수학 교육과정 내용의 '수와 연산' 학습과제 분석

다국어 초록 (Multilingual Abstract)

The purpose of this study was to concretely analysis and suggest system of contents of 「the Number and Operations Domain」 in Mathematics.
Briefly, the result of this study was summarized as follow: learning tasks of 「the Number and Operations Domain」 in Mathematics curriculum concentrated on 9 instruction that were understanding addition and subtraction, learning for four rules, understanding fraction that had the same dominator, understanding prime number/divisor/multiple, learning for addition and subtraction of fraction and reduction of fraction/reduction of fractions to a common denominator, learning for multiplication and division of fraction, understanding for set/natural number/system, understanding for real number and prime number, learning for set/proposition/complex numbers.
Learning for addition and subtraction included addition and subtraction of numbers by 50, by 100, by 1000.
Learning for four rules contained addition, subtraction, multiplication and division including four rules and understanding of fraction, addition, subtraction, multiplication and division of four figures.
Learning to understand fraction that had the same denominator comprised understanding fraction and prime numbers, understanding natural numbers that were more than five figures and learning addition and subtraction of fraction that had the same dominator.
Learning to understand prime numbers/divisor/multiple comprehended comparison of amount of prime numbers and learning addition/
subtraction, divisor and multiple.
Learning reduction of fraction/reduction of fractions to a common denominator/addition and subtraction of fraction held reduction of fraction, reduction of fractions to a common denominator, addition and subtraction of fraction that had different dominators.
Learning for multiplication and division of fraction contained multiplication of fraction, multiplication and division of fraction and prime numbers, relation between prime numbers and fraction, division of fraction and prime numbers.
Learning for set/natural numbers/system comprised basic understanding of set, characteristics of natural numbers, basic understanding of system.
Learning to understand prime numbers and real numbers comprehended learning for basic character of operation of set, proposition and complex numbers.
Learning to understand set/proposition/complex numbers contained operation of set, the characters of proposition, the basic characteristics of comple numbers.
In conclusion, for learning of 「the Number and Operations Domain」, understanding fraction that had the same dominator, understanding of prime numbers, divisor and multiple, reduction of fraction, reduction of fractions to a common denominator, addition and subtraction of fraction, multiplication and division of fraction, understanding of set, natural numbers, system, understanding of prime numbers and real numbers, understanding of set, proposition and complex numbers should be performed in that order.
In other words, learning for 「the Number and Operations Domain」should be performed like this order; reading and writing numbers→comparing the amount of numbers→four rules of numbers→understanding prime numbers→understanding the relation between fractions→understanding inclusion relation of set→understanding relation between systems→understanding the concept of numbers→understanding proposition→understanding relation between numbers→understanding relation between big numbers and decimal in real numbers→understanding operation rule of set→understanding the basic character of complex numbers→reduction of fraction and reduction of fractions to a common denominator→factorization in prime factors in natural numbers→calculation of fraction and prime numbers→operation of set and complex numbers→expressing expansion with the binary scale→exchanging fraction into prime numbers and exchanging prime numbers into fraction→calculating divisor and multiple and finding necessary and sufficient condition.

목차 (Table of Contents)

• Ⅰ. 서론 1
• Ⅱ. 이론적 배경 3
• 1.「수와 연산」영역의 교육내용 3
• 2.「수와 연산」영역의 기본학습 과제 4
• 3.「수와 연산」영역의 학습과정상 유의점 5
• 4.「수와 연산」영역의 심화학습 과제 7
• Ⅲ.「수와 연산」영역의 학습과제 분석 9
• 1. 수의 덧셈과 뺄셈 9
• 2. 사칙연산 11
• 3. 분모가 같은 분수의 이해 13
• 4. 소수/약수/배수의 이해 14
• 5. 약분/통분/그리고 분수의 덧셈과 뺄셈 15
• 6. 분수의 곱셈과 나눗셈 16
• 7. 집합/자연수/진법의 이해 17
• 8. 실수와 소수의 이해 17
• 9. 집합/명제/복소수의 이해 18
• Ⅳ. 논 의 20
• Ⅴ. 요약 및 결론 32
• 부록 34
• 참고 문헌 50