• Journal of Navigation and Port Research
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• v.32 no.8
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• pp.603-609
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• 2008

Manta-type Unmanned Undersea Test Vehicle(MUUTV) is based on the same design concept as Unmanned Undersea Vehicle called Manta Test Vehicle(MTV), which was originally built and operated by the Naval Undersea Warfare Center(Lisiewicz et al., 2000, Sirmalis et al. 2001). The authors carried out the sensitivity analysis of the response of manoeuvring motion of MUUTV to changes in hydrodynamic derivatives, In order to calculate the sensitivity indices of hydrodynamic derivatives on MUUTV, the method by Sen(2000) was adopted Basically the dynamic mathematical model with six degrees of freedom by Feldman(1979) is used but a little revised, refered to Sohn et al.(2006) and some experiment in circulating water channel. Through the present research, some hydrodynamic derivatives of significance are found out, and also the numerical simulation using simplified mathematical model based on result of sensitivity analysis is ascertained to be enough for prediction of manoeuvring characteristics of MUUTV.

• The Mathematical Education
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• v.56 no.1
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• pp.19-39
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• 2017

Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don't appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers' understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson's statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

• The Mathematical Education
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• v.58 no.4
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• pp.531-543
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• 2019

Continuous probability distribution was one of the mathematics concept that students had difficulty. This study analyzed the definition and introduction of the continuous probability distribution under the 2009-revised curriculum and 2015-revised curriculum. In this study, the following subjects were studied. Firstly, definitions of continuous probability variable in 'Probability and Statistics' textbook developed under the 2009-revised curriculum and 2015-revised curriculum were analyzed. Secondly, introductions of continuous probability distribution in 'Probability and Statistics' textbook developed under the 2009-revised curriculum and 2015-revised curriculum were analyzed. The results of this study were as follows. First, 8 textbooks under the 2009-revised curriculum defined the continuous probability variable as probability variable with all the real values within a range or an interval. And 1 textbook under the 2009-revised curriculum defined the continuous probability variable as probability variable when the set of its value is uncountable. But all textbooks under the 2015-revised curriculum defined the continuous probability variable as probability variable with all the real values within a range. Second, 4 textbooks under the 2009-revised curriculum and 4 textbooks under 2015-revised curriculum introduced a continuous random distribution using an uniformly distribution. And 5 textbooks under the 2009-revised curriculum and 5 textbooks under the 2015-revised curriculum introduced a continuous random distribution using a relative frequency density.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.319-343
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• 2006

The purpose of this study is to investigate how fifth and sixth graders recognize average and to find out suggestions for teaching/learning methods of average by examining which difference there is depending on the way of the word problem presentation. For the this purpose, was conducted experiment study with the way of the world problem presentation set up as experimental treatment. The conclusions drawn from the results obtained in the this study were as follows : First, since students who did not learn the regular course of average had various informal concepts already, it is needed to consider handling more various concepts of average in order to enable students to expand flexible thoughts. Second, compared with fifth and sixth graders showed a wide difference in informal concepts of average depending on the way of the word problem presentation. In expect data with given average, concepts of mean as algorithm, balance point, and mode indicated similar percentage, while in estimate average with given data, the percentage of students who showed the concept of mean was very high at 67.6%. That may be because problems related to mean in the current textbooks are items of 'estimate average with given data', so in types of 'estimate average with given data', students solve questions with mean as algorithm without considering situations of problems. This result suggests that it is necessary to diversify the way of the word problem presentation even in textbooks. Third, as a result of analyzing informal concepts of average, there was significant difference in grades. In addition, the results suggested that there would be difference in the concepts of average depending on gender or attributes of discrete quantity and continuous quantity.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.477-490
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• 2011

The concept of pedagogical content knowledge (PCK) has been developed and expanded to identify essential components of mathematical knowledge for teaching (MKT) by Ball and her colleagues (2008). This study proposes an alternative perspective to view MKT focusing on key developmental understandings (KDUs) that carry through an instructional sequence, that are foundational for learning other ideas. In this study we provide constructive components of KDUs in fraction multiplication by focusing on the constructs of 'three-level-of-units structure' and 'recursive partitioning operation'. Expecially, our participating preservice elementary teacher, Jane, demonstrated that recursive partitioning operations with her length model played a significant role as a KDU in fraction multiplication.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.465-479
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• 2012

For $0<p{\leq}{\infty}$ and a convex body $K$ in $\mathbb{R}^n$, Lutwak, Yang and Zhang defined the concept of dual $L_p$-centroid body ${\Gamma}_{-p}K$ and $L_p$-John ellipsoid $E_pK$. In this paper, we prove the following two results: (i) For any origin-symmetric convex body $K$, there exist an ellipsoid $E$ and a parallelotope $P$ such that for $1{\leq}p{\leq}2$ and $0<q{\leq}{\infty}$, $E_qE{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$; For $2{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, $2^{-1}{\omega_n}^{\frac{1}{n}}E_qE{\subseteq}{\Gamma}_{-p}K{\subseteq}{2\omega_n}^{-\frac{1}{n}}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$. (ii) For any convex body $K$ whose John point is at the origin, there exists a simplex $T$ such that for $1{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, ${\alpha}n(nc_{n-2,p})^{-\frac{1}{p}}E_qT{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qT$ and $V(K)=V(T)$.

• Communications of Mathematical Education
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• v.25 no.4
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• pp.681-691
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• 2011

Mathematics curriculum according to 2009 Revised National Curriculum suggests that school mathematics must cultivate interest and curiosity about mathematics in addition to creative thinking ability of students, and ability and attitude of observing and analyzing many things happening around. Centroid of a triangle in 2007 Revised National Curriculum is defined as 'an intersection point of three median lines of a triangle' and it has been instructed focusing on proof study that uses characteristic of parallel lines and similarity of a triangle. This could not teach by focusing on the centroid itself and there is a problem of planting a miss concept to students. And therefore this writing suggests centroid must be taught according to its essence that centroid is 'a dot that forms equilibrium', and a justification method about this could be different.

• Communications of Mathematical Education
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• v.29 no.2
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• pp.255-279
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• 2015

Educating for character was emphasized in 2009 reformed Korea national mathematics curriculum. Thus, in this study we basically conducted to realize the character education. This study aimed to develop the teaching and learning materials for character education in middle school. For the purpose of this study, the following study was carried out. First, we investigated the concept of character education. Second, based on this, we extracted the three factor(altruism, rationality, course orientation) for character education in mathematics teaching and learning. Third, we developed five teaching and learning models for character education. The five kinds of models are 'Respect model', 'Self-directed model', 'Cooperation-centered model', 'Self-interest model, 'Story sympathy model'. Finally, We have developed a teaching and learning materials in accordance with the models. And, we applied to the classroom and confirmed its effectiveness.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.59-75
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• 2012

This study aims to find whether the solutions for well-structured problems learned in school can be transferred to the moderately-structured problem and ill-structured problem. For these purpose, research questions were set up as follows: First, what are the patterns of changes in strategies used in solving the mathematics problems with different level of structuredness? Second, From the group using and not using proportion algorithm strategy in solving moderately-structured problem and ill-structured problem, what features were observed when they were solving that problems? Followings are the findings from this study. First, for the lower level of structuredness, the frequency of using multiplicative strategy was increased and frequency of proportion algorithm strategy use was decreased. Second, the students who used multiplicative strategies and proportion algorithm strategies to solve structured and ill-structured problems exhibited qualitative differences in the degree of understanding concept of ratio and proportion. This study has an important meaning in that it provided new direction for transfer and analogical problem solving study in mathematics education.