[논문]균등분배 상황에서 아이들의 분할전략의 구성

김아영

균등분배 상황에서 아이들의 분할전략의 구성
The Construction of Children's Partitioning Strategy on the Equal Sharing Situation 원문보기

학교수학 = School Mathematics, v.14 no.1, 2012년, pp.29 - 43

초록
AI-Helper

이 논문은 균등분배상황이 문장제나 수식 형태의 나눗셈으로 주어졌을 때, 아이들이 그 문제 상황을 도형으로 표현하고 그 도형을 분할하는 전략이 그 분할 결과를 다양한 형태의 분수로 수량화시키는 작업과 연관해 구성하는 개념적 스키머에 대하여 조사하였다. 그리고 이 때 분자와 분모 간, 제수와 피제수 간의 인수와 배수 관계들이 그 과정에 어떤 영향을 미치는지를 연구하였다. 아이들의 분할 전략은 다음 순서로 발달했다: 반복적인 이등분 수준${\rightarrow}$ 전체 양 모두 사용하기 수준${\rightarrow}$ 자연수 물건 남기기 수준${\rightarrow}$ 단수 물건 해석/복수 물건 해석 수준${\rightarrow}$ 직접 사상(mapping) 수준. 또한, 아이들이 단수 물건 해석을 복수 물건 해석과 연관시킬 수 있을 때, 그들은 마침내 나눗셈을 분수로, 분수를 나눗셈으로 개념화할 수 있었다.

Abstract ▼ AI-Helper

This paper investigated the conceptual schemes in which four children constructed a strategy representing the situation as a figure and partitioning it related to the work which they quantify the result of partitioning to various types of fractions when an equal sharing situation was given to them in contextual or an abstract symbolic form of division. Also, the paper researched how the relationship of factors and multiples between the numerator and denominator, or between the divisor and dividend affected the construction. The children's partitioning strategies were developed such as: repeated halving stage ${\rightarrow}$ consuming all quantity stage ${\rightarrow}$ whole number objects leftover stage ${\rightarrow}$ singleton object analysis/multiple objects analysis ${\rightarrow}$ direct mapping stage. When children connected the singleton object analysis with multiple object analysis, they finally became able to conceptualize division as fractions and fractions as division.

주제어

AI 본문요약
AI-Helper

* AI 자동 식별 결과로 적합하지 않은 문장이 있을 수 있으니, 이용에 유의하시기 바랍니다.

문제 정의

Therefore, this paper investigates how students' partitioning strategies are constructed longitudinally, related to quantify the result of partitioning to various forms of fractions.

가설 설정

A. How do children partition quantities and express them in various fraction forms?

제안 방법

The purpose of the pre-test interview was to assess each student's initial mathematical knowledge under investigation and to target the changes in their mathematical thinking. After that, six teaching episodes were progressed using three different types of questionnaires which induced specific type of fraction answers: proper fractions, improper fractions, and mixed numbers each. An equal sharing situation was given to them in contextual or abstract symbolic form of division, which was similar to the questionnaire in the clinical interview.
At this time, the effect of contemplating equivalent fractions was the major focus of the study. After that, to reduce the biased result caused by introducing fraction forms in different orders, and to maximize the effect of the order of introducing fraction forms, the researcher divided the children into different orders of presentation. The questions were arranged to give the children a chance to develop various partitioning strategies in different social situations especially at first teaching episode (see Appendix 1).
Again, well-partitioned diagrams by multiplicative thinking became mental images for multiplication number facts, so it re-enforced their multiplicative thinking. After they were fluent using multiplication number facts, they could analyze one problem both in single units analysis and in multiple units analysis. As a result, they understood partitioning strategies in single rule; direct mapping from the numbers in equal sharing to the numbers in the fraction answer.
Compared to most previous studies of partitioning involving quantitative research with different age groups, this study followed the change of several individual students’ partitioning strategies.
For this study, the researcher interviewed each student respectively, and each interview took about an hour. Identical questions were used for two clinical interviews (pre-test and post-test). The purpose of the pre-test interview was to assess each student's initial mathematical knowledge under investigation and to target the changes in their mathematical thinking.
She avoided the obstacle by using multiple units analysis. Over the course of the study, she also gained singleton units analysis and she conceptualized the direct mapping between the numbers in equal sharing situations and the numbers in the fraction quotient.
She started from a repeated halving stage and had difficulty quantifying the result. She avoided the obstacle by using multiple units analysis. Over the course of the study, she also gained singleton units analysis and she conceptualized the direct mapping between the numbers in equal sharing situations and the numbers in the fraction quotient.
Teaching episodes were used to construct models of the children’s mathematical thinking and guide them to develop more reflective ways of thinking about partitive quotient fraction that built on the results from the initial clinical interview.
The purpose of the pre-test interview was to assess each student's initial mathematical knowledge under investigation and to target the changes in their mathematical thinking.
He chose all shared objects and he went back to his unequal sharing strategy. Through the Problem Set 1 that was designed to generate proper fraction answers, he started to partition without thinking of cutting into one hundred pieces and got proper fraction quotients directly without converting them from percent quotients. When the number of shared objects was bigger than the number of sharers, he used a quotitive division interpretation for the fractional portion of a quotient, so he did not need to do partitioning.
When students distributed whole objects from shared objects to sharers equally in situations where the number of shared objects was bigger than the number of sharers, they distributed objects one by one, or equal small numbers like by fives to sharers without anticipation of the quotient even though they got the whole number portion of the fraction quotient using multiplication fact families when they represented equal sharing situations as division number sentences. When the researcher asked for more efficient methods for distribution of whole objects in the eighth interview, they changed their method to use multiplication facts. In addition, the whole number portion of a quotient from partitioning helped the students quantify the remaining fractional pieces correctly.

