The role of mathematical symbols in the development of number conceptualization: The case of the minus sign

Philosophical Psychology

Volumn 21, Issue 4, 2008, Pages 555-570

  Vlassis, Joëlle ^a  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

Author keywords

Equations; Language; Minus sign; Negative numbers; Negativity

Indexed keywords

EID: 51049090393     PISSN: 09515089     EISSN: 1465394X     Source Type: Journal    
DOI: 10.1080/09515080802285552     Document Type: Article

References (17)

1. Bednarz, N., Dufour-Janvier, N., Poirier, L., & Bacon, L. (1993). Socioconstructivist viewpoint on the use of symbolism in mathematics education. Alberta Journal of Educational Research, 39, 41-58.
2. Cobb, P. (2000). From representations to symbolizing: Introductory comments on semiotics and mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 17-36). Mahwah, NJ: Erlbaum.
3. Cortès, A., (1993). Analysis of errors and a cognitive model in the solving of equations. In: I. Hirabayashi, N. Nohda, K. Shigematsu, & F. L. Lin (Eds.), Proceedings of the seventeenth international conference for the Psychology of Mathematics Education (Vol. 1, pp. 146-153). Tsukuba, Japan.
4. Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49, 171-192.
5. Gallardo, A., & Rojano, T. (1994). School Algebra. Syntactic difficulties in the operativity. In D. Kirshner (Ed.), Proceedings of the sixteenth international conference for the Psychology of Mathematics Education: North American Chapter (pp. 159-165). Baton Rouge, LA.
6. Gilly, M. (1995). Approches socio-constructives du développement cognitif. In D. Gaonach & C. Golder (Eds.), Profession enseignant: manuel de psychologie pour l'enseignement (pp. 130-153). Paris: Hachette.
7. Glaeser, G. (1981). Epistémologie des nombres relatifs. Recherche en didactique des mathématiques, 2, 303-346.
8. Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling and tool use in mathematics education. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 225-274). Mahwah, NJ: Erlbaum.
9. Guichard, J.-P. (2003). Histoire de symboles: La première inconnue. Poitiers, France: IREM de Poitiers.
10. Hefendehl-Hebeker, L. (1991). Negative numbers: Obstacles in their evolution from intuitive to intellectual constructs. For the Learning of Mathematics, 11, 26-32.
11. Muntersbjorn, M. (2003). Representational innovation and mathematical ontology. Synthese, 134, 159-180.
12. Radford, L. (1998). On signs and representations, a cultural account. Scientia Paedagogica Experimentalis, 1, 277-302.
13. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical Thinking and Learning, 5, 37-70.
14. Sfard, A. (2000). Symbolizing mathematical reality into being-Or how mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 37-98). Mahwah, NJ: Erlbaum.
15. Vergnaud, G. (1989). L'Obstacle des nombres négatifs et l'introduction à l'algèbre. In N. Bednarz & C. Gamier (Eds.), Construction des savoirs (pp. 76-83). Ottawa: Agence d'ARC.
16. Vlassis, J. (2001). Solving equations with negatives or crossing the formalizing gap. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the twenty-fifth international conference for the psychology of mathematics education (Vol. 4, pp. 375-382). Utrecht, Netherlands.
17. Vlassis, J. (2002). The balance model: Hindrance or support for the solving of linear equations with one unknown. Educational Studies in Mathematics, 49, 341-359.