The extension of the natural-number domain to the integers in the transition from arithmetic to algebra

Educational Studies in Mathematics

Volumn 49, Issue 2, 2002, Pages 171-192

  Gallardo, Aurora ^a  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13844256099     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1016210906658     Document Type: Article

References (13)

1. Colebrooke, H.T.: 1817, Algebra, with Arithmetic and Measuration, from the Sanscrit of Brahmegupta and Bhascara, Murray, London.
2. Filloy, E. and Rojano, T.: 1984, 'From an arithmetic to an algebraic thought: A clinical study with 12-13 year olds', in J.M. Moser (ed.), Proceedings of the Sixth Annual Conference for the Psychology of Mathematics Education, North American Chapter, pp. 51-56. University of Wisconsin, Madison.
3. Filloy, E. and Rojano, T.: 1985, 'Operating the unknown and models of teaching (a clinical study with 12-13 year olds with high proficiency in pre-algebra)', in S.K. Damarin and M. Shelton (eds.), Proceedings of the Seventh Annual Meeting for the Psychology of Mathematics Education, North American Chapter. Columbus, Ohio.
4. Gallardo, A. and Rojano, T.: 1988, 'Difficulty areas in the acquisition of the arithmetic and algebraic language', Recherches en Didactique des Mathématiques 9(2) 155-188.
5. Gallardo, A.: 1994, El estatus de los números negatives en la resolución de ecuaciones algebraicas, Unpublished Ph D. Dissertation. Centro de Investigación y de Estudios Avanzados del IPN, México.
6. th Conference of the International Group for the Psychology of Mathematics Education, 2, 377-384. Universitat de Valencia (Spain).
7. Gallardo, A.: 2001, 'Historical-epistemological analysis in mathematics education: Two works in didactics of algebra', in R. Sutherland et al. (eds.), Perspectives on School Algebra, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 121-139.
8. Glaeser, G.: 1981, 'Epistemologie des nombres relatifs', Recherches en Didactique des Mathèmatiques 2(3), 303-346.
9. Lay-Yong, L. and Se, A.T.: 1987, 'The earliest negative numbers: how they emerged from a solution of simultaneous linear equations', Archives Internationales d'Histoire des Sciences 37, 222-269.
10. Marre, A.: 1881, Appendice au Triparty en la science des nombres de Nicolas Chuquet parisien, 14, 413-460.
11. Piaget, J.: 1960, Introducción a la Epistemología Genética. I El Pensamiento Matemático, Paidós, México, Buenos Aires, Barcelona.
12. Picutti, E.: 1983, 'I Flos. Leonardo Pisano', Physis 25, 293-387.
13. Sesiano, J.: 1985, The appearance of negative solution in medieval mathematics. Archive for History of Exact Science 32(2), 105-150 (Germany).