• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.4
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• pp.711-725
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• 2013

A heuristic with multi-byte suffix matching plays an important role in real pattern matching algorithms. By skipping many characters at a time in the process of comparing a given pattern with the text, the pattern matching algorithm based on a heuristic with multi-byte suffix matching shows a faster average search time than algorithms based on deterministic finite automata. Based on various experimental results and simulations, the previous works show that the pattern matching algorithms with multi-byte suffix matching performs well. However, there have been limited studies on the mathematical model for analyzing the performance in a standard manner. In this paper, we propose a new probabilistic model, which evaluates the performance of a heuristic with multi-byte suffix matching in an average-case search. When the theoretical analysis results and experimental results were compared, the proposed probabilistic model was found to be sufficient for evaluating the performance of a heuristic with suffix matching in the real pattern matching algorithms.

• Smart Structures and Systems
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• v.6 no.1
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• pp.39-56
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• 2010

Structural Control relies, with a great deal, on the ability of the control algorithm to identify the current state of the system, at any given point in time. When such algorithms are designed to perform in a smart manner, several smart technologies/devices are called upon to perform tasks that involve pattern recognition and control. Smart pattern recognition is proposed to replace/enhance traditional state identification techniques, which require the extensive manipulation of intricate mathematical equations. Smart pattern recognition techniques attempt to emulate the behavior of the human brain when performing abstract pattern identification. Since these techniques are largely heuristic in nature, it is reasonable to ensure their reliability under real life situations. In this paper, a neural network pattern recognition scheme is explored. The pattern identification of three structural systems is considered. The first is a single bay three-story frame. Both the second and the third models are variations on benchmark problems, previously published for control strategy evaluation purposes. A Neural Network was developed and trained to identify the deformed shape of structural systems under earthquake excitation. The network was trained, for each individual model system, then tested under the effect of a different set of earthquake records. The proposed smart pattern identification scheme is considered an integral component of a Smart Structural System. The Reliability assessment of such component represents an important stage in the evaluation of an overall reliability measure of Smart Structural Systems. Several studies are currently underway aiming at the identification of a reliability measure for such smart pattern recognition technique.

• Education of Primary School Mathematics
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• v.19 no.4
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• pp.361-380
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• 2016

This study aims to reflect on mathematical imaginations in learning mathematics and elementary students' mathematical imaginations. This was approaching a study of imagination not as psychological problems but as objects and methods of mathematics learning. First, children's mathematical narratives were analysed in terms of Egan(2008)'s basic cognitive tools using imagination, that is, metaphor, binary opposites, rhyme rhythm pattern, jokes humor, mental imagery, gossip, play, mystery. Second, how children's imaginations change under different grades was addressed.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• Korean Journal of Child Studies
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• v.29 no.1
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• pp.339-353
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• 2008

This study examined how cognitive style in young children affects mathematical problem-solving performance. Findings showed that the types of patterns presented were linked to the degree of difficulty of the tasks and that disparity between field-independent and field-dependent in cognitive style was broader when subjects worked with more complicated pattern problems. Subjects' marks varied by cognitive style when dynamic assessment was conducted, but cognitive style made no difference in their mathematical learning capability. Cognitive style had an impact not only on the task performance of the learners but on the extent to which they were in need of help during the problem-solving process. Yet, it exercised no influence on how much progress the subjects made when fully assisted.

• Proceedings of the KIPE Conference
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• 2004.07b
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• pp.625-629
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• 2004

This paper presents a systematical approach to study carrier based PWM techniques (CPWM) in diode-clamped and cascade multilevel inverters by using a proposed named multi-modulating pattern method. This method is based on the vector correlation between CPWM and the space vector PWM (SVPWM) and applicable to both multilevel inverter topologies. A CPWM technique can be described in a general mathematical equation, and obtain the same outputs similarly as of the corresponding SVPWM. Control of the fundamental voltage, vector redundancies and phase redundancies in multilevel inverter can be formulated separately in the CPWM equation. The deduced CPWM can obtain the full vector redundancy control, and fully utilize phase redundancy in a cascade inverter In this continued part, it will be deduced correlation between CPWM equations in multi-carrier system and single carrier system, present the mathematical model of voltage source inverter related to the common mode voltage and propose a general algorithm for multi-modulating modulator. The obtained theory will be demonstrated by simulation results.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.4
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• pp.379-386
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• 2013

The hemispherical resonator gyroscope is a type of vibratory gyroscope, which can measure angle or angular rate, based on its operating mode. This paper deals with the case when the hemispherical resonator gyroscope is operated in angle measurement mode. In angle measurement mode, the resonator pattern angle precesses, with respect to the external rotation input, by the principle of the Coriolis effect, so that the external rotation can be estimated, by measuring the amount of precession angle. However, this pattern angle drifts, due to the manufacturing error of the resonator. Since the drift effect causes degradation of the angle estimation performance of the resonator, the corresponding drift compensation control should be performed, to enhance the estimation performance. In this paper, a mathematical model of the hemispherical resonator gyro is first introduced. By using the mathematical model, a nonlinear observer for imperfection parameter estimation, and the corresponding compensation controller are designed to operate hemispherical resonator gyros, as angle measurement sensors.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.14 no.6
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• pp.68-73
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• 2005

Tire manufactures have dealt with noise problem by varying the pitch of the tread. The various formulas for the variations are generally determined differently, however. Often these variations are based on a combination of trial and error, intuition, and economics. Some manufactures have models and analogs to test tread patterns and their variations. These efforts, however practical, do not determine the best variation beforehand or guarantee the best results. For this reason it was felt that a general mathematical approach fur determining the best variation was needed. Moreover, the method should be completely general, easy to use, and sufficiently accurate. This paper discusses a mathematical method called Mechanical Frequency Modulation(MFM) which meets the above requirements. Thus, MFM pertains to computing an irregular time sequence of events so that the resulting excitation spectrum is shaped to a preferred form. The first part of this paper treats the theoretical basis for computing an optimum variation ; the second part discusses experimental results and simulation program which corroborate the theory.

• Research in Mathematical Education
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• v.18 no.3
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• pp.187-208
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• 2014

This study engages in the features of interaction in elementary school mathematics lessons as reflected in the class discourse. 28 pre-service teachers documented the discourse during observation of their tutor-teachers' lessons. Mapping the interaction patterns was performed by a unique graphic model developed for that purpose and enabled providing a spatial picture of the discourse conducted in the lesson. The research findings present the known discourse pattern "initiation-response-evaluation / feedback" (IRE/F) which is recurrent in all the lessons and the teacher's exclusive control over the class discourse patterns. Hence, the remaining time of the lesson for the pupils' discourse is short and meaningless.