東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

Counting and the Development of Exact Number Concepts.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Counting and the Development of Exact Number Concepts./
作者:	Schneider, Rose M.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	244 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-07, Section: B.
Contained By:	Dissertations Abstracts International83-07B.
標題:	Developmental psychology. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28721297
ISBN:	9798759999782

Counting and the Development of Exact Number Concepts.
Schneider, Rose M.

Counting and the Development of Exact Number Concepts. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 244 p.

Source: Dissertations Abstracts International, Volume: 83-07, Section: B.

Thesis (Ph.D.)--University of California, San Diego, 2021.

This item must not be sold to any third party vendors.

Although numerate humans' experience with symbolic number is finite, we nevertheless are capable of abstract numerical thought extending well beyond these limits. Such abstract thought is argued to depend on extracting two properties of exact number available within symbolic counting systems: the successor function and exact equality. On standard theories of number acquisition, children are proposed to simultaneously acquire both principles upon mastering their symbolic counting system by establishing an analogical mapping between the count list and cardinality. In this dissertation, I argue that this analogical mapping is not established until well after children master counting and that, consequently, implicit knowledge of both the successor function and exact equality emerge years after children are capable counters. In Chapter 1, I show that children who have just learned to deploy counting do not understand that adding one item to a set requires counting up one number in the count list-an analogical mapping compatible with implicit successor function. However, if implicit successor knowledge is not acquired in conjunction with counting, how does it emerge? In Chapter 2, I explore one hypothesized mechanism-mastery of counting's recursive structure-in five languages which vary in the transparency of these recursive structures (English, Cantonese, Slovenian, Hindi, and Gujarati). Across language groups, I show that implicit successor knowledge is strongly predicted by recursive counting mastery. In Chapter 3, I test another hypothesized mechanism-arithmetic instruction. I show that although arithmetic instruction is correlated with successor knowledge, it is not causally related; instead, compatible with Chapter 2, I show that recursive counting is once again predictive of implicit successor knowledge. Finally, in Chapter 4, I turn to exact equality-another property of exact number-and show that although learning to deploy counting marks a substantial shift in children's understanding of exact equality, counting on its own is insufficient to guarantee a full understanding of this logical property. Together, these studies suggest that, instead of marking a conceptual inflection point in children's understanding of number, mastering a symbolic counting system is only a first step in a gradual process of extracting conceptual knowledge from procedures.

ISBN: 9798759999782Subjects--Topical Terms:

516948
Developmental psychology.
Subjects--Index Terms:

Abstract numerical thought

Counting and the Development of Exact Number Concepts.
LDR:03532nmm a2200361 4500 001 2350309
005 20221020125236.5
008 241004s2021 ||||||||||||||||| ||eng d
020 $a 9798759999782
035 $a (MiAaPQ)AAI28721297
035 $a AAI28721297
040 $a MiAaPQ $c MiAaPQ
100 1 $a Schneider, Rose M. $3 3689781
245 1 0 $a Counting and the Development of Exact Number Concepts.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 244 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-07, Section: B.
500 $a Advisor: Barner, David.
502 $a Thesis (Ph.D.)--University of California, San Diego, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Although numerate humans' experience with symbolic number is finite, we nevertheless are capable of abstract numerical thought extending well beyond these limits. Such abstract thought is argued to depend on extracting two properties of exact number available within symbolic counting systems: the successor function and exact equality. On standard theories of number acquisition, children are proposed to simultaneously acquire both principles upon mastering their symbolic counting system by establishing an analogical mapping between the count list and cardinality. In this dissertation, I argue that this analogical mapping is not established until well after children master counting and that, consequently, implicit knowledge of both the successor function and exact equality emerge years after children are capable counters. In Chapter 1, I show that children who have just learned to deploy counting do not understand that adding one item to a set requires counting up one number in the count list-an analogical mapping compatible with implicit successor function. However, if implicit successor knowledge is not acquired in conjunction with counting, how does it emerge? In Chapter 2, I explore one hypothesized mechanism-mastery of counting's recursive structure-in five languages which vary in the transparency of these recursive structures (English, Cantonese, Slovenian, Hindi, and Gujarati). Across language groups, I show that implicit successor knowledge is strongly predicted by recursive counting mastery. In Chapter 3, I test another hypothesized mechanism-arithmetic instruction. I show that although arithmetic instruction is correlated with successor knowledge, it is not causally related; instead, compatible with Chapter 2, I show that recursive counting is once again predictive of implicit successor knowledge. Finally, in Chapter 4, I turn to exact equality-another property of exact number-and show that although learning to deploy counting marks a substantial shift in children's understanding of exact equality, counting on its own is insufficient to guarantee a full understanding of this logical property. Together, these studies suggest that, instead of marking a conceptual inflection point in children's understanding of number, mastering a symbolic counting system is only a first step in a gradual process of extracting conceptual knowledge from procedures.
590 $a School code: 0033.
650 4 $a Developmental psychology. $3 516948
650 4 $a Experimental psychology. $3 2144733
650 4 $a Cognitive psychology. $3 523881
653 $a Abstract numerical thought
653 $a Symbolic counting systems
653 $a Successor function
653 $a Exact equality
690 $a 0620
690 $a 0633
690 $a 0623
710 2 $a University of California, San Diego. $b Psychology. $3 1675458
773 0 $t Dissertations Abstracts International $g 83-07B.
790 $a 0033
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28721297