This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References. A deep sea of luminescent ideas
Abel, N. H. (1881). Œuvres Complètes. Tome I. Christiana: Grondahl & Son. [Reedición Sceaux: Éditions Jacques Gabay, 1992]
Alarcón, J., Figueras, O., Filloy, E., Gispert, M., Lema, S., Parra, B. M., Recio, J., Rojano, T. and Zubieta, G. (1981-1982). Matemáticas 100 Horas, 1 y 2. México, Bogotá, Caracas, Santiago, San Juan y Panamá: Fondo Educativo Interamericano.
al-Tûsî, S. (1986). ŒuvresMmathématiques, Algèbre et Géométrie au XIIe siècle. Tomes I et II. Texte établi et traduit par Roshdi Rashed. Paris: Les Belles Lettres.
Anbouba, A. (1978). L’algèbre arabe aux IXe et Xe siècles. Aperçu général. Journal for the History of Arabic Science, 2, 66-100.
Bachmann, H. (1955). Transfinite Zahlen. Berlin: Springer Verlag.
Bednarz, N. and Janvier, B. (1996). Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic. In N. Bednarz, C. Kieran, and L. Lee (Eds.), Approaches to Algebra: Perspectives for Research and Teaching (pp. 115-136). Dordrecht, The Netherlands: Kluwer Academic.
Bednarz, N., Radford, L, Janvier, B., and Lapage, A. (1992). Arithmetical and algebraic thinking in problem solving. In W. Geeslin and K. Graham (Eds.), Proceedings of the 16th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 65-72). Durham, NH: PME Program Committee.
Bell, A. W. (1996). Problem-solving approaches to algebra: Two aspects. In N. Bednarz, C. Kieran, and L. Lee (Eds.), Approaches to Algebra. Perspectives for Research and Teaching (pp. 167-186). Dordrecht/Boston/London: Kluwer Academic Publishers.
Benacerraf, P. (1983). What numbers could not be. In P. Benacerraf and H. Putman (Eds.), Philosophy of Mathematics. Selected Readings (pp. 272-294). Cambridge, UK: Cambridge University Press.
Boncompagni, B. (Ed.) (1857). Scritti di Leonardo Pisano Matematico del Secolo Decimoterzo. I. Il Liber Abbaci di Leonardo Pisano. Roma: Tipografia delle Scienze Matematiche e Fisiche.
Boohan, R. (1994). Interpreting the world with numbers: An introduction to quantitative modelling. In H. Mellar, J. Bliss, R. Boohan, J. Ogborn, and C. Tampsett (Eds.), Learning with Artificial Worlds (pp. 49-58). London: The Falmer Press.
Booth, L. (1984). Algebra: Children’s Strategies and Errors. Windsor: NFER-Nelson.
Bortolotti, E. (Ed.) (1966). R. Bombelli. L’Algebra. A cura di U. Forti e E. Bortolotti. Milano: Feltrinelli.
Bourbaki, N. (1966). Éléments de Mathématique. Fascicule XVII. Théorie des Ensembles. Chapitre 1 et 2. Description de la Mathématique Formelle. Théorie des Ensembles. Paris: Hermann.
Boyer, C. B. (1959). The History of the Calculus. New York: John Wiley.
Boyer, C. B. (1968). A History of Mathematics. New York: John Wiley.
Brousseau, G. (1996). Fondements et méthodes de la didactique des mathématiques. Recherches en Didactique des Mathématiques, 7, 33-115.
Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Dordrecht/Boston/ London: Kluwer Academic Publishers.
Brown, T. (2001). Mathematics Education and Language. Interpreting Hermeneutics and Post-Structuralism, revised second edition. Dordrecht/Boston/London: Kluwer Academic Publishers.
Carpenter, T., Moser, J. and Romberg, T. (Eds.) (1982). Addition and Subtraction: A Cognitive Perspective. Hillsdale, NJ: Lawrence Erlbaum.
