Teaching and Learning of University Calculus with Pythonbased Coding Education
박경은 Park Kyungeun , 이상구 Lee Sanggu , 함윤미 Ham Yoonmee , 이재화 Lee Jae Hwa
33(3) 163180, 2019
박경은 Park Kyungeun , 이상구 Lee Sanggu , 함윤미 Ham Yoonmee , 이재화 Lee Jae Hwa
DOI: JANT Vol.33(No.3) 163180, 2019
This study introduces a development of calculus contents which makes to understand the main concepts of calculus in a short period of time and to enhance problem solving and computational thinking for complex problems encountered in the real world for college freshmen with diverse backgrounds. As a concrete measure, we developed ‘Teaching and Learning’ contents and Pythonbased code for Calculus I and II which was used in actual classroom. In other words, the entire process of teaching and learning, action plan, and evaluation method for calculus class with Python based coding are reported and shared. In anytime and anywhere, our students were able to freely practice and effectively exercise calculus problems. By using the given code, students could gain meaningful understanding of calculus contents and were able to expand their computational thinking skills. In addition, we share a way that it motivated student activities, and evaluated students fairly based on data which they generated, but still instructor’s work load is less than before. Therefore, it can be a teaching and learning model for college mathematics which shows a possibility to cover calculus concepts and computational thinking at once in a innovative way for the 21st century.

Relations between undergraduates’ motivations and emotions for learning mathematics in mathematics class centered on peer discussions : focusing on their needs
박석준 Park Seokjoon , 이경원 Lee Kyungwon , 권오남 Kwon Oh Nam
33(3) 181205, 2019
박석준 Park Seokjoon , 이경원 Lee Kyungwon , 권오남 Kwon Oh Nam
DOI: JANT Vol.33(No.3) 181205, 2019
This study analyzed how university students’ motivations for learning mathematics and emotions for learning mathematics occur and how they relate to each other by introducing the factor called needs in the particular context of mathematics learning, mathematics class centered on peer discussions. We conceptualized the key concepts of the study, motivation for learning mathematics and emotion for learning mathematics. Based on them, we drew specific ways to observe motivation and emotion for learning mathematics and conduct the research. As a result, motivations for learning mathematics occurred to satisfy some needs. Also, positive emotions for learning mathematics occurred when some needs were satisfied, whereas negative emotion for learning mathematics occurred when some needs were not satisfied. Furthermore, when the needs leading to motivations for leaning mathematics were satisfied, positive emotions for learning mathematics occurred. The unfulfilled needs leading to negative emotions for learning mathematics make motivations for learning mathematics occur to satisfy those needs.

On Developments of TeachingLearning Contents and Constructivist Teaching Methods Using Mobile Applications Based on Augmented Reality in Mathematics Education
김병학 Kim Byung Hak , 송진수 Song Jinsu , 박예은 Park Ye Eun , 장요한 Jang Yo Han , 정영훈 Jeong Young Hun , 안진희 Ahn Jin Hee , 김준혁 Kim Jun Hyuk , 고은령 Go Eunryeong , 장인경 Jang In Kyung
33(3) 207229, 2019
김병학 Kim Byung Hak , 송진수 Song Jinsu , 박예은 Park Ye Eun , 장요한 Jang Yo Han , 정영훈 Jeong Young Hun , 안진희 Ahn Jin Hee , 김준혁 Kim Jun Hyuk , 고은령 Go Eunryeong , 장인경 Jang In Kyung
DOI: JANT Vol.33(No.3) 207229, 2019
In the era of the Fourth Industrial Revolution, various attempts have been made to incorporate ICT technology into mathematics teaching and learning, and the necessity and efficiency of classroom instruction using flipped learning, virtual reality and augmented reality have attracted attention. This leads to an increase in demand for instructional contents and their use in education. Therefore, there is a growing need for the development of instructional contents that can be applied in the field and the study of teaching methods.
In this point of view, this research classifies the types of teachinglearning, presents the flipped learning instruction and mathematics contents by teachinglearning types using constructivist mathematics education principles and augmented realitybased mobile applications.
These methods and lesson plans can provide a useful framework for teachinglearning in mathematics education.

