• School Mathematics
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• v.12 no.2
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• pp.177-191
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• 2010

Small Group Collaborative Instruction in school settings has been endorsed by many educational experts over the years. Some studies found that learners greatly benefit from one another through communication and interaction with their peers. These studies previously indicated improvement of a learner‘s academic ability as well as the application of the affective domain when using this type of instruction. Lower-level students with limited mathematical abilities improved their problem-solving and conceptual thinking skills when tasked to work with other learners. On the other hand, the effectiveness of this process was questioned to be less evident with higher-level performers. Therefore, this study was designed to observe the efficacy of Small Group Collaborative Instruction on higher-level students and to explore their learning process as they interact with and teach lower-level students. This study observed that higher-level students use high-level mathematical thinking skills when helping lower-level students, and they improved problem-solving ability as well as communication skills.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.135-145
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• 2011

When mathematicians solve the new problems, they present the solutions to their colleagues for getting the approval. If the solution is accepted, it will be theorems. This phenomenon also happens to classrooms in elementary and secondary school. That is main reason to emphasize mathematical communication activities in mathematics education. This study is aimed to develop teaching and learning model for the improvement of mathematical communication ability, applicate the teaching and learning model to two groups and analyze for mathematical thoughts. This study is a case study of 3rd grader's activities. Eight students, four are group applied the teaching and learning model and four are traditional group. The results have been drawn as follows: First, students in the teaching and learning model group induced richer interactions for student's understanding and investigation when we compare to those of traditional group. Second, students in the teaching and learning model group have the chance to explain their thoughts. And we can observe students to clear on their thought through speaking and discussing. This model makes students to enhance organizing, forming and clearing in their mathematical thoughts and is effective to estimate of students thought for teacher.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.745-768
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• 2010

The purpose of this study at gifted students' solving ability of the given study task by using all knowledge and tools which encompass mathematical contents and curriculums, and developing the teaching learning materials of gifted students in accordance with their level which tan enhance their mathematical thinking ability and develop creative idea. With these considerations in mind, this paper sought for the standard and procedures of teaching learning materials development according to the levels for the education of the mathematically gifted students. presented the procedure model of material development, produced teaching learning methods according to levels in the task of figurate number, and developed prototypes and examples of teaching learning materials for the mathematically gifted students. Based on the prototype of teaching learning materials for the gifted students in mathematics in accordance with their level, this research developed the materials for students and materials for teachers, and performed the modification and complement of material through the field application and verification. It confirmed various solving processes and mathematical thinking levels by analyzing the figurate number tasks. This result will contribute to solving the study task by using all knowledge and tools of mathematical contents and curriculums that encompass various mathematically gifted students, and provide the direction of the learning contents and teaching learning materials which can promote the development of mathematically gifted students.

• School Mathematics
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• v.9 no.3
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• pp.353-373
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• 2007

The purpose of this study was to provide instructional suggestions by investigating the spatial sense and spatial reasoning ability of 6th grade students. The questionnaire consisted of 20 questions, 10 for spatial visualization and 10 for spatial orientation. The number of subjects for the survey was 145. The processes through which the students solved the problems were the basis for the assessment of their spatial reasoning. The result of the survey is as follows: First, students performed better in spatial visualization than in spatial orientation. With regard to spatial visualization, they were better in transformation than in rotation. With regard to spatial orientation, students performed better in orientation sense and structure cognitive ability than in situational sense. Second, the students that weren't excellent in spatial visualization tended to answer the familiar figures without using mental images. The students who lacked spatial orientation experienced difficulties finding figures observed from the sides. Third, students had high frequency rate on the cognition and use of transformation, the development and application of visualization methods and the use of analysis and synthesis. However they had a lower rate on a systematic approach and deductive reasoning. Further detailed investigation into how students use spatial reasoning, and apply it to actual teaching practice as a device for advancing their geometric thinking is necessary.

• Education of Primary School Mathematics
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• v.15 no.1
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• pp.1-11
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• 2012

Unlike traditional cognitive theory, situated cognition theory has been understood as a pedagogical theory that highly reflects the constructivist nature of learning. In order to practice situated learning in school, situations in the classroom are very important in which real teaching and learning occurs. Due to the fact that learning is the process of mental activities which is considerably dependent on conditions and context, it focuses more on the learning process and real-situation experiences rather than the result itself. In mathematics education, teaching students the ability to solve given problems in a conventional way is not enough anymore. The purpose of this research is to suggest the direction of mathematical education in the classroom by analyzing the implications of situated cognition theory and situated learning for 'doing mathematics' in classroom teaching. In this research, we introduce briefly about situated cognition theory and situated learning, compare the phenomenon of mathematics in the classroom to that in the mathematician's mind, and finally propose the applications of situated cognition theory in the mathematics education based on three perspectives of situated cognition theory the embodiment thesis, the embedding thesis, and the extension thesis.