Cerdán, F. (in preparation). Problemas verbales aritmético-algebraicos. El método de análisis y síntesis y el método cartesiano. Tesis doctoral. Universidad de Valencia.
Clagett, M. (1959). The Science of Mechanics in the Middle Ages. Madison, Milwaukee and London: The University of Wisconsin Press.
Clagett, M. (1968). Nicole Oresme and the Medieval Geometry of Qualities and Motions. Madison, Milwaukee and London: The University of Wisconsin Press.
Colebrooke, H. T. (ed. and trans.) (1817). Algebra with Arithmetic and Mensuration from the Sanscrit. Brahmegupta and Bháscara. London: John Murray.
Cuevas, G. J. and Yeatts, K. (2001). Navigating Through Algebra in Grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
Chevallard, Y. (1983). Le passage de l’arithmétique à l’algébrique dans l’enseignement des mathématiques au Collège. Petit X, 5, 51-94.
Descartes, R. (1701). Opuscula Posthuma Physica et Mathematica. Amsterdam: Typographia P. and Blaev J.
Descartes, R. (1826). Règles pour la Direction de l’Esprit. In Œuvres de Descartes, publiées par Victor Cousin. Tome onzième. Paris: Chez F. G. Levrault, libraire.
Descartes, R. (1996). Regulæ ad Directionem Ingeni. In Œuvres de Descartes. Tome X. Édition de Charles Adam et Paul Tannery. Paris: Librairie Philosophique J. Vrin.
Drouhard, J. P. (1992). Les Écritures Symboliques de l’Algèbre Élémentaire. Thèse de doctorat, Université Dénis Diderot, Paris 7.
Duval, R. (1995). Sémiosis et Pensée Humaine. Registres sémiotiques et apprentissage intellectuels. Berne: Peter Lang.
Eco, U. (1984). Semiotics and Philosophy of Language. London: The Macmillan Press.
Edwards, C. (1979). The Historical Development of the Calculus. New York: Springer Verlag.
Figueras, O., Filloy, E. and Valdemoros, M. (1985). The development of spatial imagination abilities and contextualisation atrategies: Models sased on the teaching of fractions. In L. Streefland (Ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 328-333). Noordwijkerhout, The Netherlands.
Figueras, O., Filloy, E. and Valdemoros, M. (1986). Some considerations on the graphic representation of fractions and their interpretation. In G. Lapan and E. Ruhama (Eds.), Proceedings of the Eighth Annual Meeting of the PME-NA (pp. 78-83). East Lansing, Michigan.
Filloy, E. (1980). Álgebra del nivel medio y análisis epistemológico: de Bombelli a Vieta. Actas del V Congreso Nacional de Profesores. México.
Filloy, E. (1990). PME algebra research. A working perspective. In G. Booker et-al (Eds.), Proceedings of the Fourteenth Annual Conference for the Psychology of Mathematics Education (Vol. 1, pp. PII 1-PII 33). Oaxtepec, Morelos, México.
Filloy, E. (1991). Cognitive tendencies and abstraction processes in algebra learning. In F. Furinghetti (Ed.), Proceedings of the Fifteenth Annual Conference for the Psychology of Mathematics Education (Vol. 2, pp. 48-55). Assisi, Italia.
Filloy, E. (1993a). El libro de los cuadrados de Leonardo de Pisa. In E. Filloy, L. Puig, and T. Rojano (Eds.), Memorias del Tercer Simposio Internacional sobre Investigación en Educación Matemática. Historia de las Ideas Algebraicas (pp. 11-30). México, DF: CINVESTAV/PNFAPM.
Filloy, E. (1993b) Tendencias cognitivas y procesos de abstracción en el aprendizaje del álgebra y de la geometría. Enseñanza de las ciencias, 11(2), 160-166.
