• East Asian mathematical journal
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• v.28 no.2
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• pp.197-213
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• 2012

In this paper we study Soltan & Meidman's method that is able to be used in mathematical discovery. We analyze Soltan & Meidman's book "Tozdestva i Neravenstva v Treugolike" that is published in Moldova Republic. In this work we formulate Soltan & Meidman's method related with discovery of triangle's various equalities, and use the method to discovery mathematical equalities. As a result we suggest some new mathematical equalities related with triangle's sides and its proof.

• The Mathematical Education
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• v.48 no.2
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• pp.113-139
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• 2009

In this study, we apply the discovery method in the instruction of Permutation and Combination, and examine the effect upon the student's emotion after the instruction change. The research progressed through the instruction by the discovery method for two students of highschool Y. This research has been done for about one and half year from November 2006 to February 2008. We draw our research results through a series of processes consisted of videotaping a classroom activities, recording interview details and writing an observation diary, with the aim of the experimental instruction. In the end, we get to the conclusion that students showed a strong positive attitude on the discovery instructional method and that diverse discovery method has supplementary relation in classwork.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.

• School Mathematics
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• v.7 no.4
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• pp.427-444
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• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Research in Mathematical Education
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• v.26 no.3
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• pp.203-233
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• 2023

Recent international reform movements call for attention on modeling in mathematics classrooms. However, definitions and enactment principles are unclear in policy documents. In this case study, we investigated United States high-school mathematics teachers' experiences in a professional development program focused on modeling and its enactment in schools. Our findings share teachers' experiences around their discovery of different conceptualizations, appreciations, and conflicts as they envisioned incorporating modeling into classrooms. These experiences show how professional development can be designed to engage teachers with forms of modeling, and that those experiences can inspire them to consider modeling as an imperative feature of a mathematics program.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.13-15
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• 2010

• Journal for History of Mathematics
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• v.28 no.5
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• pp.249-262
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• 2015

Simon Stevin, a mathematician active in the Netherlands in early seventeenth century, parlayed his mathematical talents into improving navigation skills. In 1605, he introduced a technique of calculating the distance of loxodrome employed in long-distance voyages in his book, Navigation. He explained how to calculate distance by 8 different angles, and even depicted how to make a copper loxodrome model for navigators. Particularly, Stevin clarified in the 7th copper loxodrome model on the unique features of equiangular spiral curve that keeps spinning and gradually accesses from the vicinity to the center. These findings predate those of Descartes on equiangular spiral curve by more than 30 years. Navigation, a branch of actual mathematics devised for the survival of sailors on the bosom of the ocean, was also the first step to the discovery of new mathematical object.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.1B
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• pp.9-14
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• 2012

The neighbor discovery using directional antennas in mmWave band is a prerequisite for communications and this issue is crucial and urgent. In this paper, the synchronized, direct, two-way directional neighbor discovery process is analyzed mathematically for mmWave WPANs. The analysis is based on the values which are derived from the effect of using directional antennas. The neighbor discovery probability for a given amount of time is considered and several performance measures such as the optimal sojourn time are derived in closed forms. Numerical results are obtained using parameters based on the IEEE 802.15.3c. The mathematical analysis provides the theoretical basis for the directional neighbor discovery process.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.42 no.3
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• pp.577-584
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• 2017

Long Term Evolution device-to-device (LTE D2D) is a key technology to mitigate data traffic load in a cellular system. It facilitates direct data exchange between neighboring users, which is preceded by D2D discovery. Each device advertises its presence to neighboring devices by broadcasting its discovery message. In this paper, we develop a mathematical analysis to assess the probability that discovery messages are successfully transmitted at the D2D discovery stage. We make use of stochastic geometry for modeling spatial statistics of nodes in a two dimensional space. It reflects signal to noise plus interference ratio (SINR) degradation due to resource collision and in-band emission, which leads to the discovery message reception probability being modeled as a function of the distance between the transmitter and the receiver. Numerical results verify that the newly developed analysis accurately estimates discovery message reception probabilities of nodes at the D2D discovery stage.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.95-106
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• 2005

This paper is investigated conception and methodology of data selection, cleaning, integration, transformation, reduction, selection and application of data mining techniques, and model evaluation during procedure of the knowledge discovery in database (KDD) based on Mathematics. Statistical role and methodology in KDD is studied as branch of Mathematics. Also, we investigate the history, mathematical background, important modeling techniques using statistics and information, practical applied field and entire examples of data mining. Also we study the differences between data mining and statistics.