• Title/Summary/Keyword: 일반화된 산술 관점

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Fifth Graders' Understanding of Variables from a Generalized Arithmetic and a Functional Perspectives (초등학교 5학년 학생들의 일반화된 산술 관점과 함수적 관점에서의 변수에 대한 이해)

  • Pang, JeongSuk;Kim, Leena;Gwak, EunAe
    • Communications of Mathematical Education
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    • v.37 no.3
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    • pp.419-442
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    • 2023
  • This study investigated fifth graders' understanding of variables from a generalized arithmetic and a functional perspectives of early algebra. Specifically, regarding a generalized perspective, we included the property of 1, the commutative property of addition, the associative property of multiplication, and a problem context with indeterminate quantities. Regarding the functional perspective, we covered additive, multiplicative, squaring, and linear relationships. A total of 246 students from 11 schools participated in this study. The results showed that most students could find specific values for variables and understood that equations involving variables could be rewritten using different symbols. However, they struggled to generalize problem situations involving indeterminate quantities to equations with variables. They also tended to think that variables used in representing the property of 1 and the commutative property of addition could only be natural numbers, and about 25% of the students thought that variables were fixed to a single number. Based on these findings, this paper suggests implications for elementary school students' understanding and teaching of variables.

A Study on Approaches to Algebra Focusing on Patterns and Generalization (패턴과 일반화를 강조한 대수 접근법 고찰)

  • 김성준
    • School Mathematics
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    • v.5 no.3
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    • pp.343-360
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    • 2003
  • In this paper, we deal with the teaching of algebra based on patterns and generalization. The past algebra curriculum starts with letters(variables), algebraic expressions, and equations, but these formal approaching method has many difficulties in the school algebra. Therefore we insist the new algebraic approaches should be needed. In order to develop these instructions, we firstly investigate the relationship of patterns and algebra, the relationship of generalization and algebra, the steps of generalization from patterns and levels of difficulties. Next we look into the algebra instructions based arithmetic patterns, visual patterns and functional situations. We expect that these approaches help students learn algebra when they begin school algebra.

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An Analysis of the Whole Numbers and Their Operations in Mathematics Textbooks: Focused on Algebra as Generalized Arithmetic (범자연수와 연산에 관한 수학 교과서 분석 - 일반화된 산술로서의 대수 관점을 중심으로 -)

  • Pang, Jeong-Suk;Choi, Ji-Young
    • The Mathematical Education
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    • v.50 no.1
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    • pp.41-59
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    • 2011
  • Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.

Systematic Design Method of Fuzzy Logic Controllers by Using Fuzzy Control Cell (퍼지제어 셀을 이용한 퍼지논리제어기의 조직적인 설계방법)

  • 남세규;김종식;유완석
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.7
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    • pp.1234-1243
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    • 1992
  • A systematic procedure to design fuzzy PID controllers is developed in this paper. The concept of local fuzzy control cell is proposed by introducing both an adequate global control rule and membership functions to simplify a fuzzy logic controller. Fuzzy decision is made by using algebraic product and parallel firing arithematic mean, and a defuzzification strategy is adopted for improving the computational efficiency based on nonfuzzy micro-processor. A direct method, transforming the typical output of quasi-linear fuzzy operator to the digital compensator of PID form, is also proposed. Finally, the proposed algorithm is applied to an DC-servo motor. It is found that this algorithm is systematic and robust through computer simulations and implementation of controller using Intel 8097 micro-processor.