Filloy, E. and Lema, S. (1996). El Teorema de Thales: significado y sentido en un sistema matemático de signos. In F. Hitt (ed.), Investigaciones en Matemática Educativa (pp. 55-75). México, DF: Grupo Editorial Iberoamérica.
Filloy, E. and Rojano, T. (1983). Movimiento de la Incógnita, Terminación de la Aritmética? México: SME.
Filloy, E. and Rojano, T. (1984). From an arithmetical to an algebraic thought (a clinical study with 12-13 year olds). In J. Moser (ed.), Proceedings of the Sixth Annual Meeting for the Psychology of Mathematics Education, North American Chapter (pp. 51-56). Madison, WI, USA.
Filloy, E. and Rojano, T. (1985a). Obstructions to the acquisition of elemental algebraic concepts and teaching strategies. In L. Streefland (ed.), Proceedings of the Ninth Annual Conference for the Psychology of Mathematics Education (pp. 154-158). Utrecht, Holanda.
Filloy, E. and Rojano, T. (1985b). Operating the unknown and models of teaching (a clinical study with 12-13 year olds with a 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 (pp. 75-79). Columbus, OH.
Filloy, E. and Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19-25.
Filloy, E. and Rojano, T. (2001). Algebraic syntax and word problems solution: First steps. In M. van den Heuvel-Panhuizen (ed.), Proceedings of the Twenty-fifth Annual Conference for the Psychology of Mathematics Education (Vol. 2, pp. 417-424). Utrecht, The Netherlands.
Filloy, E. and Rubio, G. (1991). Unknown and variable in analytical methods for solving word arithmetic/algebraic problems. In R. G. Underhill (ed.), Proceedings of the Thirteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 64-69). Blacksburg, VA.
Filloy, E. and Rubio, G. (1993a). Didactic models, cognition and competence in the solution of arithmetic and algebra word problems. In I. Hirabayashi, N. Nohda, K. Shigematsu, and F. Lin (eds.), Proceedings of the Seventeenth International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 154-161).Tsukuba, Ibaraki, Japan.
Filloy, E. and Rubio, G. (1993b). Family of arithmetical and algebraic word problems, and the tensions between the different uses of algebraic expressions. In J. R. Becker and B. J. Pence (eds.), Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 142-148). Pacific Grove, CA.
Filloy, E. and Sutherland, R. (1996). Designing curricula for teaching and learning algebra. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds.), International Handbook of Mathematics Education (Vol. 1, pp. 139-160). Dordrecht/Boston/London: Kluwer Academic Publishers.
Filloy, E., Rojano, T. and Rubio, G. (2001). Propositions concerning the resolution of arithmetical-algebraic problems. In R. Sutherland, T. Rojano, A. Bell, and R. Lins (eds.), Perspectives on School Algebra (pp.155-176). Dordrecht/Boston/London: Kluwer Academic Publishers.
Filloy, E., Rojano, T. and Solares, A. (2002). Cognitive tendencies: The interaction between semantics and algebraic syntax in the production of syntactic errors. In A. Cockburn and E. Nardi (eds.), Proceedings of the Twenty-sixth Annual Conference for the Psychology of Mathematics Education (Vol. 4, pp. 129-136). Norwich, UK.
Filloy, E., Rojano, T. and Solares, A. (2004). Arithmetic/algebraic problem-solving and the representation of two unknown quantities. In M. Johnsen Høines, and A. B. Fuglestad (Eds.), Proceedings of the Twenty-eighth Annual Conference for the Psychology of Mathematics Education (Vol. 2, pp. 391-398). Bergen, Norway.
Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht: Reidel.
Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht: Reidel.
Fridman, L. M. (1990). Los grafos trinomiales como metalenguaje de los problemas. Matemáticas. Revista del Departamento de Matemáticas de la Universidad de Sonora, 17-18, 51-59.
Friel, S., Rachlin, S. and Doyle, D. (2001). Navigating Through Algebra in Grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
Fuson, K. (1998). Children’s Counting and Concept of Number. New York: Springer Verlag.
