• School Mathematics
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• v.12 no.1
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• pp.45-60
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• 2010

In school mathematics, gakdo(korean, ie angular measure in english) lost effectiveness as a term, on the other hand, an expression gak-ui-kugi(korean, ie size of angle in english) is prevalent these days. So it is necessary to accept this expression. It is necessary to specify in textbook that the size of angle rely on the degree of gap between two edges regardless of the length of edges. The content of curriculum manual and the content of textbooks must be reconciled. Random units for measuring the size of angle are not contained in textbooks. It can be possible, but it is not carried out actually. So, it is necessary not to require it in curriculum manual considering this circumstance. In curriculum manual, it is necessary to specify the role of 1-right angle as a standard unit, and situations to use it must be presented in textbooks. In cut-paste method of finding the sum of the size of three angles in a triangle and the sum of the size of four angles in a quadrilateral, keeping a straight angle and one rotation in mind, an explanation is based upon a premise that students know how to express the $180{^{\circ}}$ and $360{^{\circ}}$ in figure as a result. It is a leap of logic.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.99-120
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• 2001

The purpose of this thesis is to find the guiding direction of mathematical communication in lower grade students of elementary school and to present a new direction about the effect of using concrete material in communication. It is expected that mathematical communication increases when concrete material is used for the students of the lower grades, who are in concrete operational period. Therefore, this study ai s to investigate what characteristics there are in mathematical communication of second grade students and what effect concrete materials have on mathematical communication and learning. The analysis of the teaching record shows that the second grade students use alternative terms in the process of communication since they are not familiar with mathematical symbols or terms, which is a characteristic of communication in a mathematics class in which concrete material is used. In the process of teaming the students apply their living experiences to their teaming. Since a small number of students lead class, the interaction between students is also led by them. The direction of communication in a small group is not centered around solution of a problem, and most students show a more interest in finding answers than in the process of learning. The effect that concrete material has on communication plays an important role in promoting students' speaking activity; it allows students to identify and correct their errors more easily. It also makes students' activities more predictable, and it increases a small group activities through the medium of concrete material. However, it was also noticed that students' listening activities are not appropriately developed since they do not pay attention to a teacher who uses concrete material. The effects that concrete material has on mathematics class can be summarized as follows. Concrete material promotes students' participation in class by triggering their interest of learning of mathematics and helps them to understand the course of learning. It also helps the teaming and formation of concepts for children of low academic performance. And it makes a phased learning possible according to students' ability to use concrete material and to solve a problem. Based upon the results above mentioned, the use of concrete material is absolutely needed in mathematics classes of lower grade elementary school students since it increases communication and gives much influence on mathematics learning. Therefore, teachers need to develop teaching or learning method which can help increase communication, considering the characteristics of students' communication.

• The Mathematical Education
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• v.61 no.2
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• pp.339-357
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• 2022

This study explores pre-service secondary mathematics teachers (PSTs)' noticing competency. 17 PSTs participated in this study as a part of the mathematics teaching method class. Individual PST's essays regarding the question 'what effective mathematics teaching would be?' that they discussed and wrote at the beginning of the course were collected as the first data. PSTs' written analysis of an expert teacher's teaching video, colleague PSTs' demo-teaching video, and own demo-teaching video were also collected and analyzed. Findings showed that most PSTs' noticing level improved as the class progressed and showed a pattern of focusing on each key aspect in terms of the Teaching for Robust Understanding of Mathematics (TRU Math) framework, but their reasoning strategies were somewhat varied. This suggests that the TRU Math framework can support PSTs to improve the competency of 'what to attend' among the noticing components. In addition, the instructional reasoning strategies imply that PSTs' noticing reasoning strategy was mostly related to their interpretation of noticing components, which should be also emphasized in the teacher education program.

• Education of Primary School Mathematics
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• v.19 no.3
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• pp.193-210
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• 2016

In the $10{\div}2.4$ problem situation, we could find that curious upper and middle level students' solution. They solved $10{\div}2.4$ and wrote the result as quotient 4, remainder 4. In this curious response, we researched how students realize quotient and remainder in division of decimal. As a result, many students make errors in division of decimal especially in remainder. From these response, we constructed fraction based teaching method about division of decimal. This method provides new aspects about quotient and remainder in division of decimal, so we can compare each aspects' strong points and weak points.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.515-531
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• 2008

The visual cryptography scheme is a simple method which can be decoded directly the secret information in human visual system without performing any cryptographic computations. For some secret of image type, we scatter them to random n images and if any threshold (or more) of them are stacked together then original image is visible. In this paper we consider (2,n) visual cryptography scheme and show a construction method of the sample matrix using the rule of binomial coefficients $_nC_2$. This scheme can contribute interesting and effectiveness to the study of mathematics.