• Research in Mathematical Education
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• v.4 no.1
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• pp.45-55
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• 2000

The rapid proliferation of wireless networks provides a ubiquitous channel for delivering instructional materials at the convenience of the user. By delivering content through portable devices linked to the Internet, the full spectrum of multimedia capabilities is available for engaging the user's interest. This capability encompasses not only text but images, video, speech generation and voice recognition. Moreover, the incorporation of machine learning capabilities at the source provides the ability to tailor the material to the general level of expertise of the user as well as the immediate needs of the moment: for instance, a request for information regarding a particular city might be covered by a leisurely presentation if solicited from the home, but more tersely if the user happens to be driving a car. This paper presents system architecture to support mobile instruction in conjunction with knowledge-based tutoring capabilities. For concreteress, the general concepts are examined in the context of a system for mathematics education on the Web.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.285-299
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• 2013

Problem posing activity of which a learner reinterprets an original problem via a new problem suggested, is a learning method which encourages an active participation and approves self-directed learning ability of the learner. Especially gifted students need to get used to a creative attitude to modify or reinterpret various mathematical materials found in everyday usual lives creatively in steady manner via such empirical experience beyond the question making level of the textbook. This paper verifies the possibility of lesson on question making strategy utilization for creativity development of gifted class, and analyzes various cases of students' trials to modify the rules of a board game called Rummikub in application of their own mathematics after learning What-If-Not strategy.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.717-746
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• 2014

The study aimed to explore how to improve mathematical thinking through metacognitive learning by stressing metacognitive abilities as a core strategy to increase mathematical creativity and problem-solving abilities. Theoretical exploration was followed by an analysis of correlations between metacognitive abilities and various ways of mathematical thinking. Various metacognitive teaching and learning methods used by many teachers at school were integrated for sharing. Also, the methods of learning application and assessment of metacognitive thinking were explored. The results are as follows: First, metacognitive abilities were positively related to 'reasoning, communication, creative problem solving and commitment' with direct and indirect effects on mathematical thinking. Second, various megacognitive ability-applied teaching and learning methods had positive impacts on definitive areas such as 'anxiety over Mathematics, self-efficacy, learning habit, interest, confidence and trust' as well as cognitive areas such as 'learning performance, reasoning, problem solving, metacognitive ability, communication and expression', which is a result applicable to top, middle and low-performance students at primary and secondary education facilities. Third, 'metacognitive activities, metaproblem-solving process, personal strength and weakness management project, metacognitive notes, observation tables and metacognitive checklists' for metacognitive learning were suggested as alternatives to performance assessment covering problem-solving and thinking processes. Various metacognitive learning methods helped to improve creative and systemic problem solving and increase mathematical thinking. They did not only imitate uniform problem-solving methods suggested by a teacher but also induced direct experiences of mathematical thinking as well as adjustment and control of the thinking process. The study will help teachers recognize the importance of metacognition, devise and apply teaching or learning models for their teaching environments, improving students' metacognitive ability as well as mathematical and creative thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.471-489
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• 2012

2007 Curriculum Revision adopted new Inquiry Activities in mathematical textbooks. So it is critical to analyze the problems of actual application of Inquiry activities in the classrooms. For this purpose, we analyzed the Inquiry activities of Measurement Area of the textbooks and find the appropriate solutions. Secondly, we develop the reorganization materials to fix and solve the existing problems found in the previous problem analysis, and apply the development materials and examine the effects afterwards. The results of the survey indicated that most of teachers are well aware of the importance of Inquiry Activities. However, many teachers answered that Inquiry activities does contain neither diverse strategic approaches nor solutions accommodating with various learning levels of students. The most difficult points to educate Inquiry Activities are that it is difficult to teach students based on individual learning level and that activities consist of mainly short answers that makes it difficult to do in-depth Inquiry Activities. Analyzing Inquiry Activities in the textbook shows that Inquiry Activities in some chapters were constructed as simple sentence questions or presented with the solving process in the questions themselves. The following application classes were implemented by partially taking advantage of the newly developed reorganization materials. Then, the effects were measured by before and after questionnaires, the survey to teachers, and the results of activities. The reorganization materials were effective at arousing the curiosity from students as well as enabling the natural ability-level driven classes.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.51-74
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• 2009

The purpose of this study is to search for various strategies that could self-regulated learning within cyber home study efficiently, to operate the cyber home study based on such strategies, to manage and support students' learning and to investigate what effects it would have on the ability of self-regulated learning and attitude. In this study, an operational strategy for cyber home study according to the compositional elements of self-regulated learning based on prior studies. Then, the study developed the learning contents of cyber home study and operated cyber home study according to the operational strategy. From the results of the analysis obtained in this study, the following conclusions can be drawn as follows. First, A learner's self-regulated learning capability is able to be improved by self-regulated leaning strategies. Cyber home study that would enable students to implement the leaning on their own through learning contents and operating strategies corresponding to them was the environment that could help their self-regulated learning. Second, in order to find out students' satisfaction for the application of cyber home study, the study compared the survey of cyber home study with the frequency and percentage by each question and the mean value of technical statistics. Cyber home study let students have positive recognition on mathematical learning, and especially as shown in the results of the interview, it was helpful to improve students' interest and confidence as well as their mathematical learning.