Galois, É. (1846). Œuvres mathématiques d’Évariste Galois. Le Journal de Liouville, XI, 381-444. [Reedición Œuvres Mathématiques, Publiées en 1846 dans le Journal de Liouville, Suivies d’une étude par Sophus Lie. Sceaux: Éditions Jacques Gabay, 1989.]
Ginsburg, H., Inoue, N. and Seo, K. (1999). Young children doing mathematics: Observations of everyday sctivities. In J. V. Copley (ed.), Mathematics in the Early Years (pp. 88-99). Reston, Va.: National Council of Teachers of Mathematics, and Washington, D.C.: National Association for the Education of Young Children.
Glassner, J.-J. (2000). Écrire à Sumer. L’Invention du Cunéiforme. Paris: Seuil.
Grant, E. (1969). Nicole Oresme, De Proportionibus and Pauca Respicientes. Madison, Milwaukee and London: The University of Wisconsin Press.
Grant, E. (1971). Nicole Oresme and the Kinematics of Circular Motions. Madison, Milwaukee and London: The University of Wisconsin Press.
Greenes, C., Cavanagh, M., Dacey, L., Findell, C. and Small, M. (2001). Navigating Through Algebra in Prekindergarten-Grade 2. Reston, VA: National Council of Teachers of Mathematics.
Hamilton, N. and Landin, J. (1961). Set Theory and The Structure of Arithmetic. Boston: Allyn and Bacon, Inc.
Heath, Th.(1921). A History of Greek Mathematics.2 vols. Oxford: Clarendon Press. [Reprinted in New York: Dover, 1981.]
Høyrup, J. (1985). Varieties of mathematical discourse in pre-modern socio-cultural contexts: Mesopotamia, Greece, and the Latin Middle Ages. Science and Society, XLIX, 4-41.
Høyrup, J. (1986). Al-Khwârizmî, Ibn Turk, and the Liber Mensurationum: On the origins of Islamic algebra. ERDEM, 2, 445-484.
Høyrup, J. (1987). The formation of ‘Islamic Mathematics’. Sources and conditions. Science in Context, 1, 281-329.
Høyrup, J.(1991).‘Oxford’ and‘Cremona’: On the relations between two versions of al-Khwârizmî’s Algebra. Filosofi og videnskabsteori på Roskilde Universitetcenter.3. Række: Preprint og Reprints nr. 1.
Høyrup, J. (1999a). The founding of Italian vernacular algebra. Filosofi og videnskabsteori på Roskilde Universitetcenter. 3. Række: Preprint og Reprints 1999 nr. 2.
Høyrup, J. (1999b). VAT. LAT. 4826. Jacopo da Firenze, Tractatus algorismi. Preliminari transcription of the manuscript, with occasional commentaries. Filosofi og videnskabsteori på Roskilde Universitetcenter. 3. Række: Preprint og Reprints 1999 nr. 3.
Høyrup, J. (2002a). Lengths, Widths, Surfaces. A Portrait of Old Babylonian Algebra and Its Kin. New York: Springer-Verlag.
Høyrup, J. (2002b). Pre-Modern “Algebra”: A concise survey of that which was shaped into the technique and discipline we know, Quaderni di Ricerca in Didattica G.R.I.M., 11, http://math.unipa.it/∼grim/quaderno11.htm.
Hughes, B. (1981). Jordanus de Nemore. De Numeris Datis, Berkeley, CA: University of California Press.
Hughes, B. (1986). Gerard of Cremona’s translation of al-Khwârizmî’s al-jabr: A critical edition. Mediaeval Studies, 48, 211-263.
Ifrah, G. (1994). Histoire Universelle des Chiffres. L’Intelligence des Hommes Racontée par les Nombres et le Calcul. Paris: Robert Laffont.
Isbell, J. R. (1960). A definition of ordinal numbers. American Mathematical Monthly, 67(1), 51-52.
