• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.391-410
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• 2017

This study aims to analyze mathematically gifted students' characteristics of generalization and justification for a given mathematical task and induce didactical implications for individual teaching methods by students' learning styles. To do this, we identified the learning styles of three mathematically gifted 6th graders and observed their processes in solving a given problem. Paper-pencil environment as well as dynamic geometrical environment using Geogebra were provided for three students respectively. We collected and analyzed qualitatively the research data such as the students' activity sheets, the students' records in Geogebra, our observation reports about the processes of generalization and justification, and the records of interview. The results of analysis show that the types of the students' generalization are various while the level of their justifications is identical. Futhermore, their preference of learning environment is also distinguished. Based on the results of analysis, we induced some implications for individual teaching for mathematically gifted students by learning styles.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.11-35
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• 2001

Many teachers report familiarity with and adherence to reform ideas, but their actual teaching practices do not reflect a deep understanding of reform. Given the challenges in implementing reform, this study intended to explore the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals. To this end, this study compared and contrasted the classroom social norms and sociomathematical norms of two United States second-grade teachers who aspired to implement reform. This study is an exploratory, qualitative, comparative case study. This study uses the grounded theory methodology based on the constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The two classrooms established similar social norms including an open and permissive learning environment, stressing group cooperation, employing enjoyable activity formats for students, and orchestrating individual or small group session followed by whole group discussion. Despite these similar social participation structures, the two classes were remarkably different in terms of sociomathematical norms. In one class, the students were involved in mathematical processes by which being accurate or automatic was evaluated as a more important contribution to the classroom community than being insightful or creative. In the other class, the students were continually engaged in significant mathematical processes by which they could develop an appreciation of characteristically mathematical ways of thinking, communi-eating, arguing, proving, and valuing. It was apparent from this study that sociomathematical norms are an important construct reflecting the quality of students' mathematical engagement and anticipating their conceptual learning opportunities. A re-theorization of sociomathematical norms was offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.273-289
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• 2001

Given that the culture of the mathematics classroom has been perceived as an important topic in mathematics education research, this paper deals with the construct of sociomathematical norms which can be used as an analytical tool in understanding classroom mathematical culture. This paper first reviews the theoretical foundations of the construct such as symbolic interactionism and ethnomethodology, and describes the actual classroom contexts in which social and sociomathematical norms were originally identified. This paper then provides a critical analysis of the previous studies with regard to sociomathematical norms. Whereas such studies analyze how sociomathematical norms become constituted and stabilized in the specific classroom contexts, they tend to briefly document sociomathematical norms mainly as a precursor to the detailed analysis of classroom mathematical practice. This paper reveals that the trend stems from the following two facts. First, the construct of sociomathematical norms evolved out of a classroom teaching experiment in which Cobb and his colleagues attempted to account for students' conceptual loaming as it occurred in the social context of an inquiry mathematics classroom. Second, the researchers' main role was to design instructional devices and sequences of specific mathematical content and to support the classroom teacher to foster students' mathematical learning using those sequences Given the limitations in terms of the utility of sociomathematical norms, this paper suggests the possibility of positioning the sociomathematical norms construct as more centrally reflecting the quality of students' mathematical engagement in collective classroom processes and predicting their conceptual teaming opportunities. This notion reflects the fact that the construct of sociomathematical norms is intended to capture the essence of the mathematical microculture established in a classroom community rather than its general social structure. The notion also allows us to see a teacher as promoting sociomathematical norms to the extent that she or he attends to concordance between the social processes of the classroom, and the characteristically mathematical ways of engaging. In this way, the construct of sociomathematical norms include, but in no ways needs to be limited to, teacher's mediation of mathematics discussions.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.453-474
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• 1998

This study is focused on the possibility if we can use graphic calculators in teaching and learning school mathematics. This study is consisted with four main chapters. In chapter II, the functions of the graphic calculator EL-9600 produced by Sharp Corporation was analyzed focused on the possibilities if the functions could be used in teaching and learning school mathematics. Calculating of real numbers and complex numbers, solving equations and system of linear equations, calculating of matrices, graphing of several functions including polynomial functions, trigonometric functions, exponential and logarithmic functions, calculation of differential and integrals, arranging of statical data, graphing of statistical data, testing of statistical hypotheses, and other more useful functions were founded. In Chapter III, a mathematics textbook developed by Core-Plus Mathematics Project was analyzed focused on how a graphic calculator was used in teaching and learning mathematics, In the textbook, graphic calculator was used as a tool in understanding mathematical concepts and solving problems. Graphic calculator is not just a tool to do complex computations but a tool used in the processes of doing mathematics, In chapter IV, the 7th mathematics curriculum for korean secondary schools was analyzed to find the contents could be taught by using graphic calculators. Most of the domains, except geometric figure, were found that they could be taught by using graphic calculators, In chapter V, a model of a unit using graphic calculator in teaching 7th mathematics curriculum was developed. In this model, graphic calculator was used as a tool in the processes of understanding mathematical concepts and solving problems. This study suggests the possibilities that we can use graphic calculators effectively in teaching and learning mathematical concepts and problem solving for most domains of secondary school mathematics.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.67-82
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• 2014

