• Education of Primary School Mathematics
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• v.25 no.4
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• pp.459-475
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• 2022

The equal sign and equivalence are the most basic and core concepts in elementary mathematics, but there has been lack of research on how to teach these concepts with textbooks. Given this, this study analyzed elementary mathematics textbooks in terms of three instructional elements (i.e., emphasizing the meaning of the equal sign as a relational symbol, dealing with an equation as an object for reasoning, and using an equation with a missing value). In particular, this study analyzed 10 different mathematics textbook series that are newly used in 2022 and examined the overall trends and characteristics for teaching the equal sign and equivalence. The results of this study showed that the activities emphasizing the meaning of the equal sign as a relational symbol were most noticeable but the activities dealing with an equation as an object for reasoning or using an equation with a missing value were relatively rare. Based on the results of the analysis, this study provides textbook writers with implications on what to further consider in covering the equal sign and equivalence.

• The Mathematical Education
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• v.9 no.2
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• pp.1-46
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• 1971

In this report. it is assumed in the first chapter. various motives for modernizing of school mathematics can be indicated as the development of modern mathematics the highly advanced technology. the emergence of computor, and the progress of symbol logic. It is also confirmed that its modernizing process contains the modernization of contents in school mathematics. the broad application of school mathematics. the intellectualization of school mathematics. and the variation of its educational process. And the following chapter of this report is composed of the comparative study on the modernizing tendency of school mathematics among the SMSG of U. S. A., the mathematical education in France. and the late tendancy of Japan. The most significant part of the report is the chapter which propose the new program for school mathematics. It establishes the direction of school mathematics and its purpose. And at the same time it divides its fundamental conceptions into six parts according to school grades; the number. the operation. the functional relation. the quality and measure, the geometry, and the statistics. For the perspective of school mathematics, it is probable that the program for education and training of teachers could be realized, if it were spported by the system of specializing teachers and of functional teachers with advanced technology of education. Particularly the education of teachers contains the training of teachers as well as educational administrators or parents. Finally, the report concludes that the necessity of research required for the development of school mathematics must be emphasized in regard to the established program of teacher training.

• School Mathematics
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• v.5 no.3
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• pp.361-384
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• 2003

The purpose of this study was to investigate students' problem solving process based on the model of IDEAL if they learn to solve word problems of simultaneous linear equations through structure-representation instruction. The problem solving model of IDEAL is followed by stages; identifying problems(I), defining problems(D), exploring alternative approaches(E), acting on a plan(A). 160 second-grade students of middle schools participated in a study was classified into those of (a) a control group receiving no explicit instruction of structure-representation in word problem solving, and (b) a group receiving structure-representation instruction followed by IDEAL. As a result of this study, a structure-representation instruction improved word-problem solving performance and the students taught by the structure-representation approach discriminate more sharply equivalent problem, isomorphic problem and similar problem than the students of a control group. Also, students of the group instructed by structure-representation approach have less errors in understanding contexts and using data, in transferring mathematical symbol from internal learning relation of word problem and in setting up an equation than the students of a control group. Especially, this study shows that the model of direct transformation and the model of structure-schema in students' problem solving process of I and D stages.

• The Mathematical Education
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• v.61 no.2
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• pp.305-322
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• 2022

Angle has a variety of aspects, such as figure, measurement, and rotation, but is mainly introduced from a figure perspective and a quantitative perspective of the angle is also partially experienced in the elementary mathematics textbooks. The purpose of this study was to examine how the angle concept introduction and development pattern in elementary school mathematics textbooks are linked or changed in middle school mathematics textbooks, and based on this, was to get the direction of writing math textbooks and implications for guidance. To this end, 57 math textbooks for the first grade of middle school were collected from the first to the 2015 revised curriculum. As a result of the study, it was found that middle school textbooks had a greater dynamic aspect of each than elementary school textbooks, and the proportion of quantitative attributes of angle was higher in addition to qualitative and relational attributes. In other words, the concept of angle in middle school textbooks is presented in a more multifaceted and complex form than in elementary school textbooks. Finally, matters that require consensus within elementary, secondary, and secondary schools were also proposed, such as the use of visual expression or symbol, such as the use of arrows and dots, and the use of mathematical terms such as vertex of angle and side of angle.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.1
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• pp.14-25
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• 1995

