NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
PDF on ERIC Download full text
ERIC Number: EJ1069798
Record Type: Journal
Publication Date: 2012
Pages: 11
Abstractor: As Provided
ISSN: ISSN-1886-1350
Spontaneous Meta-Arithmetic as the First Step toward School Algebra
Caspi, Shai; Sfard, Anna
PNA, v6 n2 p61-71 2012
Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the "official" algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses.
Universidad de Granada Didáctica de la Matemática: Persamiento Numerico, FQM-193. Campus de Cartuja, Granada, Spain 18071. Tel: +34-958-241503; Fax: +34-958-246359; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Grade 7; Junior High Schools; Middle Schools; Elementary Education; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Israel
Grant or Contract Numbers: N/A