Changing in Perception of PreMathematics Teachers about ProjectBased Learning
김용석 Kim Yongseok , 김소형 Kim Sohyung , 한선영 Han Sunyoung
33(3) 231254, 2019
김용석 Kim Yongseok , 김소형 Kim Sohyung , 한선영 Han Sunyoung
DOI: JANT Vol.33(No.3) 231254, 2019
As the teachercentered education is transformed into learningcentered education, the active knowledge construction of learner becomes important. Along with this change, projectbased learning is receiving attention. However, there are many problems to apply the results of research to preservice teachers because most of the previous studies have focused on elementary·middle·high school students. Therefore, this study examined the changes in perceptions of preservice mathematics teachers while projectbased learning progressed for one year. Preservice mathematics teachers had less experience with projectbased learning than group discussions, group activities. Also their perceptions was classified as five factors: ‘Instructional effects’, ‘Application and participant of projectbased learning’, ‘Achievement’, ‘Diffusion of projectbased learning’, ‘Student motivation’. Preservice mathematics teachers responded positive changes in perception that projectbased learning could be motivated to students but they responded negative changes in perception that projectbased learning could be distributed to school. They responded positive changes in perception that teachers can show their achievements by projectbased learning but they responded negative change in perception that teachers would be fun to apply projectbased learning. Also, they responded positive changes in perception that teachers and students were easy to apply or utilize projectbased learning.

A pedagogical discussion based on the historical analysis of the the development of the prime concept
강정기 Kang Jeong Gi
33(3) 255273, 2019
강정기 Kang Jeong Gi
DOI: JANT Vol.33(No.3) 255273, 2019
In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.

Analysis of trends in mathematics education research using text mining
진미르 Jin Mireu , 고호경 Ko Ho Kyoung
33(3) 275294, 2019
진미르 Jin Mireu , 고호경 Ko Ho Kyoung
DOI: JANT Vol.33(No.3) 275294, 2019
In order to understand the recent trends in mathematics education research papers, data mining method was applied to analyze journals of the mathematics education posterior to the year of 2016. Text mining method is useful in the sense that it utilizes statistical approach to understand the linkages and influencing relationship between concepts and deriving the meaning that data shows by visualizing the process. Therefore, this research analyzed the key words largely mentioned in the recent mathematics education journals. Also the correlation between the subjects of mathematics education was deduced by using topic modeling. By using the trend analysis tool it is possible to understand the vital point which researchers consider it as important in recent mathematics education area and at the same time we tried to use it as a fundamental data to decide the upcoming research topic that is worth noticing.

An International Comparison study in Mathematics Curriculum  Contents for Angle among the Korea, Singapore U.K., Australia and U.S.
최은 Choi Eun , 김서영 Kim Seo Yeong , 권오남 Kwon Oh Nam
33(3) 295317, 2019
최은 Choi Eun , 김서영 Kim Seo Yeong , 권오남 Kwon Oh Nam
DOI: JANT Vol.33(No.3) 295317, 2019
Angle concept is widely used in all mathematics curriculums and is a basic concept in geometric domain. Since angle have a multifaceted and affect subsequent learning, it is necessary for students to understand various angle concepts. In this study, Singapore, U.K., Australia, and U.S. are selected as comparable countries to examine the anglerelated contents and learning process that appear in the curriculum as a whole, and then look at the perspectives and the size aspects of angle in detail and give implications to the Korean curriculum based on them. According to the analysis, the four countries except Korea, supplement angle, complement angle, angles on a straight line, angles at a point, and finding angle were explicitly covered in the curriculum. And most countries gradually covered anglerelated contents over several years, compared to Korea which intensively studied in a particular school year. In common, definition of angle was described as static, measurement of angle was described as dynamic. But in Korean curriculum, dynamic views on angles are described later and less compared to other countries, and range of angle size was narrower than in other countries’. From this comparison, this study suggest to discuss how to place and develop various contents of characteristics of angle in curriculum, address the angle using both static and dynamic perspectives, and introduce the angle size as the amount of rotation to learn the reflex angle, 180°, 360° angle.

An Analysis of Understanding Level of High School Students Shown in Trigonometric Functions
이유빈 Lee Yu Bin , 조정수 Cho Cheong Soo
33(3) 319334, 2019
이유빈 Lee Yu Bin , 조정수 Cho Cheong Soo
DOI: JANT Vol.33(No.3) 319334, 2019
In this study, using the tasks related trigonometric functions, the degree of high school students’ understanding of the function concept was examined through the level of Hitt(1998). First, the degree of the students' understanding was classified by level, then the concept understanding was reclassified by the process or the object. As a result, high school students’ concept understanding showed incompleteness in three stages. It was possible to know that the process in the interpretation of the graph is the main perspective, and the operation of algebraic representation is regarded as important. Based on these results, it seems necessary to study the teachinglearning method which can understand trigonometric functions from various perspectives. It seems necessary to study a lesson model that can reach function concept’s understanding level 5 that maintains consistency between problem solving and representation system.

