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김부윤,이양 釜山大學校 師範大學 1997 교사교육연구 Vol.34 No.-
In this note, inducing method of matrices and linear transformations in high school will be introduced.
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중등교육과정에서의 최대공약수와 최소공배수의 지도법에 관한 연구
김부윤,이양 釜山大學校 師範大學 1997 교사교육연구 Vol.34 No.-
In this note, we discuss an effective method of teaching g.c.d. and l.c.m. in high school class.
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김부윤,이지성,Kim, Boo-Yoon,Lee, Ji-Sung 한국수학사학회 2007 Journal for history of mathematics Vol.20 No.3
We review the eastern frog jump game and the western solitaire to apply the Baduk Pieces Game to mathematical education. This study introduce a didactical method of Baduk Pieces Game which is constructed with simplification, generalization, and extension. This didactical applications of the Baduk Pieces Game gives the students opportunities of patterns, generalization, and problem solving strategies.
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김부윤,정영우,Kim, Boo-Yoon,Chung, Young-Woo 영남수학회 2010 East Asian mathematical journal Vol.26 No.4
We study mathematization of natural thinking and some materials developed in geometric construction of regular n-polygons. This mathematization provides a nice model for illustrating interesting approaches to trigonometric functions and trigonometric ratios as well as their inter-connections. Thereby, results of this paper will provide the procedure of the development for these concepts in natural way, which will be helpful for understanding background knowledges.
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김부윤,정영우,박영식,Kim, Boo-Yoon,Chung, Young-Woo,Park, Young-Sik 영남수학회 2010 East Asian mathematical journal Vol.26 No.2
We study the theoretical background on the relationship between the equality property and operations treated in different sub-areas in secondary school mathematics curriculum respectively studied. Furthermore, we discuss in detail the equality property in rational numbers field $\mathbb{Q}$ and the real numbers field $\mathbb{R}$. Through this study, professional knowledges of school teachers are enhanced so that these aforementioned knowledges are connected smoothly to teaching activities in classrooms.
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김부윤,정경미 대한수학교육학회 2009 학교수학 Vol.11 No.4
Various theories of mathematics education which have been considered by many European researchers particularly, in France, recently are introduced. The Anthropological Theory of the didactic discussed by Chevallard will be briefly introduced. Then the praxeology as Anthropological model according to Che vallard's theory will be discussed. The necessity of Anthropological Theory, its background of development through the transition process of didactic, and its basic elements will be discussed further. Additionally, teaching limit of sequences in high school mathematics will be suggested according to the theory. 이 논문에서는 최근 유럽, 특히 프랑스에서 많은 연구자들에 의해 고려되어지고 있는 수학 교육의 다양한 이론들을 소개한다. 그 중에서도 Chevallard (1985;1992;1998)에 의해 논의되었던 교수학의 인류학적 이론(The Antro -pological Theory of the Didactic)에 대해 간단히 소개한 다음, 이것에 의해 제안된 인식론적 모델인 인간행동학(Praxeology)에 대해 논의한다. 또한 교수학에 인류학을 도입해야 하는 필요성과 이 이론이 어떻게 교수학적 변환 과정을 통하여 발전되었는지 그 배경과 교수학의 인류학적 이론의 기본 요소들을 제시된다. 마지막으로 ‘수열의 극한’ 교수에 대한 문제를 이 이론에 근거하여 분석한다.
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Byproduct Mathematization에 관한 연구
김부윤,정영우 대한수학교육학회 2010 수학교육학연구 Vol.20 No.2
Concepts in mathematics have been formulated for unifying and abstractizing materials in mathematics. In this procedure, usually some developments happen by necessity as well as for their own rights, so that various interesting materials can be produced as byproducts. These byproducts can also be established by themselves mathematically, which is called byproduct mathematization (sub-mathematization). As result, mathematization and its byproduct mathematization interrelated to be developed to obtain interesting results and concepts in mathematics. In this paper, we provide explicit examples:the mathematization is the continuity of trigonometric functions, while its byproduct mathematization is various trigonometric identities. This suggestion for explaining and showing mathematization as well as its byproduct mathematization enhance students to understand trigonometric functions and their related interesting materials. 본 연구에서는 수학적 지식이 구명되고 형식화되는 과정을 ‘수학화(mathemati- zation)’와 ‘곁가지의 수학화(byproduct mathematization)’란 개념으로 정의하고 분석하였다. 수학화는 수학적 개념들 간의 내적연결성 및 당위성을 경험하도록 교수․학습 활동을 구성하는데 있어 하나의 모델이 된다. 그리고 구체적 예로 ‘삼각함수의 연속성에 대한 수학화’와 ‘삼각함수의 덧셈정리의 곁가지의 수학화’를 구성하였다. 이러한 수학화는 교사의 전문성 신장을 위한 학문적 배경 지식을 주며, 가르칠 지식에 대한 다양한 지도 관점을 제공한다.
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김부윤,정영우,Kim, Boo-Yoon,Chung, Young-Woo 한국수학사학회 2008 Journal for history of mathematics Vol.21 No.1
We investigate the inducing method of irrational numbers in junior high school, under algebraic as well as geometric point of view. Also we study the treatment of irrational numbers in the 7th national curriculum. In fact, we discover that i) incommensurability as essential factor of concept of irrational numbers is not treated, and ii) the concept of irrational numbers is not smoothly interconnected to that of rational numbers. In order to understand relationally the incommensurability, we suggest the method for inducing irrational numbers using construction in junior high school.
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