대상 데이터

Four students from a inner city fifth grade mathematics class the Southwestern United States participated in the study. One boy and one girl were chosen from the high mathematics performance group and the other boy and girl were chosen from the low mathematics performance group, each based on their mathematics teacher nomination (see [Table III-1]).

성능/효과

However, the form of fraction answers did not show direct mapping from the numbers in equal sharing situation to the numbers in their fraction answer. In conclusion, students who used multiple units analysis developed multiplicative thinking, economical partitioning strategies, and a good procedural skill with multiplication number facts.
The results showed not only the development trajectory of children’s partitioning strategy, but it also revealed how and why they changed their partitioning strategies until they discovered direct mapping from the numbers in equal sharing situations to the numerator and denominator in fraction answer, so it tied the development children’s partitioning strategies to the development of partitive quotient fraction.

내보내기 구분	파일저장 인쇄 메일전송
구성항목	기본정보 상세정보 관리번호, 논문명, 저널/프로시딩명, 저자 , 발행년, 권, 호, 시작페이지, 끝페이지, 발행기관 관리번호, 논문명, 대등논문명, 저자 , 저널/프로시딩명, 발행기관, 발행년, 발행언어, 권, 호, 시작페이지, 끝페이지, ISBN, ISSN, 주제분야, 키워드, 초록(한글), 초록(영문), 저자(소속기관)
저장형식	Text(ASCII format) Excel format RefWorks Direct Export RIS format (for Reference Manager, ProCite, EndNote), Scholar's Aids, Mendeley
메일정보	받는사람 (필수) @ 보내는사람 (선택) @ 제목 내용 KISTI 검색결과 이메일 서비스
안내	총 건의 자료가 검색되었습니다. 다운받으실 자료의 인덱스를 입력하세요. (1-10,000) 검색결과의 순서대로 최대 10,000건 까지 다운로드가 가능합니다. 데이타가 많을 경우 속도가 느려질 수 있습니다.(최대 2~3분 소요) 다운로드 파일은 UTF-8 형태로 저장됩니다. 파일의 내용이 제대로 보이지 않을실 때는 웹브라우저 상단의 보기 -> 인코딩 -> 자동선택 여부를 확인하십시오. ~ Text(ASCII format) Excel format

연합인증

균등분배 상황에서 아이들의 분할전략의 구성
The Construction of Children's Partitioning Strategy on the Equal Sharing Situation 원문보기

초록
AI-Helper

Abstract ▼ AI-Helper

주제어

AI 본문요약
AI-Helper

문제 정의

가설 설정

제안 방법

대상 데이터

성능/효과

이 논문을 인용한 문헌

저자의 다른 논문 :

관련 콘텐츠

원문 보기

연관된 기능

이 논문과 함께 이용한 콘텐츠

AI-Helper ※ AI-Helper는 오픈소스 모델을 사용합니다.

선택된 텍스트

연합인증

균등분배 상황에서 아이들의 분할전략의 구성 The Construction of Children's Partitioning Strategy on the Equal Sharing Situation 원문보기

초록 용어보기논문에서 용어와 풀이말을 자동 추출한 결과로, 시범 서비스 중입니다. AI-Helper

Abstract ▼ AI-Helper

주제어

AI 본문요약 엑셀 다운로드 AI-Helper

문제 정의

가설 설정

제안 방법

대상 데이터

성능/효과

이 논문을 인용한 문헌

저자의 다른 논문 :

김아영 (1)

관련 콘텐츠

원문 보기

연관된 기능

이 논문과 함께 이용한 콘텐츠

AI-Helper ※ AI-Helper는 오픈소스 모델을 사용합니다.

선택된 텍스트

균등분배 상황에서 아이들의 분할전략의 구성
The Construction of Children's Partitioning Strategy on the Equal Sharing Situation 원문보기

초록
AI-Helper

AI 본문요약
AI-Helper