A Generalized Fraction: An Entity Smaller Than One on the Mental Number Line

被引：75

作者：

Kallai, Arava Y. ^{[1
]}

Tzelgov, Joseph ^{[2
,3
]}

机构：

[1] Univ Pittsburgh, Dept Psychol, Ctr Learning Res & Dev, Pittsburgh, PA 15260 USA

[2] Ben Gurion Univ Negev, Dept Psychol, IL-84105 Beer Sheva, Israel

[3] Ben Gurion Univ Negev, Achva Acad Coll, IL-84105 Beer Sheva, Israel

来源：

JOURNAL OF EXPERIMENTAL PSYCHOLOGY-HUMAN PERCEPTION AND PERFORMANCE | 2009年 / 35卷 / 06期

基金：

以色列科学基金会;

关键词：

mental representations; numerical cognition; fractions; automatic processing; NUMERICAL FRACTIONS; RATIONAL NUMBERS; REPRESENTATION; MODEL; AUTOMATICITY; SPEED; INTERFERENCE; EXPERTISE; JUDGMENTS; STUDENTS;

D O I：

10.1037/a0016892

中图分类号：

B84 [心理学];

学科分类号：

04 ; 0402 ;

摘要：

The representation of fractions in long-term memory (LTM) was investigated by examining the automatic processing of such numbers in a physical comparison task, and their intentional processing in a numerical comparison task. The size congruity effect (SiCE) served as a marker of automatic processing and consequently as an indicator of the access to the primitives of numerical representation in LTM. Mixed pairs composed of a natural number and a fraction showed both a SiCE and a distance effect. The SiCE for mixed pairs was stable across relative sizes of natural numbers compared to the fraction digits (Experiment 4). However, comparing pairs of fractions revealed a strong influence of fractional components: An inverse SiCE was found for pairs of unit fractions (Experiment 1), while no SiCE was found for pairs of non-unit fractions (Experiments 2-3). This leads to the conclusions that: (I) there are no unique representations of distinct fraction values in LTM, and (2) there is a representation of a "generalized fraction" as an "entity smaller than one" that emerges from the notational structure common to all fractions.

引用

页码：1845 / 1864

页数：20

共 60 条

[1]

Anderson J.R., 1993, Rules of the mind

[2]

Banks W.P., 1977, PSYCHOL LEARNING MOT, V11, P101, DOI DOI 10.1016/S0079-7421(08)60476-4

[3]

Bargh J., 1997, ADV SOC COG, V10, P1

[4] THE ECOLOGY OF AUTOMATICITY - TOWARD ESTABLISHING THE CONDITIONS NEEDED TO PRODUCE AUTOMATIC PROCESSING EFFECTS [J].

BARGH, JA .

AMERICAN JOURNAL OF PSYCHOLOGY, 1992, 105 (02) :181-199

[5] ADAPT: A developmental, asemantic, and procedural model for transcoding from verbal to arabic numerals [J].

Barrouillet, P ;

Camos, V ;

Perruchet, P ;

Seron, X .

PSYCHOLOGICAL REVIEW, 2004, 111 (02) :368-394

[6] Representing quantity beyond whole numbers: Some, none, and part [J].

Bialystok, E ;

Codd, J .

CANADIAN JOURNAL OF EXPERIMENTAL PSYCHOLOGY-REVUE CANADIENNE DE PSYCHOLOGIE EXPERIMENTALE, 2000, 54 (02) :117-128

[7] The mental representation of numerical fractions:: Real or integer? [J].

Bonato, Mario ;

Fabbri, Sara ;

Umilta, Carlo ;

Zorzi, Marco .

JOURNAL OF EXPERIMENTAL PSYCHOLOGY-HUMAN PERCEPTION AND PERFORMANCE, 2007, 33 (06) :1410-1419

[8] Neuroscience - Knowledge of number: Its evolution and ontogeny [J].

Carey, S .

SCIENCE, 1998, 282 (5389) :641-642

[9] Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum [J].

Cramer, KA ;

Post, TR ;

delMas, RC .

JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION, 2002, 33 (02) :111-144

[10] The neural basis of the Weber-Fechner law: a logarithmic mental number [J].

Dehaene, S .

TRENDS IN COGNITIVE SCIENCES, 2003, 7 (04) :145-147

← 1 2 3 4 5 6 →