Iwasaki, H. and Yamaguchi, T. (1997). The cognitive and symbolic analysis of the generalization process: the comparison of algebraic signs with geometric figures. In E. Pehkonen (ed.), Proceedings of the Twenty First Annual Conference for the Psychology of Mathematics Education (Vol. 3, pp. 105-112). Lahti, Finland.
Jones, C. V. (1978). On the Concept of One as a Number. Doctoral dissertation, University of Toronto.
Kalmykova, Z. I. (1975). Processes of analysis and synthesis in the solution of arithmetic problems. In J. Kilpatrick, I. Wirszup, E. G. Begle, and J. W. Wilson. (eds.), Soviet Studies in the Psychology of Learning and Teaching Mathematics. Vol. XI. Analysis and Synthesis as Problem Solving Methods (pp. 1-171). Stanford, CA: NCTM.
Kaput, J. J. (1987). Representations systems and mathematics. In C. Janvier (ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 19-26). Hillsdale, NJ: Lawrence Erlbaum.
Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner and C. Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra (Vol. 4, pp. 167-194). Hillsdale, NJ/Reston, VA: Lawrence Erlbaum Associates/National Council of Teachers of Mathematics
Kasir, D. S. (1931). The Algebra of Omar Khayyam. New York, NY: Bureau of Publications Teacher College of Columbia University.
Kieran, C. (1980). . In R. Karplus (ed.), Proceedings of the Fourth Conference of the International Group for the Psychology of Mathematics Education (pp. 163-169). Berkeley, CA, University of California,.
Kieran, C. (1981). . Educational Studies in Mathematics, 12, 317-326.
Kieran, C. and Filloy, E. (1989). El aprendizaje del álgebra escolar desde una perspectiva psicológica. Enseñanza de las Ciencias, 7, 229-240.
Kieran, C. and Sfard, A. (1999). Seeing through symbols: The case of equivalent expressions. Focus on Learning Problems in Mathematics, 21(1), 1-17.
Kirshner, D. (1987). The Grammar of Symbolic Elementary Algebra. Doctoral dissertation, University of British Columbia, Vancouver.
Klein, J. (1968). Greek Mathematical Thought and the Origins of Algebra. Cambridge, MA: MIT Press. [Reprinted in New York: Dover, 1992.]
Krutetskii, V. D. (1976). The Psychology of Mathematical Abilities in School Children. Chicago: The University of Chicago Press.
Kuhn, T. S. (1962). The Structure of Scientific Revolutions. Chicago: The University of Chicago Press.
Lagrange, J. L. de. (1899). Œuvres. Publiées par les soins de J.-A. Serret. Tome troisième. Paris: Gauthier-Villars. [Reprinted in Hildesheim and New York: Georg Olms Verlag, 1973.]
Lakatos, I. (1976). Proofs and Refutations. Cambridge, UK: Cambridge University Press.
Lee, L. (1996). An initiation into algebraic culture through generalization activities. In N. Bednarz, C. Kieran and L. Lee (eds.), Approaches to Algebra. Perspectives for Research and Teaching (pp. 87-106). Dordrecht/Boston/London: Kluwer Academic Publishers.
Levey, M. (ed.) (1966). The Algebra of Abû Kâmil, in a Commentary by Mordecai Finzi. Hebrew text and translation, and commentary. Madison, WI: The University of Wisconsin Press.
Malara, N. and Navarra, G. (2003). ArAl Projec. Atrithmetic Pathways Towards Favouring Pre-algebraic Thinking. Bologna: Pitagora Editrice.
Marre, A. (1880). Notice sur Nicolas Chuquet et son Triparty en la science des nombres. Bulletino di Bibliografia e Storia delle Scienze Matematice e Fisice, 13, 555--659 and 693-814.
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran and L. Lee (Eds.), Approaches to Algebra. Perspectives for Research and Teaching (pp. 65-86). Dordrecht/Boston/London: Kluwer Academic Publishers.
