• The Mathematical Education
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• v.53 no.1
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• pp.25-40
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• 2014

Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in 'Mathematics II' and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of 'function-derivatives', the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.

• Journal of Music and Human Behavior
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• v.3 no.1
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• pp.63-76
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• 2006

Melody is defined as adding spatial dimension to the rhythm which is temporal concept. Being able to understand melodic pattern and to reproduce the pattern also requires cognitive skills. Since 1980, there has been much research on the relationship between academic skills and music cognitive skills, and how to transfer the skills learned in music work to the academic learning. The study purported to examine various research outcomes dealing with the correlational and causal relationships between musical and academic skills. The two dominating theories explaining the connection between two skills ares are "neural theory" and "near transfer theory." The theories focus mainly on the transference of spatial and temporal reasoning which are reinforced in the musical learning. The study reviewed the existing meta-analysis studies, which provided evidence for positive correlation between academic and musical skills, and significance of musical learning in academic skills. The study further examined specific skills area that musical learning is correlated, such as mathematics and reading. The research stated that among many mathematical concepts, proportional topics have the strongest correlation with musical skills. Also with reading, temporal processing also has strong relationship with auditory skills and motor skills, and further affect language and literacy ability. The study suggest that skills learned in the musical work can be transferred to other areas of learning and structured music activities may be every efficient for children for facilitating academic concepts.

• Journal of the Korean School Mathematics Society
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• v.13 no.1
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• pp.125-141
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• 2010

The aim of this paper is to develop a web-based Virtual Learning System for discrete mathematics learning using CAS (Computer Algebra System), The system contains a series of contents that are common between secondary und university curriculum in discrete mathematics such as sets, relations, matrices, graphs etc. We designed and developed web-based virtual learning contents contained in the proposed system based on Mathematia, webMathematica and phpMath taking advantages of rapid computation and visualization. The virtual learning system for discrete math provides movie lectures and 'practice mode' authored with phpMath in order to enhance conceptual understanding of each movie lesson. In particular, matrix learning is facilitated with conceptual diagram that provides interactive quizzes. Once the quiz results are submitted, Bayesian inference network diagnoses strong and weak parts of learning nodes for generating diagnostic reports to facilitate personalized learning. As part of formative evaluation, the overall responses were collected for future revision of the system with 10 university students.