• School Mathematics
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• v.19 no.1
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• pp.137-151
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• 2017

This study aims to investigate the possibility of elementary students' generalization from three-digit numbers to multi-digit numbers in principles for addition and subtraction. One of main changes was the reduction of range of numbers for addition and subtraction from four-digit to three-digit. It was hypothesized that the students could generalize the principles of addition and subtraction after learning the three-digit addition and subtraction. To achieve the purpose of this study, we selected two groups as a sampling. One is called 'group 2015' who learned four-digit addition and subtraction and the other is called 'group 2016' who learned addition and subtraction only to three-digit. Because of the particularity of these subjects, this study covered two years 2015~2016. We applied our addition and subtraction test which contains ten three-digit or four-digit addition and subtraction items, respectively. We collected their results of the test and analyzed their differences using t-test. The results showed statistically meaningful difference between the mean score of the two groups only for four-digit subtraction. Based on the result, we discussed and made some didactical suggestions for teaching multi-digit addition and subtraction.

• School Mathematics
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• v.18 no.1
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• pp.175-191
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• 2016

In the elementary school mathematics textbook that has been revised in 2013, the instructional sequence for teaching addition and subtraction, which had remained unchanged for three decades since 1982, was finally changed in 2013. Particularly, the addition and subtraction of two-digit numbers without regrouping, such as 72+25=97 or 85-24=61, are taught earlier than the composing and decomposing of the number 10 using other numbers. This study examines the appropriacy and validity of these changes. However, the reason for these changes in the national curriculum or teacher's guide could not be determined. Further, several references emphasize the addition of two single-digit numbers, such as 7+8=15, and the subtraction of a single-digit number from a number between 11 and 19, such as 16-9=7, as basic facts. In other countries' textbooks, the teaching of addition and subtraction up to the number 20 is prioritized before teaching the addition and subtraction of two-digit numbers without regrouping. The results of this study indicate that these changes in the instructional sequence in the textbook that was revised in 2013 need to be reconsidered.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.469-486
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• 2022

Counting occupies a fundamental and important position in mathematical learning due to its relation to number concepts and numeral operations. In particular, counting up to large numbers is an essential learning element in that it is structural counting that includes the understanding of place values as well as the one-to-one correspondence and cardinal principles required by counting when introducing number concepts in the early stages of number learning. This study aims to derive didactical implications by investigating the possibility of and the strategies for counting large numbers that is expected to have no students' experience because it is not composed of current textbook activities. To do this, 89 second-grade elementary school students who learned the three-digit numbers and experienced group-counting and skip-counting as textbook activities were provided with questions asking how many penguins were in a picture where 260 penguins were irregularly arranged and how to count. As a result of analyzing students' responses in terms of the correct answer rate, the strategy used, and their cognitive characteristics, the incorrect answer rate was very high, and the use of decimal principles, group-counting, counting by one, and partial sum strategies were confirmed. Based on these analysis results, several didactical implications were derived, including the need to include counting up to large numbers as textbook activities.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.235-249
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• 2014

In this paper, teaching contents in area between Korea and Japan's first grade math textbooks are compared. Based on the results of this comparison, implications for improving our grade 1 math textbooks are obtained as follows. Firstly, when describing the configuration of two-digit numbers, it needs to be considered that, after the mathematical description of a concrete material representing two-digit numbers, then it should be processed mathematically. Secondly, with respect to the composition and decomposition of numbers, use of the expression of 'some number and some number' needs to be considered. Thirdly, when reading addition expression and subtraction expression with an equal sign, the way of reading them with terms 'sum' and 'difference' respectively needs to be reconsidered. Fourthly, use of the distinct expression for the supplementing situation and the merging situation respectively and use of the distinct expression for the removing situation and the comparing situation respectively need to be considered. Fifthly, the jump in representing the expression of subtraction of two numbers as the expression of the subtraction or mixed operation of three numbers to explain (some number)-(some number) with borrowing need to be resolved.

• Phonetics and Speech Sciences
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• v.5 no.1
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• pp.3-10
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• 2013

This study proposes a method to measure mental fatigue using speech technology, which has not been used in previous research and is easier than existing complex and difficult methods. It aims at establishing a relationship between the human voice and mental fatigue based on experiments to measure the influence of mental fatigue on the human voice. Two monotonous tasks of simple calculation such as finding the sum of three one digit numbers were used to measure the feeling of monotony and two sets of subjective questionnaires were used to measure mental fatigue. While thirty subjects perform the experiment, responses to the questionnaire and speech data were collected. Speech features related to speech source and the vocal tract filter were extracted from the speech data. According to the results, speech parameters deeply related to mental fatigue are a mean and standard deviation of fundamental frequency, jitter, and shimmer. This study shows that speech technology is a useful method for measuring mental fatigue.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.16 no.4
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• pp.33-41
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• 2006

