A Comparative Study on Congruence and Symmetry in Elementary Mathematics Textbooks of Korea, Japan, Hong Kong, Finland, and Singapore
방정숙 Pang Jeongsuk , 김유경 Kim Yukyung
56(3) 235-255, 2017
방정숙 Pang Jeongsuk , 김유경 Kim Yukyung
DOI: JANT Vol.56(No.3) 235-255, 2017
This study compared and contrasted the topics related to congruence and symmetry in the elementary mathematics textbooks series of Korea, Japan, Hong Kong, Finland, and Singapore in three aspects: (a) when to teach, (b) what to teach, and (c) how to teach.
Firstly, the results of when to teach showed differences across the countries with a variation of teaching the topics among grades from 3 to 6. Secondly, the results of what to teach revealed subtle but significant differences. Regarding congruence, Korea and Japan deal with congruence in a systematic manner, while Finland tends to address the brief definition of congruence, and Hong Kong and Singapore focus on teaching tessellation which implies congruence. Regarding symmetry, Korea and Japan deal only with a symmetric figure for a line and that for a point, while Hong Kong includes a rotational symmetry and Finland extends further to cover the figures positioned in a symmetry both for a line and for a point. Lastly, the results of how to teach demonstrated that Korea tends to focus on the procedure of drawing both triangles to be congruent and symmetric figures.
This implies that we need to consider alternative methods such as using various instructional materials and making an explicit connection among mathematical concepts in teaching congruence and symmetry.
|
Inquiry-Based Learning of Circumcenter Using Teaching Tools
최수경 Choi Su Kyoung , 강윤수 Kang Yun Soo
56(3) 257-280, 2017
최수경 Choi Su Kyoung , 강윤수 Kang Yun Soo
DOI: JANT Vol.56(No.3) 257-280, 2017
The purpose of this study is to analyze middle school students` learning characteristics they showed on the inquiry-based learning process of circumcenter using various teaching tools, and then to identify the effects of using teaching tools in the middle school students` learning process of circumcenter. For this purpose, we developed teaching materials for inquiry-based learning of circumcenter using textbook, origami, ruler and compass, GeoGebra and sand experiment. Then we applied them on the learning process of circumcenter for five groups of middle school students. From the analyzing of audio/video materials and documents which are collected from the process of participants` inquiry-based learning of circumcenter, we identified the following results.
First, inquiry-based learning of circumcenter using various teaching tools promoted mathematical discourses among participants of this study. For example, they conjectured mathematical properties or justified their opinions after manipulated teaching tools in the process of learning circumcenter.
Second, inquiry-based learning of circumcenter using various teaching tools promoted participants` divergent thinking. They tried many inquiry methods to find new mathematical properties relate to circumcenter. For example, they tried many inquiry methods to know whether there is unique circle containing four vertices of given quadrangles.
Third, we found several didactic implications relate to inquiry-based learning of circumcenter using various teaching tools which are due to characteristics of teaching tools themselves. Participants showed several misconceptions about mathematical properties during they participated inquiry-based activity for learning of circumcenter using various teaching tools. We identified their misconceptions were not due to any other variables containing their learning characteristics but to characteristics of teaching tools.
|
An Analysis of Middle School Student`s Eye Movements in the Law of Large Numbers Simulation Activity
최인용 Choi In Yong , 조한혁 Cho Han Hyuk
56(3) 281-300, 2017
최인용 Choi In Yong , 조한혁 Cho Han Hyuk
DOI: JANT Vol.56(No.3) 281-300, 2017
This study analyzed the difficulties of middle school students in computer simulation of the law of large numbers through eye movement analysis. Some students did not attend to the simulation results and could not make meaningful inferences. It is observed that students keep the existing concept even though they observe the simulation results which are inconsistent with the misconceptions they have. Since probabilistic intuition influence student`s thinking very strongly, it is necessary to design a task that allows students to clearly recognize the difference between their erroneous intuitions and simulation results. In addition, we could confirm through eye movements analysis that students could not make meaningful observations and inferences if too much reasoning was needed even though the simulation included a rich context. It is necessary to use visual representations such as graphs to provide immediate feedback to students, to encourage students to attend to the results in a certain intentional way to discover the underlying mathematical structure rather than simply presenting experimental data. Some students focused their attention on the visually salient feature of the experimental results and have made incorrect conclusion. The simulation should be designed so that the patterns of the experimental results that the student must discover are not visually distorted and allow the students to perform a sufficient number of simulations. Based on the results of this study, we suggested that cumulative relative frequency graph showing multiple results at the same time, and the term `generally tends to get closer` should be used in learning of the law of large numbers. In addition, it was confirmed that eye-tracking method is a useful tool for analyzing interaction in technology-based probabilistic learning.
