• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.101-116
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• 2005

The purpose of this study is to survey mathematics teacher's cognition of proof along with their proof forms of expression and proof ability, and to explore the relationship between their proof scheme and teaching practice. This study shows that mathematics teachers tend to regard proof as a deduction from assumption to conclusion and that they prefer formal proof with mathematical symbols. Mathematics teachers also recognize that prof is an important area in school mathematics but they reveal poor understanding of teaching methods of proof. Teachers tend to depend on the proof style employed in mathematics textbooks. This study demonstrates that a proof scheme is a major factor of determining the teaching method of proof.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.19-35
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• 2018

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.281-302
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• 2015

In the current study, answer sheets from 8007 students in 236 Korean schools were selected and analyzed to examine errors that emerge in the process of solving descriptive questions of the National Educational Achievement Assessment in mathematics. Questions used in the analysis were response assessment covering middle school mathematics topics: "mathematical symbols and equations" and "functions." The behavioral domain of the questions was that of "problem solving and computation," which requires establishing an equation for a word problem and allows the calculation of an answer that meets a certain condition. The analysis results revealed various errors in each stage of each question, from understanding to solving; the study attempts to conjecture causes for these errors and draw pedagogical implications.

• Research in Mathematical Education
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• v.15 no.1
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• pp.1-14
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• 2011

Logo has influenced many researchers and learners for the past decades as a 20 turtle geometry environment in the perspective of constructionism. Logo uses the metaphor of 'playing turtle' that is intrinsic, local and procedural. We, then, design an environment in which the metaphor of 'playing turtle' is applied to construct 3D objects, and we figure out ways to represent 3D objects in terms action symbols and 3D building blocks. For this purpose, design three kinds of representation systems, and asked students make various 3D artifacts using various representation systems. We briefly introduce the results of our investigation into students' cognitive burden when they use those representation systems, and discuss the future application measures and the design principles of Logo-based 3D microworld.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.121-141
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• 2016

In Korea where there is the national curriculum and teachers depend highly on textbooks, the school mathematics is based on curriculum and textbooks. Especially considering responsibility that textbooks should reflect the curriculum properly, it is necessary to analyze the connection of mathematics curriculum and textbooks in order to review and improve the quality of our mathematics education. This research analyzes the connection of curriculum and textbooks for 5~6 grades and aims to have some implications for revision of the textbooks when application of elementary mathematics textbooks based on the 2009 revised national curriculum is completed to all grades. Following the preceding research for 1~2 and 3~4 grades, this research sets 5~6 grades as a subject of analysis and has four contents of analysis; analysis of textbooks based on restructured achievement criteria, analysis of connections between unit objectives of textbooks and the reconstructed achievement criteria, analysis of textbooks related to mathematical terms and symbols, and analysis of textbooks related to mathematical process. The result of analysis has some implications to develop textbooks based on the 2015 revised national curriculum.

• The Mathematical Education
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• v.40 no.2
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• pp.241-252
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• 2001

Many high school students are having difficulties for studying advanced mathematics concepts. It is more complicated than in junior high school and they are losing interest and confidence. In this paper, advanced mathematics concepts are not just basic concepts such as natural numbers, fractions or figures that can be learned through life experience but concepts that are including variables, functions, sets, tangents and limits are more abstract and formal. For the students to understand these ideas is too heavy a burden and so many of the students concentrate their efforts on just memorizing and not understanding. It is necessary to search for a meaningful method of teaching for advanced mathematics that covers deductive methods and symbols. High school teachers are always asking themselves the following question, “How do we help the students to understand the concept clearly and instruct it in a meaningful way?” As a solution we propose the followings : I. To ensure they have the right understanding of concept image involved in the concept definition. II. Put emphasis on the process of making mental representations and the role of intuition. III. To instruct students and understand them as having many chance of the instructional conversation. In conclusion, we studied the meaningful method of teaching with the theory of Ausubel related to the above proposed methods. To understand advanced mathematics concepts correctly, the mutual understanding of both teachers and students is necessary.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.181-204
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• 2014

This research aims to have some implications for revision of curriculum and textbooks by analysing connections between the 2009 revised national curriculum and its textbooks in elementary school mathematics. The results of analyses for 3~4 grades can be summarized in four aspects: Firstly, we noticed that the reconstructed achievement criteria were reflected properly in the textbooks except for use of calculators in 'Numbers and Operations'. Secondly, the analysis of connections between unit objectives of textbooks and the reconstructed achievement criteria suggests that 10 units must receive attention. Especially, the range of decimal numbers for adding and subtracting needs to be corrected. Thirdly, mathematical terms and symbols excluding 'unit fraction' were found in the textbooks. Finally, mathematical processes were also fully reflected in the textbooks. However 'simplifying' as a strategy for problem solving was only missing. This result shows good or poor connections between the curriculum and its textbooks, therefore it is expected to be used effectively to revise the national curriculum for mathematics and its textbooks.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.1-12
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• 2022

In this paper we prove an even characteristic analogue of the result of Andrade on lower bounds for moment of quadratic Dirichlet L-functions in odd characteristic. We establish lower bounds for the moments of Dirichlet L-functions of characters defined by Hasse symbols in even characteristic.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.343-350
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• 2013

In this paper we prove that if Toeplitz operators $T^{\alpha}_u$ with symbols in RW satisfy ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}{\rightarrow}0$ as $z{\rightarrow}{\partial}\mathbb{D}$ then $T^{\alpha}_u$ is compact and also prove that if $T^{\alpha}_u$ is compact then the Berezin transform of $T^{\alpha}_u$ equals to zero on ${\partial}\mathbb{D}$.