Matz, M. (1982). Towards a process model for high school algebra errors. In D. Seeman and J. S. Brown (eds.), Intelligent Tutoring Systems (pp. 25-50). New York: Academic Press.
Mazzinghi, M. A. di. (1967). Trattato di Fioretti. (Arrighi, G. Ed.) Pisa: Domus Galileana.
Nassar, A. (2001). El Efecto de Enseñar Algunas Estrategias de Resolución de Problemas en la Actuación de los Alumnos del Nivel 3º de Secundaria al Resolver Problemas Verbales Algebraicos en Gaza (Palestina), Tesis doctoral. Universitat de València.
Nemirovsky, R. (1996). Mathematical narratives, modeling and algebra. In N. Bednarz, C. Kieran and L. Lee (eds.), Approaches to Algebra. Perspectives for Research and Teaching (pp. 197-220). Dordrecht/Boston/London: Kluwer Academic Publishers.
Neugebauer, O. (1969). The Exact Sciences in Antiquity. New York: Dover.
Peirce, C. S. (1931-58). Collected Papers of Charles Sanders Peirce. Edited by Charles Hartshorne and Paul Weiss (vols. 1-6) and by Arthur Burks (vols. 7-8). Cambridge, MA: The Belknap Press of Harvard University Press.
Peirce, C. S. (1982). Writings of Charles S. Peirce: A Chronological Edition, 6 vols. to date. Edited by Edward C. Moore, Max Fisch, Christian J. W. Kloesel et-al. Bloomington: Indiana University Press.
Pimm, D. (1987). Speaking Mathematically. Comunication in Mathematics Classrooms. London: Routledge.
Polya, G. (1957). How to Solve It. 2nd. edition. Princeton, NJ: Princeton University Press.
Polya, G. (1966). Mathematical Discovery. 2 vols. New York: John Wiley and Sons.
Puig, L. (1994). El De Numeris Datis de Jordanus Nemorarius como sistema matemático de signos. Mathesis, 10(1), 47-92.
Puig, L. (1996). Elementos de Resolución de Problemas. Granada: Comares, col. Mathema.
Puig, L. (1997). Análisis fenomenológico. In L. Rico (Ed.), La Educación Matemática en la Enseñanza Secundaria (pp. 61-94). Barcelona: ICE/Horsori.
Puig, L. (1998). Componentes de una historia del álgebra. El texto de al-Khwârizmî restaurado. In F. Hitt (Ed.), Investigaciones en Matemática Educativa II (pp. 109-131). México, DF: Grupo Editorial Iberoamérica.
Puig, L. and Cerdán, F. (1988). Problemas Aritméticos Escolares. Madrid: Ed. Síntesis.
Puig, L. and Cerdán, F. (1990). Acerca del carácter aritmético o algebraico de los problemas verbales. In E. Filloy, and T. Rojano (Eds.), Memorias del Segundo Simposio Internacional sobre Investigación en Educación Matemática (pp. 35-48). Cuernavaca, Morelos: PNFAPM.
Puig, L. and Rojano, T. (2004). The history of algebra in mathematics education. In K. Stacey, H. Chick, and M. Kendal (eds.), The Teaching and Learning of Algebra: The 12th ICMI study (pp. 189-224). Boston/Dordrecht/New York/London: Kluwer Academic Publishers.
Radford, L. (2000a). The historical origins of algebraic thinking. In R. Sutherland, T. Rojano, A. Bell, and R. Lins (Eds.), Perspectives on School Algebra (pp. 13-36). Dordrecht/Boston/ London: Kluwer Academic Publishers.
Radford, L. (2000b). Signs and meanings in students’ emergent algebraic thinking: A semiotic analysis, Educational Studies in Mathematics, 42(3), 237-268.
Radford, L. (2003). On the epistemological limits of language. Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123-150.
