and analyzed in terms of three instructional elements (i.e. inferring conceptsof pi, understanding properties of pi, and applying relationships). We derived the need to emphasize various contexts for estimation of pi, presentation of problem situations that provide motivation to actually measure diameters and circumferences, providing an opportunity to explore the properties of measurement, and an experience the flexibility of selecting an approximate value of pi. Based on the above conclusions and pedagogical implications through the research results., we suggested ways to teach the concept of pi in elementary mathematics and improvement points for developing textbooks focusing on the context of introduction of pi and the use of technological tools.

Case Study on College Calculus Education for Vocational High School Graduates with Coding
이재화 Lee Jae Hwa , 이상구 Lee Sanggu , 함윤미 Ham Yoonmee
36(4) 611626, 2022
이재화 Lee Jae Hwa , 이상구 Lee Sanggu , 함윤미 Ham Yoonmee
DOI: JANT Vol.36(No.4) 611626, 2022
In this study, we introduced the case of college calculus course for vocational high school graduates with coding. We suggest this case as an alternative to overcome mathematics anxiety. Contents, python/SageMath codes, and textbook for this course, which help students to easily and quickly review middle and high school mathematics, were newly developed by authors. Due to the use of codes and chat with classmates in learning management system, most of the students who took this course reported that they no longer felt anxious in complex mathematics problems, had a full understanding of calculus concepts, could solve almost problems in any calculus textbooks with or without codes, and could explain calculus concepts to other students in their own words. In this way if mathematics and coding is properly used in mathematics education, it helps students with weak mathematical backgrounds or mathematics anxiety to restore confidence in mathematics in college. This could be applicable in secondary mathematics education.

A Fabrication of an Angle Trisection Tool Using Veprtskii's Method
한인기 Han Inki
36(4) 627644, 2022
한인기 Han Inki
DOI: JANT Vol.36(No.4) 627644, 2022
In this study various angle trisection tools based on Archimedes' insertion method were investigated, some tools were fabricated and their characteristics were compared. Through these works, it was found that factors such as the convenience of use, arbitrariness of the trisected angle, and simplicity of structure should be considered in the production and utilization of the trisection tool.
Considering the factors described above, attention was paid to the method proposed by Veprtskii A.I. in 1888 as a making method of the angle trisection tool. In this study, we improved the method proposed by Veprtskii A.I., we used two wooden chopsticks and a string to make an angle trisection tool. The improved trisection tool had fewer parts than other trisection tools, a simple structure, and more convenient usage. In particular, this tool divided an arbitrary angle(not a specific angle) into the same three parts, and the production cost was low and the production process was simple. This tool is expected to be widely used in concrete activities related to the properties of the exterior angles of triangles and the properties of isosceles triangles in mathematics classrooms.