The main contribution of this paper can be summarized in two items as follws. Firstly, a modelling of mobile communication channel with Rayleigh fading characteristics is presented. Actual signal environments can be approximated as being real measurements by a proper mathematical representation of fluctuation of channel parameters due to Doppler effect, that is determined by the relative speed between transmitter and receiver, and noises, that vary at each sampling time. Secondly, an alternative procedure of synthesizing an adaptive equalizers is presented for recovering original signals that have been corrupted through the modelled channel. In order to compute the optimal tap coefficients for a high speed data(512 k symbol/sec) on a real-time basis, the CGM that guarantees fast and stable convergency is adopted during the training period of each frame. The coefficients obtained by the CGM are used as initial values for the LMS algorithm to trace the optimal coefficients during the data period that vary at each sampling time due to the mobility and noise at the receiver. Using the modelling presented in this paper, distributions of received signal power in various signal environments are demonstrated. The performance of the eqalizer proposed in this paper is shown as a function of BER under the various signal circumstances of mobile communications.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.6
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• pp.19-24
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• 1998

In this paper, a new closed form expression for the average symbol error rate(SER) of generalized selection combining(SC), whereby the two(three) signals with the two(three) largest amplitudes are combined from the original diversity branches in the channel, for MPSK signals in a frequency-nonselective slowly m-distributed Nakagami fading channel is derived. In order to analyze the error performance for a generalized SC, the Order-Statistics is applied. To derive the SER of MPSK signals with SC, the new expression of pdf is introduced and many other mathematical methods are used. Comparing the derived SER with that of MRC, we find adequate diversity branch number from total Lth-order diversity branches.

• Journal of Fisheries and Marine Sciences Education
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• v.25 no.1
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• pp.233-245
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• 2013

The purpose of this study is to analyse the effects on the academic achievement and learning motive in mathematics class by use of Cornell-note method at an elementary school. Thus, Cornell-mathematic note is designed for the experiment in order to recognize the effects how the Cornell-note influences students' mathematics academic achievement and learning motive. This experiment was carried out for 13 weeks and the target was 28 students. The group was consisted of 6rd grade students in elementary school located in Busan. To see the effects of Cornell-note method after experiment, post-test was carried out about mathematics academic achievement and learning motive. The results of this study are as follows: There was meaningful difference before and after test about mathematics academic achievement and learning motive. The academic achievement and learning motive in mathematics were improved after Cornell-note applied. Improvement of learning motive caused progress of academic achievement in mathematics class. The Cornell-note way is not appropriate, however, to reinforce mathematical communication ability and to attract students' interest. Therefore, systematic symbol is necessary and consider about adoption of story-telling way.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.7A
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• pp.725-733
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• 2006

In this paper, we propose an algorithm which makes the frequency of output signal synchronize with frequency of input signal in Equalization Digital On-channel Repeater (EDOCR) system which was proposed to overcome the disadvantage of conventional Digital On-Channel Repeater (DOCR). Also, we verify the algorithm by using the mathematical equivalent model and analysis the performance by implying the algorithm to EDOCR. The main idea is to use the frequency offset information, which comes from carrier recovery in the receiving part of EDOCR, when the demodulated symbol is re-modulated in transmitting part. Based on the proposed algorithm, EDOCR not only makes the output signal synchronized with input signal in frequency but also emit the output signal which satisfies the ATSC transmission standard without additional equipments such as Global Positioning System (GSP).

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.155-166
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• 2023

In 2018, Andrews introduced the partition functions ${\mathfrak{EO}}$(n) and ${\bar{\mathfrak{EO}}}$(n). The first of these denotes the number of partitions of n in which every even part is less than each odd part, and the second counts the number of partitions enumerated by the first in which only the largest even part appears an odd number of times. In 2021, Pore and Fathima introduced a new partition function ${\mathfrak{EO}}_e$(n) which counts the number of partitions of n which are enumerated by ${\bar{\mathfrak{EO}}}$(n) together with the partitions enumerated by ${\bar{\mathfrak{EO}}}$(n) where all parts are odd and the number of parts is even. They also proved some particular congruences for ${\bar{\mathfrak{EO}}}$(n) and ${\mathfrak{EO}}_e$(n). In this paper, we establish infinitely many families of congruences modulo 2, 4, 5 and 8 for ${\bar{\mathfrak{EO}}}$(n) and modulo 4 for ${\mathfrak{EO}}_e$(n). For example, if p ≥ 5 is a prime with Legendre symbol $({\frac{-3}{p}})=-1$, then for all integers n ≥ 0 and α ≥ 0, we have ${\bar{\mathfrak{EO}}}(8{\cdot}p^{2{\alpha}+1}(pn+j)+{\frac{19{\cdot}p^{2{\alpha}+2}-1}{3}}){\equiv}0$ (mod 8); 1 ≤ j ≤ (p - 1).