Radford, L. (2004). The Cultural-Epistomological Conditions of the Emergence of Algebraic Symbolism. Paper presented at the 2004 History and Pedagogy of Mathematics Conference, Uppsala, Sweden.
Rashed, R. (ed.) (1984). Diophante. Tome III. Les Arithmétiques. Livre IV, et Tome IV, Livres V, VI et VII. Texte de la traduction arabe de Qustâ ibn Lûqâ établi et traduit par Roshdi Rashed. Paris: Les Belles Lettres.
Rashed, R. and Vahebzadeh, B. (1999). Al-Khayyâm mathématicien. Paris: Librairie Scientifique et Technique Albert Blanchard.
Rojano, T. (1985). De la artimética al álgebra: un estudio clínico con niños de 12 a 13 años de edad. Unpublished Doctoral dissertation, Centro de Investigación y de Estudios Avanzados del IPN, D.F., México.
Rosen, F. (1831). The Algebra of Mohammed Ben Musa. London: Oriental Translation Fund. Rotman, B. (1988). Toward a semiotics of mathematics. Semiotica, 72, 1-35.
Rotman, B. (1993). Ad Infinitum… The Ghost in Turing’s Machine. Stanford, CA: Stanford University Press.
Rotman, B. (2000). Mathematics as Sign. Writing, Imagining, Counting. Stanford, CA: Stanford University Press.
Russell, B. (1973). Is mathematics purely linguistic? In D. Lackey (Ed.), Essays in Analysis by Bertrand Russell (pp. 295-306). London: George Allen and Unwin Ltd.
Schmandt-Besserat, D. (1992). Before Writing. I. From Counting to Cuneiform. Austin: University of Texas Press.
Sesiano, J. (ed.) (1982). Books IV to VII of Diophantus’ Arithmetica in the Arabic Translation attributed to Qustâ ibn Lûqâ. Berlin, Heidelberg, New York: Springer
Verlag. Sesiano, J. (1993). La version latine médiévale de l’Algèbre d’Abû Kâmil. In M. Folkerts, and J. P. Hogendijk (Eds.), Vestigia Mathematica. Studies in Medieval and Early Modern Mathematics in Honour of H. L. L. Busard (pp. 315-452). Amsterdam and Atlanta, GA: Editions Rodopi B. V.
Sigler, L. E. (1987). Leonardo Pisano Fibonacci. The Book of Squares. An annotated translation into modern English by L. E. Sigler. Orlando, FL: Academic Press.
Sigler, L. E. (2002). Fibonacci’s Liber Abaci. A Translation into Modern English of Leonardo Pisano’s Book of Calculation. Translated by Laurence E. Sigler. New York/Berlin/ Heidelberg: Springer Verlag.
Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 42(3), 379-402.
Stevin, S. (1634). Les Œuvres Mathématiques de Simon Stevin de Bruges, edited by Girard. Leyden: Elzevirs.
Szabó, Á. (1977). Les débuts des mathématiques grecques. Paris: Vrin.
Taisbak, C. M. (2003). Euclid’s Data. The Importance of Being Given. Copenhagen: Museum Tusculanum Press.
Talens, J. and Company, J. M. (1984). The textual space: On the notion of text. The Journal of the Midwest Modern Language Association, 17(2), 24-36.
Tannery, P. (Ed.) (1893). Diophanti Alexandrini Opera Omnia cum Graecis Commentariis. Edidit et latine interpretatus est Paulus Tannery. 2 vols. Stuttgart: B. G. Teubner. [Reprinted in 1974.]
Thorndike, E. L. et al. (1923). The Psychology of Algebra. New York: The Macmillan Company.
Usiskin, Z. (1999). Conceptions of school algebra and uses of variables. In B. Moses (ed.), Algebraic Thinking, Grades K-12: Readings from NCTM’s School-Based Journals and Other Publications (pp. 7-13).
