• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.841-862
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• 2013

This study analyzed issues in the mathematics curriculum concerning the cognitive development of the vector and inner product concepts in the light of Tall's and Watson's research(Tall, 2004a; Tall, 2004b; Watson et al., 2003; Watson, 2002). Some suggestions in teaching the vector and inner product concepts were elaborated in the terms of these analyses. First, the position vector needs to be represented by an arrow on the coordinate system in order to introduce the component form of a vector represented by a directed line segment. Second, proofs of the vector operation law should be carried out by symbolic manipulations based on the algebraic concept of a vector in the symbolic world. Third, it is appropriate that the inner product is defined as $\vec{a}{\cdot}\vec{b}=a_1b_1+a_2b_2$ (when, $\vec{a}=(a_1,a_2)$, $\vec{b}=(b_1,b_2)$) when it comes to considering the meaning of the inner product relevant to vector space in the formal world. Cognitive growth of concepts of the vector and inner product can be properly induced through revising explanation methods about the concepts in the curriculum in the basis of the above suggestions.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.59-72
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• 2007

There are three kinds of order of instruction in mathematics, that is, historical order, theoretical organization and lecturing organization-order. Simply speaking, each lecturing organization-order is a combination of two preceding orders. The problem is how to combine between them. In a recent paper, we concretely considered this problem for the case of the concept of angle. The present paper analogously discuss with the concept of vectors. To begin with, we investigate theoretical organization and historical order of the concept of vectors as materials for the construction of its lecturing organization-order. It enables us to establish 4 stages in historical order of the concept of vectors proper to its theoretical organization. As a consequence, we suggest several criteria and forms for constructing its lecturing organization-order.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.443-465
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• 2023

This study examines the content of vectors and matrices in Artificial Intelligence Mathematics textbooks (AIMTs) from the 2015 revised mathematics curriculum. We analyzed the implementation of foundational mathematical concepts, specifically definitions and related sub-concepts of vectors and matrices, in these textbooks, given their importance for understanding AI. The findings reveal significant variations in the presentation of vector-related concepts, definitions, sub-concepts, and levels of contextual information and descriptions such as vector size, distance between vectors, and mathematical interpretation. While there are few discrepancies in the presentation of fundamental matrix concepts, differences emerge in the subtypes of matrices used and the matrix operations applied in image data processing across textbooks. There is also variation in how textbooks emphasize the interconnectedness of mathematics for explaining vector-related concepts versus the textbooks place more emphasis on AI-related knowledge than on mathematical concepts and principles. The implications for future curriculum development and textbook design are discussed, providing insights into improving AI mathematics education.

• School Mathematics
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• v.13 no.4
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• pp.615-632
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• 2011

The purpose of the study was to investigate the mathematical knowledge for teaching (MKT) of pre-service and in-service mathematics teachers on the concept of vector. 80 pre-service and 124 in-service mathematics teachers were asked to perform three questions based on MKT's subdomain. The results show that pre-service teachers have stronger common content knowledge(CCK). On the other hand, in-service teachers have stronger specialized content knowledge(SCK), knowledge of content and teaching(KCT) compared to those of pre-service teachers. The paper proposes CCK, SCK and KCT about the concept of vector and discusses the relationships between subdomains of MKT.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.105-126
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• 2007

The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 1997.11a
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• pp.53-62
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• 1997

본 논문에서는 전자문서의 개념적 분류기법을 제안한다. 기존의 문서분류는 대부분 문서에 나타난 용어를 기반으로 분류하므로 개념적인 분류가 불가능하다. 제안된 기법에서는 한국어 시소러스를 사용하여 문서에 나타난 용어 뿐 아니라 용어의 상하위 개념을 기준으로 문서를 분류할 수 있다. 특히, 제안된 방법은 확률 벡터를 사용하는 방식으로써 점진적인 학습이 가능하다는 장점도 가진다.

• Proceedings of the Korean Information Science Society Conference
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• 2005.11b
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• pp.646-648
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• 2005

인터넷의 급속한 성장과 더불어 사용자들은 인터넷을 통해 많은 정보를 얻을 수 있게 되었으며 최신 뉴스를 실시간으로 접근할 수 있게 되었다. 이에 따라 방대한 정보 속에 사용자 관심사에 맞는 정보를 효과적으로 검색하기 위한 여러 방법들이 연구되어 왔다. 하지만 기존의 많은 선행 연구들은 단어 빈도 기반의 키워드 벡터 모델을 이용하여 사용자의 관심사를 학습하고 있다. 이러한 키워드 벡터 모델은 사용자의 선호도를 명확하게 기술하지 못하고 키워드를 이용한 특징 벡터 (feature-vector)는 개념들 사이의 관계를 찾기 어려운 한계를 가지고 있다. 이를 개선하기 위해 본 논문에선 계층적 개념 인덱싱(Hierarchical Concept Indexing)을 이용한 온톨로지 형태의 개인화된 사용자 프로파일을 만드는 방법을 제안한다. 생성된 사용자 프로파일에 개념 간의 유사도와 개념에 대한 사용자의 관심도를 고려하여 보다 개인의 선호도에 맞는 기사를 제공한다. 실험에서는 제안된 방법의 성능 평가를 위해서 기존의 키워드 벡터 모델의 학습 방법인 WebMate 시스템과 비교 분석하였다. 그 결과 제안하는 방법이 키워드 벡터를 이용한 학습 방법보다 향상된 성능을 보였다.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.153-155
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• 1998

본 논문에서는 개념을 기반으로 문서의 분류를 하는 확률벡터 모델의 분류기TAXON(Concept-based Text Categorization System)의 개선을 도모한다. TAXON은 한국어 문장을 분석하여 명사를 추출하고 명사의 개념을 시소러스 도구를 통해 획득한 후 이를 벡터화하여 주제와 입력 문서와의 관계성을 검사하는 문서 분류기이다. 본 논문은 문서 분류기 TAXON의 성능을 향상시키기 위하여 확률벡터 계산에 가중치 부여 휴리스틱을 도입한다. 그리고 시소러스 도구를 확장하여 문서 분류의 질을 높인다.

• The Transactions of the Korea Information Processing Society
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• v.3 no.1
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• pp.167-180
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• 1996

In the scalar processing oriented machine scalar operations must be performed for the vector processing as many as the number of vector components. So called a vector processing mechanism by the von Neumann operational principle. Accessing vector data hasto beperformed by theevery pointing ofthe instruction or by the address calculation of the ALU, because there is only a program counter(PC) for the sequential counting of the instructions as a memory accessing device. It should be here proposed that an access unit dimensionally to address components has to be designed for the compensation of the organizational hardware defect of the conventional concept. The necessity for the vector structuring has to be implemented in the instruction set and be performed in the mid of the accessing data memory overlapped externally to the data processing unit at the same time.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.133-152
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• 2004

In this paper, we discuss students' conceptual development of eigen value and eigen vector in differential equation course based on reformed differential equation using the mathematical model of mass spring according to historico-generic principle. Moreover, in setting of small group interactive learning, we investigate the students' development of mathematical attitude.