The term "objectification" has various definitions or perspectives. Nevertheless, it's pursued commonly by groups from various perspectives who emphasize the activities of becoming aware of a process as a totality, realizing that transformations can act on that totality, that is, turning processes into object. The purpose of this study is to identify how students objectify the concept of repetition regarding permutation and combination and find difficulties of objectification focusing on teacher's and students' discourse from common emphasis on previous researches associated with objectification. Students objectified the concept of repetition by replacing talk about processes with talk about objects regarding repetition and using discursive forms that presented phenomena in an impersonal way. The difficulties of objectification were derived from close linkage between the way of using keywords regarding repetition and everyday language.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.1-27
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• 2014

In the present study, we analyze the four participating 9th grade students' mathematical reasoning processes in their dragging activities while solving open-ended geometry problems in terms of abduction, induction and deduction. The results of the analysis are as follows. First, the students utilized 'abduction' to adopt their hypotheses, 'induction' to generalize them by examining various cases and 'deduction' to provide warrants for the hypotheses. Secondly, in the abduction process, 'wandering dragging' and 'guided dragging' seemed to help the students formulate their hypotheses, and in the induction process, 'dragging test' was mainly used to confirm the hypotheses. Despite of the emerging mathematical reasoning via their dragging activities, several difficulties were identified in their solving processes such as misunderstanding shapes as fixed figures, not easily recognizing the concept of dependency or path, not smoothly proceeding from probabilistic reasoning to deduction, and trapping into circular logic.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.509-525
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• 2016

This study is a follow-up study of the previous research for teacher education(Kim Nam Hee, 2006, 2009, 2013, 2014). This study was conducted with third grade students of the college of education in 2016. In this study, we guided to allow pre-service teachers to develop their teaching research ability and teaching practical skills using the results obtained from the in-service teachers training courses. Processes mainly performed in this study are as follows; learning the theory on Socrates' method, case study for thought experiment activities, instructional simulation using a Socrates' method, class analysis, textbook analysis, peer evaluation, self-assessment. Observing tutorial examples by in-service teachers, pre-service teachers were expanding their limited knowledge and experience. By analyzing the results obtained from this research processes, we checked the points to put more attention in future pre-service teachers education.

• Convergence Security Journal
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• v.18 no.2
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• pp.33-40
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• 2018

ICT technology has been applied to various educational fields, but applying to educational test field is limited. Computer-based test (CBT) can overcome temporal and spatial constraints of conventional paper-based test, but is vulnerable to fraud by test parties. In this paper, we propose real-time monitoring and process management methods to enhance the security of CBT. In the proposed methods, the test screens of students are periodically captured and transferred to the professor screen to enable real-time monitoring, and the possible processes used for cheating can be blocked before testing. In order to monitor the screen of many students in real time, effective compression of the captured original image is important. We applied three-step compression methods: initial image compression, resolution reduction, and re-compression. Through this, the original image of about 6MB was converted into the storage image of about 3.8KB. We use the process extraction and management functions of Windows API to block the processes that may be used for cheating. The CBT system of this paper with the new security enhancement methods shows the superiority through comparison of the security related functions with the existing CBT systems.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.2
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• pp.357-372
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• 2012

Existing e-learning systems not only require complex admission processes but also do not give stepwise education methods according to individual learners' characteristic. These circumstances cause learners to lose educational interest so that their educational efficiency decreases. In particular, the present e-learning systems do not provide educational approaches suitable for infant and elementary children. Under this system, the e-learning education for children does not proceed completely without guardians. To solve this problem, we design and implement an English e-learning system for elementary children based on friendly and comfortable user interfaces. For children, the proposed system reflects their age and individual interesting per each e-learning stage. This system supports both the Web application platform and smart phone application platform for various client requirements. The proposed system manages 3 classes as English learning content. Learners can experience their own English e-learning course in each class, which is compiled by current educational ability. In addition to the general functions in e-learning system, the proposed system develops content buffering algorithm to reduce data traffic in server.

• Journal of the Korea Society of Computer and Information
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• v.16 no.12
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• pp.131-137
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• 2011

Operating Systems is a discipline which handles complex and abstract concepts related to its components and the principles of how an operating system works. However, most of the OS courses have been textbook-oriented theoretical classes. For students who are familiar with various kinds of media, theoretical classes lead to a decline in the understanding of a lecture and difficulty concentrating. They have tried to make use of educational tools to help students understand a lecture and arouse their interests consistently. This paper describes the design and implementation of a disk scheduling simulator which shows the service processes of disk I/O requests visually. The disk scheduling simulator can be used for demonstrations of the disk scheduling algorithms. The results of the academic achievement evaluation and survey showed that a disk scheduling simulator is useful as an educational tool which causes the interests about operating systems and enhances the understanding of a lecture.