• The Mathematical Education
• /
• v.42 no.3
• /
• pp.353-368
• /
• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

• Research in Mathematical Education
• /
• v.18 no.4
• /
• pp.237-256
• /
• 2014

This paper reports findings from a written assessment which was designed to investigate Chinese primary school students' understanding of the equal sign and equation structure. The investigation included a sample of 110 Grade 3, 112 Grade 4, and 110 Grade 5 students from four schools in China. Significant differences were identified among the three grades and no gender differences were found. The majority of Grades 3 and 4 students were found to view the equal sign as a place indicator meaning "write the answer here" or "do something like computation", that is, holding an operational view of the equal sign. A part of Grade 5 students were found to be able to interpret the equal sign as meaning "the same as", that is, holding a relational view of the equal sign. In addition, even though it was difficult for Grade 3 students to recognize the underlying structure in arithmetic equation, quite a number of Grades 4 and 5 students were able to recognize the underlying structure on some tasks. Findings in this study suggest that Chinese primary school students demonstrate a relational understanding of the equal sign and a strong structural sense of equations in an earlier grade. Moreover, what found in the study support the argument that students' understanding of the equal sign is influenced by the context in which the equal sign is presented.

• Journal of Computing Science and Engineering
• /
• v.11 no.4
• /
• pp.130-141
• /
• 2017

Feature selection is one of the most challenging problems of pattern recognition and data mining. In this paper, a feature selection algorithm based on an improved version of binary differential evolution is proposed. The method simultaneously optimizes two feature selection criteria, namely, set approximation accuracy of rough set theory and relational algebra based derived score, in order to select the most relevant feature subset from an entire feature set. Superiority of the proposed method over other state-of-the-art methods is confirmed by experimental results, which is conducted over seven publicly available benchmark datasets of different characteristics such as a low number of objects with a high number of features, and a high number of objects with a low number of features.

• Proceedings of the Korean Information Science Society Conference
• /
• 2005.07b
• /
• pp.214-216
• /
• 2005

데이터 웨어하우스에서는 데이터를 다양한 관점으로 분석하기 위해 데이터를 다차원 형태로 유지한다. 이 다차원 데이터를 간단하고 편리한 형태로 사용자에게 표현하기 위해 피벗 테이블이 이용된다. 피벗 테이블은 데이터에 대한 요약된 정보를 제공하는데 널리 사용되는 편리한 표현 방법이지만, 실제 값이 열의 제목으로 나오기 때문에 많은 개수의 열을 가질 수 있다. 이러한 피벗 테이블을 그대로 저장할 경우 관계 DBMS의 테이블 컬럼 수에 제약을 받게 되며, 데이터 저장 및 질의 처리에 성능이 떨어질 수 있다. 이 논문은 관계 데이터베이스의 테이블을 이용하여 피벗 테이블을 효율적으로 저장하는 방법을 제안한다. 이때, 피벗 테이블에 대한 질의물 저장된 형태의 테이블에 적용 가능하도록 질의를 변환시켜야 한다. 따라서 이 연구에서는 피벗 테이블에 대한 관계 연산자들(실렉션, 프로젝션, 합집합, 차집합 카디션 곱)을 효율적으로 변환하는 질의 변환 방범을 제안한다.

• Journal of Computing Science and Engineering
• /
• v.7 no.1
• /
• pp.1-20
• /
• 2013

Over the past generation, data warehousing and online analytical processing (OLAP) applications have become the cornerstone of contemporary decision support environments. Typically, OLAP servers are implemented on top of either proprietary array-based storage engines (MOLAP) or as extensions to conventional relational DBMSs (ROLAP). While MOLAP systems do indeed provide impressive performance on common analytics queries, they tend to have limited scalability. Conversely, ROLAP's table oriented model scales quite nicely, but offers mediocre performance at best relative to the MOLAP systems. In this paper, we describe a storage and indexing framework that aims to provide both MOLAP like performance and ROLAP like scalability by essentially combining some of the best features from both. Based upon a combination of R-trees and bitmap indexes, the storage engine has been integrated with a robust OLAP query engine prototype that is able to fully exploit the efficiency of the proposed storage model. Specifically, it utilizes an OLAP algebra coupled with a domain specific query optimizer, to map user queries directly to the storage and indexing framework. Experimental results demonstrate that not only does the design improve upon more naive approaches, but that it does indeed offer the potential to optimize both query performance and scalability.

• Journal of Korea Spatial Information System Society
• /
• v.4 no.1 s.7
• /
• pp.5-14
• /
• 2002

The generalization of geospatial data is an important way in deriving a new database from an original one. The generalization of a geospatial object changes not only its geometric and aspatial attributes but also results in propagation to other objects along their relationship. We call it generalization propagation of geospatial databases. Without proper handling of the propagation, it brings about an inconsistent database or loss of semantics. Nevertheless, previous studies in the generalization have focused on the derivation of an object by isolating it from others. And they have proposed a set of generalization operators, which were intended to change the geometric and aspatial attributes of an object. In this paper we extend the definition of generalization operators to cover the propagation from an object to others. In order to capture the propagation, we discover a set of rules or constraints that must be taken into account during generalization procedure. Each generalization operator with constraints is expressed in relational algebra and it can be converted to SQL statements with ease. A prototype system was developed to verify the correctness of extended operators.

• Journal of KIISE
• /
• v.43 no.4
• /
• pp.489-496
• /
• 2016

XML can effectively express structured or semi-structured data as well as relational databases. XQuery is a query language for retrieving information for such an XML document. In this paper, an XQuery composer is designed and implemented, with an API provided for XQuery processors, and a proper processor is registered. This composer shows query results immediately processed by the processor. As this composer contains a parser for XQuery, it can compose XQuery effectively using a diverse dialog box designed for XQuery grammar. A dialog box is affiliated with a clause region, which is a region that algebra operates from the parsing tree. It can compose path expressions for an XML document easily as it shows an element tree from DTD graphically. Path expressions are composed automatically by marking elements in the structural hierarchy and by specifying the predicate of an element partially.

• Journal of Educational Research in Mathematics
• /
• v.11 no.2
• /
• pp.363-384
• /
• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.