Realization of signifiers and mathematics understanding: Focused on the elapsed time
한채린 Han¸ Chaereen
60(3) 249-264, 2021
한채린 Han¸ Chaereen
DOI: JANT Vol.60(No.3) 249-264, 2021
This article is devoted to investigating young learners’ understanding of elapsed time from socio-cultural perspectives. The socio-cultural perspective benefits to access and personalize mathematics learning as how to have a mathematical object to be able to realize signifiers with the help of many other mathematical words and mediators. In terms of the realization of signifiers, I analyzed performances on elapsed time tasks of students in Grades 3 (n=115) and interviewed focal students. Quantitative analysis on students’ performance identified that students perform differently when the task provided with the analog clock signifier. It suggested that students might think in a different way upon the given signifier even for the same elapsed time, especially when given as the analog clock. Qualitative analysis on focal students' interviews visualized how the students’ understanding were different by displaying individual realization trees on elapsed time. The particular location of the analog clock signifier on each realization tree provided a personalized explanation about low performance on the task with analog clock signifier. The finding suggested that the realization of a specific signifier could be a key point in elapsed time understanding. I discussed why a majority of students face difficulty in elapsed time learning indicated analog clock and the advantage of moving elapsed time strands to higher grades in the school mathematics curriculum.
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An analysis of types and functions of questions presented in data and chance area of elementary school mathematics textbooks
도주원 Do¸ Joowon
60(3) 265-279, 2021
도주원 Do¸ Joowon
DOI: JANT Vol.60(No.3) 265-279, 2021
In this study, by analyzing of types and functions of questions presented in Data and Chance area of the mathematics textbooks for grades 1-6 of the 2015 revised curriculum, the characteristics of the questions presented in the textbook were identified, and implications for teaching and learning related to the questions in this textbook were obtained. Types and functions of the presented questions showed different proportions of appearance according to the grade clusters, and this seems to be related to the learning contents for each grade clusters and the characteristics of grade clusters. In addition, it can be seen that the functions of questions are related to the types of questions. Teachers should have pedagogical content knowledge about Data and Chance area as well as developmental characteristics for each grade clusters. In addition, the teacher should present an suitable question for the level of grade clusters and the nature of the content to be taught so that effective learning can be achieved based on the understanding of the characteristics and functional characteristics of each type of questions. The results of this study can contribute to statistical teaching in a progressive direction by providing a foundation for textbook writing and teaching/learning.
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Examining the breadth and depth of knowledge required in the teacher employment test for secondary mathematics
이소연 Lee¸ So Yeon , 김래영 Kim¸ Rae Young
60(3) 281-295, 2021
이소연 Lee¸ So Yeon , 김래영 Kim¸ Rae Young
DOI: JANT Vol.60(No.3) 281-295, 2021
This study examines the breadth and depth of knowledge of the teacher employment test for secondary mathematics. For the breadth of knowledge, we attempted to figure out the range of knowledge in terms of the content areas using the standards from the Korea Society Educational Studies in Mathematics[KSESM](2008). For the depth of knowledge, we chose Anderson & Krathwohl(2001) framework to analyze levels of each item in the test. The results from the analysis of 180 items in the teacher employment test between 2014 and 2021 show that while items in mathematics education have considerable variation in terms of range and levels of knowledge, those in some subjects of mathematics can be found only certain level of knowledge. i.e., merely certain topics or levels of knowledge have been heavily evaluated. Thus, considering the breadth and depth of knowledge teachers should have, the current exam needs to be improved in terms of teacher knowledge. It does not mean that every topic and every level of knowledge should be evaluated. However, it is a meaningful opportunity to think about what kinds of knowledge teachers should have in relation to K-12 mathematics curriculum and how we can evaluate the knowledge. More collaborative effort is inevitable for the improvement of teacher knowledge and teacher employment test.
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Mathematics teachers’ Key Developmental Understandings for teaching equation writing
최윤형 Choi¸ Yunhyeong , 이수진 Lee¸ Soo Jin
60(3) 297-319, 2021
최윤형 Choi¸ Yunhyeong , 이수진 Lee¸ Soo Jin
DOI: JANT Vol.60(No.3) 297-319, 2021
The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)’s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants’ attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.