Exploring Alternative Ways of Teaching derivatives
김선희 Kim Sun Hee , 김태석 Kim Tae Seok , 조진우 Cho Jin Woo
33(3) 335354, 2019
김선희 Kim Sun Hee , 김태석 Kim Tae Seok , 조진우 Cho Jin Woo
DOI: JANT Vol.33(No.3) 335354, 2019
The purpose of this study is to explore alternative ways of teaching derivatives in a way that emphasizes intuition. For this purpose, the contents related to derivatives in Korean curriculum and textbooks were analyzed by comparing with contents in Singapore Curriculum and textbooks. Singapore, where the curriculum deals with derivatives relatively earlier than Korea, introduces the concept of derivatives and differentiation as the slope of tangent instead of the rate of instantaneous change in textbook. Also, Singapore use technology and inductive extrapolation to emphasize intuition rather than form and logic. Further, from the results of the exploration of other foreign cases, we confirm that the UK and Australia also emphasized intuition in teaching derivatives and differentiation. Based on the results, we discuss the meaning and implication of introducing derivatives and teaching differentiation in a way that emphasizes intuition. Finally, we propose the implications for the alternative way of teaching differentiation.

A Development of Research Tool for Mathematics Teachers’ Perceptions of Mathematics Education
김홍겸 Kim Hongkyeom , 정시훈 Jung Sihun , 김소민 Kim Somin , 허난 Huh Nan
33(3) 355376, 2019
김홍겸 Kim Hongkyeom , 정시훈 Jung Sihun , 김소민 Kim Somin , 허난 Huh Nan
DOI: JANT Vol.33(No.3) 355376, 2019
Since the second comprehensive mathematics education plan was announced in 2012, many policies have been implemented based on it. However, due to many changes in various social situations and revision of the curriculum, new plans and policy proposals for mathematics education are strongly required. But, we need to recognize what the changes in the current social and educational situation ask for education in order to make meaningful policy. Therefore, in this study, we intend to develop an appropriate questionnaire to investigate mathematics teachers’ perceptions and educational status of mathematics by analyzing former domestic and international studies on the related field and reflecting the educational situation in Korea. When developing questions, experts' opinions were consulted and preliminary onsite survey studies were conducted to maintain the suitability and reliability of the questions. Through these procedure, 33 questions were developed in three areas: teachers’ recognition on mathematics education, educational status of mathematics education, and ICT utilization. It will be used as a tool to investigate math teachers’ perception and current status of mathematics education and the results from this survey will be useful for developing mathematics education policies for the future.

A mathematics teacher’s discursive competence on the basis of mathematical competencies
최상호 Choi Sangho , 김동중 Kim Dongjoong
33(3) 377394, 2019
최상호 Choi Sangho , 김동중 Kim Dongjoong
DOI: JANT Vol.33(No.3) 377394, 2019
The purpose of this study is to scrutinize the characteristics of a teacher’s discursive competence on the basis of mathematical competencies. For this purpose, we observed all semesterlong classes of a middle school teacher, who changed her own teaching methods for the last 20 years, collected video clips on them, and analyzed classroom discourse. Data analysis shows that in problem solving competency, she helped students focus on mathematically important components for problem understanding, and in reasoning competency, there was a discursive competence which articulated thinking processes for understanding the needs of mathematical justification. And in creativity and confluence competency, there was a discursive competence which developed class discussions by sharing peers’ problem solving methods and encouraging students to apply alternative problem solving methods, whereas in communication competency, there was a discursive competency which explored mathematical relationships through the need for multiple mathematical representations and discussions about their differences. These results can provide concrete directions to developing curricula for future teacher education by suggesting ideas about how to combine practices with PCK needed for mathematics teaching.

An Analysis of Components of Reasoning Process according to the Levels of Cognitive Demands of the Reasoning Tasks Focused on the Highschool level Mathematical Sequence
오영석 Oh Youngseok
33(3) 395423, 2019
오영석 Oh Youngseok
DOI: JANT Vol.33(No.3) 395423, 2019
The purpose of the study is to analyze the levels of cognitive demands and components of the reasoning process presented in the mathematical sequence section of three high school mathematics textbooks in order to provide implications for the development of reasoning tasks in the future mathematics textbooks. The results of the study have revealed that most of the reasoning tasks presented in the mathematical sequence section of the three high school mathematics textbooks seemed to require lowlevel cognitive demands and that lowlevel cognitive demands reasoning tasks required only a component of one reasoning process. On the other hand, only a portion of the reasoning tasks appeared to require highlevel of cognitive demands, and highlevel cognitive demands reasoning tasks required various components of reasoning process. Considering the results of the study, it seems to suggest that we need more highlevel cognitive demands reasoning tasks to develop highlevel cognitive reasoning that would provide students with learning opportunities for various processes of reasoning, and that would provide a deeper understanding of the nature of reasoning.
