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Fraction instruction that fosters mu...

Vanhille, Lee Stuart.

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Fraction instruction that fosters multiplicative reasoning.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Fraction instruction that fosters multiplicative reasoning./
作者:	Vanhille, Lee Stuart.
面頁冊數:	159 p.
附註:	Source: Dissertation Abstracts International, Volume: 64-08, Section: A, page: 2818.
Contained By:	Dissertation Abstracts International64-08A.
標題:	Education, Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3101987

Fraction instruction that fosters multiplicative reasoning.
Vanhille, Lee Stuart.

Fraction instruction that fosters multiplicative reasoning. - 159 p.

Source: Dissertation Abstracts International, Volume: 64-08, Section: A, page: 2818.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.

Research indicates that students' success is relatively low in regards to operations on fractions (e.g., computing 1/2 ÷ 1/3), rational-number concepts (e.g., estimating the sum of two fractions), and proportional reasoning (e.g., finding the unknown side between two similar rectangles, 2:3::5:?). Because these topics require an understanding of multiplicative relations (e.g., six is one-and-a-half times bigger than four), an instructional program for fractions that emphasizes multiplicative reasoning may positively impact proportional reasoning. This study involved a teaching experiment with sixth-grade students for operations on fractions. Data were gathered from two control classes that received textbook instruction and an experimental class that received fraction instruction that emphasized partitioning experiences and multiplicative relations, including training in a distributive model for multiplication of a whole number by a mixed number (e.g., 11/2 x 6 is 6 once plus half of six) and the use of ratio tables to evaluate multiplicative relations in families of equivalent fractions. Students were administered, as pre- and posttests, three paper-and-pencil tests, one that measured fraction computation and two that measured multiplicative relations; the students were also administered in an interview setting untrained proportionality problems. Results indicated that the three classes showed equal achievement on the measure of fraction computation; however, on the three measures of multiplicative reasoning, including proportional reasoning, the experimental class significantly outperformed the control classes.Subjects--Topical Terms:

1017588
Education, Mathematics.

Fraction instruction that fosters multiplicative reasoning.
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245 1 0 $a Fraction instruction that fosters multiplicative reasoning.
300 $a 159 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-08, Section: A, page: 2818.
500 $a Adviser: Arthur J. Baroody.
502 $a Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
520 $a Research indicates that students' success is relatively low in regards to operations on fractions (e.g., computing 1/2 ÷ 1/3), rational-number concepts (e.g., estimating the sum of two fractions), and proportional reasoning (e.g., finding the unknown side between two similar rectangles, 2:3::5:?). Because these topics require an understanding of multiplicative relations (e.g., six is one-and-a-half times bigger than four), an instructional program for fractions that emphasizes multiplicative reasoning may positively impact proportional reasoning. This study involved a teaching experiment with sixth-grade students for operations on fractions. Data were gathered from two control classes that received textbook instruction and an experimental class that received fraction instruction that emphasized partitioning experiences and multiplicative relations, including training in a distributive model for multiplication of a whole number by a mixed number (e.g., 11/2 x 6 is 6 once plus half of six) and the use of ratio tables to evaluate multiplicative relations in families of equivalent fractions. Students were administered, as pre- and posttests, three paper-and-pencil tests, one that measured fraction computation and two that measured multiplicative relations; the students were also administered in an interview setting untrained proportionality problems. Results indicated that the three classes showed equal achievement on the measure of fraction computation; however, on the three measures of multiplicative reasoning, including proportional reasoning, the experimental class significantly outperformed the control classes.
520 $a Qualitative analyses of student reasoning on proportion problems indicated that students in the experimental instruction used much more often than students in the control classes partitioning and distributive strategies.
520 $a Also of interest in the experimental instruction is the development of a model for partitive division of fractions, which model can be a valuable tool in understanding and determining unit rates. In partitive division, the task is to find the amount of the first quantity in one unit of the second quantity. For example, in the problems $6 ÷ 2 lbs., $6 ÷ 1 1/2 lbs., and $3 /4 ÷ 2/3 lb., the student must determine the cost of one pound. Little work has been done to develop models for such problems.
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