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An analysis of in-service teachers’ perceived interactivity with AI teachers through RPP(Role-Play Presentation)
고호경 Ko¸ Ho Kyoung , 허난 Huh¸ Nan , 노지화 Noh¸ Jihwa
60(3) 321-340, 2021
고호경 Ko¸ Ho Kyoung , 허난 Huh¸ Nan , 노지화 Noh¸ Jihwa
DOI: JANT Vol.60(No.3) 321-340, 2021
As many changes in the future society represented by the age of artificial intelligence(AI) are expected to come, efforts are being made to draw the shape of the future education and various research methods are being employed to support the attempts. While many research studies use methods for deriving generalized results such as expert survey and trend analysis in along with a review of literature, there are attempts to apply the scenario methodology to explore ideas and information needed within a changing context. A scenario method, one of the experiential learning strategies, aims to seek various and alternative approaches by establishing a plan from the present conditions considering future changes. In this study, in-service teachers’ perceptions and expectations of the interactivity between human and AI teachers were visualized by applying the role-play presentation technique that grafted the concept of role-play game to the scenario method. In addition, the mandal-art method was introduced to support in conducting productive discussion during the teachers’ collaboration. This method appeared to help to depict teachers' perceptions of AI teachers in the detailed and concrete form, which may flow in the abstract otherwise. Through analyses of the teachers’ role-play presentations with the implementation of the madal-art method it was suggested that most teachers would want to collaborate with an AI teacher for improved instruction and individualized student learning while they would take the instructional authority over the AI teacher in the classroom.
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Pre-service teachers’ motivation in group activities for developing knowledge for teaching and practical competency: The case of the task value
최송희 Choi¸ Song-hee , 김동중 Kim¸ Dong-joong
60(3) 341-362, 2021
최송희 Choi¸ Song-hee , 김동중 Kim¸ Dong-joong
DOI: JANT Vol.60(No.3) 341-362, 2021
The purpose of this study is to explore the qualitative characteristics of pre-service teachers’ motivation while they are participating in group activities for developing mathematical essay assessment problem and revising it. For this purpose, we analyzed individual factors about group learning activities as well as contextual factors about practical competency (in developing and revising mathematical essay assessment problem through collecting data of student responses to the problem). As results of data analyses, autonomy, among individual factors regarding group learning activities, was one of the main characteristics in attainment value, utility value, and intrinsic value, whereas task, authority, and grouping, among contextual factors regarding practical competency, appeared to have a positive impact on task value. These results suggest how to think of specific ideas and articulate them in designing a curriculum to develop student-evaluation expertise for pre-service teachers.
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Analyzing research questions from pre-service mathematics teachers in statistical problem solving process
김소형 Kim¸ Sohyung , 한선영 Han¸ Sunyoung
60(3) 363-386, 2021
김소형 Kim¸ Sohyung , 한선영 Han¸ Sunyoung
DOI: JANT Vol.60(No.3) 363-386, 2021
To learn statistics meaningfully, we must provide an opportunity to experience the process of solving statistical problems with actual data. In particular, exploration questions at the problem setting stage are important for students to successfully guide them from the beginning to the conclusion of the statistical problem solving process. Therefore, in this study, a mixed research method was carried out for the exploration questions of pre-service mathematics teachers during the problem setting stage. As a result, some pre-service mathematics teachers categorized incorrect statistical questions because they did not clearly define the meaning or variables of the questions in the process of categorizing them from possible questions. In addition, questions that cannot be solved statistically were categorized due to misconceptions about statistical knowledge. Second, only 50% of the pre-service mathematics teachers met all 6 conditions suitable for solving statistical problems, while there maining they met only a few conditions. Therefore, the conclusion of this study is as follows. First of all, they should be given the opportunity to experience all the statistical problem solving processes through teacher education because they do not have enough experience in statistical problem solving. Secondly, since the problem setting stage is very important in the statistical problem solving process, a series of subdivided processes are also required in the problem setting stage.
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Reflections on the application of progressivism and constructivism in mathematics education
박정선 Park¸ Jeongseon , 신재홍 Shin¸ Jaehong
60(3) 387-407, 2021
박정선 Park¸ Jeongseon , 신재홍 Shin¸ Jaehong
DOI: JANT Vol.60(No.3) 387-407, 2021
The present study was conducted on the assumptions that both progressivist and constructivist education emphasized the subjective knowledge of learners and confronted similar problems when the derived educational principles from the two perspectives were adopted and applied to mathematics research and practice. We argue that progressivism and constructivism should have clarified the meaning, purpose, and direction of ‘emphasizing subjective knowledge’ in application to the particular educational field. For the issue, we reflected Dewey’s theory on the application of past progressivism, and aligned with it, we took a critical view of the educational applications of current constructivism. As a result, first, the meaning of emphasizing subjective knowledge is that each of the students constructs a unique mathematical reality based on his or her experience of situations and cognitive structures, and emphasizes our understanding of this subjective knowledge as researchers/observers. Second, the purpose of emphasizing subjective knowledge is not to emphasize subjective knowledge itself. Rather, it concerns the meaningful learning of objective knowledge: internalization of objective knowledge and objectification of subjective knowledge. Third, the application of the emphasis on subjective knowledge does not specify certain teaching/learning methods as appropriate, but orients us toward a genuine learner-centered reform from below. The introspections, we wish, will provide new momentum for discussion to establish constructivism as a coherent theory in mathematics classrooms.
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