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The Mental Representation of Fractio...

Liu, Yingyi.

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The Mental Representation of Fractions: Its Relations to the Approximate Number System and Whole Number Knowledge.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Mental Representation of Fractions: Its Relations to the Approximate Number System and Whole Number Knowledge./
Author:	Liu, Yingyi.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2014,
Description:	158 p.
Notes:	Source: Dissertation Abstracts International, Volume: 76-10(E), Section: A.
Contained By:	Dissertation Abstracts International76-10A(E).
Subject:	Educational psychology. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3707436
ISBN:	9781321821055

The Mental Representation of Fractions: Its Relations to the Approximate Number System and Whole Number Knowledge.
Liu, Yingyi.

The Mental Representation of Fractions: Its Relations to the Approximate Number System and Whole Number Knowledge. - Ann Arbor : ProQuest Dissertations & Theses, 2014 - 158 p.

Source: Dissertation Abstracts International, Volume: 76-10(E), Section: A.

Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2014.

The thesis examines the similarity, association and difference between the representation of fractions and that of whole numbers from a developmental perspective. It proposes three hypotheses. Firstly, it hypothesized that the representations of both whole numbers and fractions rely on the Approximate Number System (ANS), an innate system to make sense of quantity. Secondly, it proposed that the learning of whole number knowledge provides students with a mental structure about the bidirectional mapping between the ANS and number symbols and the linear arrangement of numbers on the assumed mental number line. Thirdly, the difference between the representation of fractions and that of whole numbers was hypothesized to lie in that (1) the magnitudes of fractions are not accessed automatically, and (2) the spatial-numerical association (i.e., SNARC effect) is not established for the representation of fractions.

ISBN: 9781321821055Subjects--Topical Terms:

517650
Educational psychology.

The Mental Representation of Fractions: Its Relations to the Approximate Number System and Whole Number Knowledge.
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100 1 $a Liu, Yingyi. $3 3290537
245 1 4 $a The Mental Representation of Fractions: Its Relations to the Approximate Number System and Whole Number Knowledge.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2014
300 $a 158 p.
500 $a Source: Dissertation Abstracts International, Volume: 76-10(E), Section: A.
500 $a Advisers: Yu-jing Ni; Ling-po Shiu.
502 $a Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2014.
520 $a The thesis examines the similarity, association and difference between the representation of fractions and that of whole numbers from a developmental perspective. It proposes three hypotheses. Firstly, it hypothesized that the representations of both whole numbers and fractions rely on the Approximate Number System (ANS), an innate system to make sense of quantity. Secondly, it proposed that the learning of whole number knowledge provides students with a mental structure about the bidirectional mapping between the ANS and number symbols and the linear arrangement of numbers on the assumed mental number line. Thirdly, the difference between the representation of fractions and that of whole numbers was hypothesized to lie in that (1) the magnitudes of fractions are not accessed automatically, and (2) the spatial-numerical association (i.e., SNARC effect) is not established for the representation of fractions.
520 $a To investigate the hypothesized similarity, association and difference between the mental representation of fractions and that of whole numbers, students from grade four, five, six and seven as well as college students were tested in a range of tasks involving the quantity discrimination, whole numbers and fractions.
520 $a As for the role of the ANS, results showed that ANS acuity was related to individual differences in the fraction estimation on a number line and fraction comparison accuracy but not in the size of the distance effect. However, the effect of ANS acuity was not consistent across grades.
520 $a As for the role of whole number knowledge, results indicated that in grade four to grade six, whole number knowledge predicted individual differences in the fraction estimation on the number line in terms of accuracy and pattern of estimates. In grade seven, estimation accuracy observed with whole numbers was predictive of that of fractions. Students showed a linear representation of fractions before they received formal instructions on fractions. Whole number knowledge was found to predict individual differences in comparing fractions in sixth and seventh graders. Whole number knowledge did not predict the size of the distance effect across grades.
520 $a Finally, the size congruity effect and the SNARC effect were not observed.
520 $a The results help to understand how the representation of fractions develops within the constraints of the ANS and whole number knowledge. Fractions are learned by accessing the magnitude codes in the ANS and with the help of another symbolic number system, whole number knowledge. The way in which the mental representation of fractions is linked to magnitudes and spatial information seems to be different from that for whole numbers.
590 $a School code: 1307.
650 4 $a Educational psychology. $3 517650
650 4 $a Mathematics education. $3 641129
690 $a 0525
690 $a 0280
710 2 $a The Chinese University of Hong Kong (Hong Kong). $b Educational Psychology. $3 3290538
773 0 $t Dissertation Abstracts International $g 76-10A(E).
790 $a 1307
791 $a Ph.D.
792 $a 2014
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3707436