• Journal of Science Education
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• v.33 no.2
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• pp.207-219
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• 2009

This study aims to investigate the key common topics identified and discussed in relevant literature associated with the integrative efforts among STEM disciplines. The key methodology and pedagogy were examined and the significant benefits of using the design method for STEM education were discussed. Meta-analysis was employed and qualitative approach was mainly used to synthesize the major findings and conclusions of the 33 empirical studies. The findings of this meta-analysis revealed that the types and names describing the design methods used the various terms, but the key features have reflected the similar pedagogical benefits and key characteristics. The engineering design is an effective strategic methodology and pedagogy for STEM education. In addition, the design methods show the key benefits including (1) to improve academic achievement, (2) to promote students' affective gains, (3) to facilitate collaborative learning, and (4) to explore STEM related careers and jobs. The collaborative works among STEM professions are needed to promote the benefits of using design methods for integrating STEM subjects.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.11
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• pp.5643-5646
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• 2012

Background and Objectives: Increase of mortality rates of gastric cancer in Iran and the world in recent years reveal necessity of studies on this disease. Here, hazard function for gastric cancer patients was estimated using Wavelet and Kernel methods and some related factors were assessed. Materials and Methods: Ninety-five gastric cancer patients in Fayazbakhsh Hospital between 1996 and 2003 were studied. The effects of age of patients, gender, stage of disease and treatment method on patient's lifetime were assessed. For data analyses, survival analyses using Wavelet method and Log-rank test in R software were used. Results: Nearly 25.3% of patients were female. Fourteen percent had surgery treatment and the rest had treatment without surgery. Three fourths died and the rest were censored. Almost 9.5% of patients were in early stages of the disease, 53.7% in locally advance stage and 36.8% in metastatic stage. Hazard function estimation with the wavelet method showed significant difference for stages of disease (P<0.001) and did not reveal any significant difference for age, gender and treatment method. Conclusion: Only stage of disease had effects on hazard and most patients were diagnosed in late stages of disease, which is possibly one of the most reasons for high hazard rate and low survival. Therefore, it seems to be necessary a public education about symptoms of disease by media and regular tests and screening for early diagnosis.

• Journal of Korean Society of Transportation
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• v.34 no.3
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• pp.248-262
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• 2016

The study documents the analysis on characters and symbols shown in the pavement markings in the perspective of mathematics educators. The purpose of this study is to propose a pavement marking method that can enhance readability from the driver's eye position. To this end, this study analyzed the figure of the pavement markings that can be actually recognized by the projective geometry perspective. As a result, it proposed alternatives to the current pavement markings by introducing the concept of the compression ratio. Results of the study are as follows. First, the rule was established to obtain the compression ratio. If the observation of two viewing angles are x and y, then the compression ratio S is ${\sin}y/{\cos}\(\frac{x-y}{2}\)$. Second, we presented two alternatives to the pavement marking method for the displayed information. One is a method for improving the pavement markings in terms of the compression ratio, the other is a method by varying vertical length of the pavement markings while holding its width constant. Based on the outcomes from this study, a mathematical analysis can be further studied for the perception of speed according to the types of pavement marking line.

• The Mathematical Education
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• v.45 no.4 s.115
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• pp.481-491
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• 2006

Diffy is a simple mathematical puzzle that provides elementary-school students with subtraction practice. The idea appears to have originated in the late nineteenth century with E. Ducci of Itali. Thirty years ago Professor J. Copley of the University of Houston introduced the diffy game to teachers in elementary schools and it widely spreaded out. During the diffy activity we naturally guess many interesting conjectures. First, does diffy always end? Second, does the head of diffy always exist? Third, for an arbitrary given natural number n, is there any possible method to find the diffy with the given length n? In this study I give the necessary and sufficient condition for the existence of the head of diffy. Using this condition I classify all possible heads of diffy and provide an algorithm to find the diffy with any given length n. With this algorithm I find four natural numbers with diffy length 200. To ensure my numbers are correct, I make a diffy program for Mathematica and check they are correct. I suggest the diffy game is good for enlarging the mathematical thinking to all graded students, especially gifted and talented students, It will produce rational consideration and synthetic judgement.

• Research in Mathematical Education
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• v.8 no.2
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• pp.107-114
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• 2004

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.