RSA cryptosystem is of great use in systems such as IC card, mobile system, WPKI, electronic cash, SET, SSL and so on. RSA is performed through modular exponentiation. It is well known that the Montgomery multiplier is efficient in general. The critical path delay of the Montgomery multiplier depends on an addition of three operands, the problem that is taken over carry-propagation makes big influence at an efficiency of Montgomery Multiplier. Recently, the use of the Carry Save Adder(CSA) which has no carry propagation has worked McIvor et al. proposed a couple of Montgomery multiplication for an ideal exponentiation, the one and the other are made of 3 steps and 2 steps of CSA respectively. The latter one is more efficient than the first one in terms of the time complexity. In this paper, for faster operation than the latter one we use binary signed-digit(SD) number system which has no carry-propagation. We propose a new redundant binary adder(RBA) that performs the addition between two binary SD numbers and apply to Montgomery multiplier. Instead of the binary SD addition rule using in existing RBAs, we propose a new addition rule. And, we construct and simulate to the proposed adder using gates provided from SAMSUNG STD130 $0.18{\mu}m$ 1.8V CMOS Standard Cell Library. The result is faster by a minimum 12.46% in terms of the time complexity than McIvor's 2 method and existing RBAs.

• Speech Sciences
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• v.10 no.2
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• pp.249-258
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• 2003

This study attempted to examine a speaker identification method using difference sum and correlation coefficient determined from a pair of intensity level matrices of band-pass-filtered numeric sounds produced by ten female speakers of similar age and height. Subjects recorded three digit numbers at a quiet room at a sampling rate of 22 kHz on a personal computer. Collected data were band-pass-filtered at five different band ranges. Then, matrices of five intensity levels at 100 proportional time points were obtained. Pearson correlation coefficients and the sum of absolute intensity differences between a pair of given matrices were determined within and across the speakers. Results showed that very high correlation coefficient and small difference sum generally occurred within each speaker but some individual variation was also observed. Thus, the matrix pair with a higher coefficient and a smaller difference sum was averaged to form each individual's model. Comparison among the speakers yielded generally low coefficients and large differences, which suggests successful speaker identification, but among them there were a few cases with very high coefficients and small differences. Future studies will focus on finer band ranges and additional spectral parameters at some peak points of the intensity contour at a low frequency band.

• Education of Primary School Mathematics
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• v.17 no.3
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• pp.205-230
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• 2014

New teaching and learning theory on various aspects about class is needed to implement education which reflects constructivism, ideally. For an ideal learner-centered mathematics class, tangible and intangible elements related to education(view of knowledge, view of leaner, teacher's role, evaluation, the form of class, learning, teaching material, etc.) should be integrated from a constructive perspective and especially, teaching material has to be premised on that learners have intellectual abilities to construct knowledge themselves, and reflect integrity of knowledge, diversity and others, and contain open attributes. In addition to this, teaching material should have characteristics different from those when objective epistemology applies, so there is a need to analyze whether teaching material has those characteristics. For this, this study compared and analyzed <1. Three-Digit Numbers> which belongs to the domain of numbers and operations out of the units of mathematics(3) textbook of the 2009 revised curriculum for the first and second grade that first introduced story-telling, and <3. Understanding of Place Values> for the second grade of constructive math class used in the U.S.

• Education of Primary School Mathematics
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• v.22 no.3
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• pp.181-203
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• 2019

Even though the properties of operations in multiplication serve a fundamental basis of conceptual understanding the multiplication with whole numbers for elementary students, there has been lack of research in this field. Given this, the purpose of this study was to analyze instructional methods related to the properties of operations in multiplication (i.e., commutative property of multiplication, associative property of multiplication, distributive property of multiplication over addition) in a series of mathematics textbooks of Korea, Japan, and the US. The overall analysis was conducted in the following two aspects: (a) when and how to deal with the properties of multiplication in three instructional context (i.e., introduction, application, generalization), and (b) what models use to represent the properties of multiplication. The results of this showed that overall similarities in introducing the properties of multiplication .in (one digit) ${\times}$ (one digit) as well as emphasizing the divers representation. However, subtle but meaningful differences were analyzed in applying and generalizing the properties of multiplication. Based on these results, this paper closes with some implications on how to teach the properties of operations in multiplication properties in elementary mathematics.

• Journal of Chest Surgery
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• v.49 no.sup1
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• pp.44-52
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• 2016

Background: This study investigates the perception of the general public regarding the concentration to metropolitan, hospitals of cardiac and cerebrovascular surgeries, and the perceived public need for government policies to resolve this issue. Methods: A total of 800 participants were recruited for our telephone interview survey. Quota sampling was performed, adjusting for age and sex, to select by various geographic regions. Sampling with random digit dialing was performed; we called the randomly generated telephone numbers and made three attempts for non-responders before moving on to a different telephone number. Results: Our sample population was 818 participants, 401 men (49.0%) and 417 women (51.0%). Our data showed that 85.5% of participants thought that cardiac surgery and neurosurgery patients are concentrated in large hospitals in Seoul. The principle reason for regional patients to want to receive surgery at major hospitals in Seoul was because of poor medical standards associated with regional hospitals (87.7%). We found that a vast majority of participants (97.5%) felt that government policies are needed to even out the clustering of cardiac surgery and neurosurgery patients, and that this clustering may be alleviated if policies that can specifically enhance the quality and the capacity of regional hospitals to carry out surgeries are adopted (98.3%). Conclusion: Government policy making must reflect public desiderata, and we suggest that these public health needs may be partially resolved through government-designated cardiac and neurosurgery specialist hospitals in regional areas.