|
Teaching Methodology for Future Mathematics Classroom :Focusing on Students` Generative Question in Ill-Structured Problem
나미영 Na Miyeong , 조형미 Cho Hyungmi , 권오남 Kwon Oh Nam
56(3) 301-318, 2017
나미영 Na Miyeong , 조형미 Cho Hyungmi , 권오남 Kwon Oh Nam
DOI: JANT Vol.56(No.3) 301-318, 2017
This paper explores students` question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we `learn` or `study` socially. In other words, we haven`t provided students with autonomous research and learning opportunities under `the dominant paradigm of visiting works`. As an alternative, he suggests that we should move on to a new didactic paradigm for `questioning the world a question`, and proposes the Study and Research Courses (SRC) as its pedagogical structure.
This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students` presentation materials and classroom video records, and then analyzed based on SRC structure.
As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively.
This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.
|
A Study on Development of Teaching and Learning Materials for `Mathematics Project Inquiry Subject
천선빈 Sunbin Cheon , 이종학 Jong Hak Lee , 김원경 Won Kyung Kim
56(3) 319-340, 2017
천선빈 Sunbin Cheon , 이종학 Jong Hak Lee , 김원경 Won Kyung Kim
DOI: JANT Vol.56(No.3) 319-340, 2017
The purpose of this study is to develop teaching and learning materials for the mathematics project inquiry subject. Since this subject is newly opened in the 2015 revised mathematics curriculum, there are no textbooks and materials. Hence it is required to help teachers plan lessons of the mathematics project inquiry subject.
For this study, developing directions and objectives are established. Ten hours of lesson plan and teaching and learning materials are also developed for the two themes of `big data` and `industrial mathematics`. Suitability and validity of the developed material are verified positively from a survey of 8 teachers and 2 professionals. The detailed result findings are as follows.
First, teaching and learning notes are suggested for each lesson plan. They are comprised of building inquiry plan, doing inquiry, summarizing results, and presentation.
Second, driving questions of each theme are developed as“ What is the big data and where is it used for ?” and “ How various is the use of the industrial mathematics ?” respectively.
Third, poster-types of each project product are developed.
Fourth, three inquiry activity sheets and examples which are theme selection, inquiry plan, and group activity are developed.
Fifth, 4 assessment sheets of self, peer, group, and teacher-use are developed.
|
The Relationship between Mathematics Teachers` Noticing and Responsive Teaching:In the Context of Teaching for All Students` Mathematical Thinking
김희정 Hee-jeong Kim , 한채린 Chaereen Han , 배미선 Mi Seon Bae , 권오남 Oh Nam Kwon
56(3) 341-363, 2017
김희정 Hee-jeong Kim , 한채린 Chaereen Han , 배미선 Mi Seon Bae , 권오남 Oh Nam Kwon
DOI: JANT Vol.56(No.3) 341-363, 2017
This case study contributes to the efforts on identifying the essential features of responsive teaching practice where students` mathematical thinking is central in instructional interactions. We firstly conceptualize responsive teaching as a type of teachers` instructional decisions based on noticing literature, and agree on the claim which teachers` responsive decisions should be accounted in classroom interactional contexts where teacher, students and content are actively interacting with each other. Building on this responsive teaching model, we analyze classroom observation data of a 7th grade teacher who implemented a lesson package specifically designed to respond to students` mathematical thinking, called Formative Assessment Lessons. Our findings suggest the characteristics of responsive teaching practice and identify the relationship between noticing and responsive teaching as: (a) noticing on students` current status of mathematical thinking by eliciting and anticipating, (b) noticing on students` potential conceptual development with follow-up questions, and (c) noticing for all students` conceptual development by orchestrating productive discussions. This study sheds light on the actual teachable moments in the practice of mathematics teachers and explains what, when and how to support teachers to improve their classroom practice focusing on supporting all students` mathematical conceptual development.
|