• The Mathematical Education
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• v.51 no.1
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• pp.1-19
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• 2012

In this study, contents of 'the 2007 revised curriculum handbook' and 16 kinds of mathematics textbooks were analyzed first. The purpose of this study is to examine the understanding state of students at general high schools by making questionnaires to survey the understanding state on contents of chapter of complex number based on above analysis. Results of research can be summarized as follows. First, the content of chapter of complex number in textbook was not logically organized. In the introduction of imaginary number unit, two kinds of marks were presented without any reason and it has led to two kinds of notation of negative square root. There was no explanation of difference between delimiter symbol and operator symbol at all. The concepts were presented as definition without logical explanations. Second, students who learned with textbook in which problems were pointed out above did not have concept of complex number for granted, and recognized it as expansion of operation of set of real numbers. It meant that they were confused of operation of complex numbers and did not form the image about number system itself of complex number. Implications from this study can be obtained as follows. First, as we came over to the 7th curriculum, the contents of chapter of complex number were too abbreviated to have the logical configuration of chapter in order to remove the burden for learning. Therefore, the quantitative expansion and logical configuration fit to the level for high school students corresponding to the formal operating stage are required for correct configuration of contents of chapter. Second, teachers realize the importance of chapter of complex number and reconstruct the contents of chapter to let students think conceptually and logically.

• Geophysics and Geophysical Exploration
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• v.20 no.2
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• pp.100-113
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• 2017

Induced polarization (IP) method is based on the measurement of a polarization effect known as overvoltage of the ground. IP techniques have been usually used to find mineral deposits, however, nowadays widely applied to hydrogeological investigations, surveys of groundwater pollution and foundation studies on construction sites. IP surveys can be classified by its source type, i.e., time-domain IP estimating chargeability, frequency-domain IP measuring frequency effect (FE), and complex resistivity (CR) and spectral IP (SIP) measuring complex resistivity. Recently, electromagnetic-based IP has been studied to avoid the requirement for spike electrodes to be placed in the ground. In order to understand IP methods in this study, we: 1) classify IP surveys by source type and measured data and illustrate their basic theories, 2) describe historical development of each IP forward modeling and inversion algorithm, and finally 3) introduce various case studies of IP measurements.