Mental Arithmetic in Africa and America: Strategies, Principles, and Explanations

Petitto, Andrea L.; Ginsburg, Herbert P.

doi:10.1080/00207598208247433

Cited by 29 publications

(4 citation statements)

References 3 publications

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“…A key principle in multiplication is that of commutativity: if a 6 b = c, then b 6 a = c. An understanding of commutativity may lead to a reduction in the number of multiplicative combinations that children need to learn (Baroody, 1999;Trivett, 1980). There is evidence that children find the concept of commutativity in multiplication difficult (Frydman & Bryant, 1988Nunes & Bryant, 1995;Pettito & Ginsburg, 1982;Piaget, Kaufmann, & Bourquin, 1977Resnick, 1992). Researchers have also suggested that, whereas an understanding of the principle of commutativity in addition may emerge in the absence of school instruction (Cowan & Renton 1996;Groen & Resnick, 1977;Pettito & Ginsburg, 1982), children may only acquire the principle of commutativity in multiplication through formal schooling (Pettito & Ginsburg, 1982;Schliemann, Araujo, Cassunde, Macedo, & Niceas, 1998).…”

Section: Conceptual Principles In Multiplicative Problemsmentioning

confidence: 99%

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Squire

Davies

Bryant

2004

Brit J of Edu Psychol

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Nine- and 10-year-olds understand commutativity, but are unable to use the distributive principle in multiplication. Their errors suggest that they may confuse some of the principles of multiplication with those of addition. When children do begin to understand the principle of distributivity, they most easily apply it in the context of Isomorphism of measures multiplication problems. The implications for mathematical education are discussed.

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Section: Conceptual Principles In Multiplicative Problemsmentioning

confidence: 99%

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Squire

Davies

Bryant

2004

Brit J of Edu Psychol

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“…Given that in the remote community, there is a) not large amounts of circulating state currency (and thus lack of access to different denominations and the everyday numerical activities associated with currency) and b) that the base unit of sales and purchasing is most often 5, sellers without formal schooling develop a mathematical practice that centers on what is directly useful in their day-to-day lives—multiples of 5. While this study did not measure how participants solved the multiplication problems, prior studies of adults without formal education have shown evidence of the use of one-to-many correspondences among Brazilian fishermen ( 81 ) and a variety of strategies among African adults without formal schooling ( 82 ).…”

Section: Discussionmentioning

confidence: 94%

Diverse mathematical knowledge among indigenous Amazonians

O’Shaughnessy,

Cruz Cordero,

Mollica

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane’, for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane’ children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane’ communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five—which has a distinct role in the local economy—even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.

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“…In particular Ginsburg [135] and Petitto and Ginsburg [246] compared their research findings on mental arithmetic in West Africa with those obtained in North America. Etuk [84] examined Piaget's theory with Yoruba children (Nigeria).…”

Section: Studies In Related Disciplinesmentioning

confidence: 98%

On mathematics in the history of Sub-Saharan Africa

Gerdes

1994

Historia Mathematica

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FOR DIRK STRUIK ON HIS 100TH BIRTHDAY 2This article presents an overview of research findings and of sources on or related to mathematics in the history of Africa south of the Sahara. Topics such as counting and numeration systems, mathematical games and puzzles, geometry, graphs, and continental and international connections are included. Attention is paid to the objectives of research in the history of mathematics in Africa, to methodology, to the relationship with ethnomathematical research, and to the uses of research findings in mathematics education. Some possible directions for further research are also identified. ¢ 1994 Academic Press, Inc.Cet article pr6sente un panoramique des r6sultats de recherche et des sources d'information relatifs ~. l'histoire de la math6matique en Afrique sub-saharienne. I1 comporte des th~mes tels que le comptage et les syst~mes de num6ration, les jeux et les puzzles math6matiques, la g6om6trie, les graphes, et les connexions continentales et internationales. L'accent est mis sur les objectifs de la recherche sur l'histoire de la math6matique en Afrique, sa m6thodo-logie, sa relation avec la recherche ethnomath6matique, et les usages des r6sultats de la recherche dans l'enseignement de la math6matique. Quelques directions possibles pour approfondir la recherche sont 6galement identifi6es. © 1994 Academic Press, Inc.Este artigo apresenta uma vista panorgtmica dos resultados de investigag~to e das fontes de informa@.o relacionados coma hist6ria da matem~tica na ,~.frica ao Sul do Sahara. Incluem-se t6picos tais como contagem e sistemas de numerag~to, jogos e puzzles matem~i-ticos, geometria, grafos e conex6es continentais e internacionais. Presta-se ateng~to aos objectivos da investigaq~o respeitante ~ hist6ria da matem~itica em/ffrica, h metodologia, b. relaq~o com pesquisa etnomatem~.tica e aos usos dos resultados de investigagao, na educaq~o matem~itica. Identificam-se tamb6m algumas direcg6es possiveis para continuar a investigaq~to.

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Mental Arithmetic in Africa and America: Strategies, Principles, and Explanations

Cited by 29 publications

References 3 publications

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Diverse mathematical knowledge among indigenous Amazonians

On mathematics in the history of Sub-Saharan Africa

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