• East Asian mathematical journal
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• v.32 no.4
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• pp.545-563
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• 2016

The aim of this study was to observe processes and implication to a given program for the 20 gifted children grade 5 by making the number from 1 to 100 with natural numbers 4,4,9 and 9. Revelation of creativity, mathematical tendency of students and meaningful responses were observed by the qualitative records of this game activity and the analysis of result. The major result of a study is as follows: The mathematical creativities of students were revealed and developed by this activity. And the mathematical attitude were changed and developed, so student could actively participate. And students could experience collaborative and social composition learning by presentations and discussion, competition with a permissive atmosphere and open-game rule. It was meaningful that mathematical ideas (negative number, square root, factorial, [x]: the largest integer not greater than x, absolute value, percent, exponent, logarithm etc.) were suggested and motivated by students themselves.

• 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.

• School Mathematics
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• v.10 no.3
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• pp.357-374
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• 2008

The complex number system is supposed to introduce first chapter in the first grade of high school. When number system is expanded to complex numbers, the main aim is to understand preservation of algebraic structure with regard to the flow of curriculum and textbook. This research reviewed overall alternative articulation and treatment of textbooks from a logical viewpoint. Two research questions are developed below. First, in the structure of the current curriculum, when we consider student's 'level', how are the alternative articulation and treatment of textbooks in complex unit on a logical point of view? Second, What are more logical alternative articulation and treatment? What alternative articulation and treatment are suitable for a running goal? and what are the improvement which is definitive?

• Korean Journal of Agricultural and Forest Meteorology
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• v.11 no.2
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• pp.61-71
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• 2009

Most deciduous trees in temperate zone are dormant during the winter to overcome cold and dry environment. Dormancy of deciduous fruit trees is usually separated into a period of rest by physiological conditions and a period of quiescence by unfavorable environmental conditions. Inconsistent and fewer budburst in pear orchards has been reported recently in South Korea and Japan and the insufficient chilling due to warmer winters is suspected to play a role. An accurate prediction of the flowering time under the climate change scenarios may be critical to the planning of adaptation strategy for the pear industry in the future. However, existing methods for the prediction of budburst depend on the spring temperature, neglecting potential effects of warmer winters on the rest release and subsequent budburst. We adapted a dormancy clock model which uses daily temperature data to calculate the thermal time for simulating winter phenology of deciduous trees and tested the feasibility of this model in predicting budburst and flowering of Niitaka pear, one of the favorite cultivars in Korea. In order to derive the model parameter values suitable for Niitaka, the mean time for the rest release was estimated by observing budburst of field collected twigs in a controlled environment. The thermal time (in chill-days) was calculated and accumulated by a predefined temperature range from fall harvest until the chilling requirement (maximum accumulated chill-days in a negative number) is met. The chilling requirement is then offset by anti-chill days (in positive numbers) until the accumulated chill-days become null, which is assumed to be the budburst date. Calculations were repeated with arbitrary threshold temperatures from $4^{\circ}C$ to $10^{\circ}C$ (at an interval of 0.1), and a set of threshold temperature and chilling requirement was selected when the estimated budburst date coincides with the field observation. A heating requirement (in accumulation of anti-chill days since budburst) for flowering was also determined from an experiment based on historical observations. The dormancy clock model optimized with the selected parameter values was used to predict flowering of Niitaka pear grown in Suwon for the recent 9 years. The predicted dates for full bloom were within the range of the observed dates with 1.9 days of root mean square error.