Reston, VA: National Council of Teachers of Mathematics. Vallejo, J. M. (1841). Tratado Elemental de Matemáticas, Escrito de Orden de S. M. para Uso de los Caballeros Seminaristas del Seminario de Nobles de Madrid y Demás Casas de Educación del Reino. Cuarta Edición Corregida y Considerablemente Aumentada. Tomo I. Parte primera, que contiene la Aritmética y Álgebra. Madrid: Imprenta Garrasayaza.
Van Der Waerden, B. L. (1954). Science Awakening I: Egyptian, Babylonian & Greek Mathematics. Groningen: Noordhoff.
Van Dooren, W., De Bock, D., Depaepe, F., Janssens, D. and Verschaffel, L. (2003). The illusion of linearity: Expanding the evidence towards probabilistic reasoning. Educational Studies in Mathematics, 53, 113-138.
Van Egmond, W. (1980). Practical mathematics in the Italian renaissance. (A Catalog of Italian Abacus Manuscripts and Printed Books to 1600). Firenze, Italy: Annali dell’Instituto e Museo di. Storia della Scienza, fascicolo 1, Instituto e Museo di Storia della Scienza.
Van Schooten, F. (1646). Francisci Vietæ Opera Mathematica. Lugduni Batavorum: Ex Officinâ Bonaventuræ & Abrahami Elzeviriorum.
Ver Eecke, P. (1952). Leonard de Pise. Le Livre des Nombres Carrés. Traduit pour la première fois du latin médiéval en Français, avec une introduction et des notes par Paul Ver Eecke. Paris: Albert Blanchard.
Ver Eecke, P. (1959). Diophante d’Alexandrie. Les Six Livres d’Arithmétiques et le Livre des Nombres Polygones. Traduit du grec, avec une introduction et des notes par Paul Ver Eecke. Paris: Albert Blanchard.
Ver Eecke, P. (1973). Leonardo de Pisa. El Libro de los Números Cuadrados. Traducción de la versión francesa de Paul Ver Ecke de Pastora Sofía Nogués Acuna. Buenos Aires: Editorial Universitaria de Buenos Aires.
Vergnaud, G. (1981). L’Enfant la Mathématique et la Réalité. Berne: Peter Lang.
Vergnaud, G. (1982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In T. P. Carpenter, J. M. Moser, and T. A. Romberg (eds.), Addition and Subtraction: A Cognitive Perspective (pp. 39-59). Hillsdale, NJ: Lawrence Erlbaum.
Verschaffel, L., Greer, B. and De Corte, E. (2000). Making Sense of Word Problems. Lisse: Swets & Zeitlinger.
Von Neumann, J.(1923). Zur Einführung der transfiniten Zahlen. Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephine, Sectio Scientiarum Mathematicarum, 1, 199-208. [Translated as “On the Introduction of Transfinite Numbers” by J. Van Heijenoort. In J. van Heijenoort (Ed.), (1967). From Frege to Gödel. A Source Book in Mathematical Logic,1879-1931(pp.346-354). Cambridge, MA: Harvard University Press.]
Vuillemin, J. (1962). La Philosophie de l’Algèbre. Paris: Presses Universitaires de France.
Witmer, T. R. (ed.) (1983). François Viète. The Analytic Art. Kent, OH: The Kent State University Press.
Wittgenstein, L. (1956). Remarks on the Foundations of Mathematics. Edited by G. H. von Wright, R. Rhees, and G. E. M. Anscombe. Oxford: Basil Blackwell. [Wittgenstein, L. (1984). Bemerkungen über die Grundlagen der Mathematik. Herausgegeben von G. H. von Wright, R. Rhees, and G. E. M. Anscombe. Suhrkamp:Frankfurt am Main.]
Zazkis, R. and Liljeddahl, P. (2001). Exploring multiplicative and additive structure of arithmetic sequences. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the Twenty Fifth Annual Conference for the Psychology of Mathematics Education (Vol. 4, pp. 439-446). Utrecht, The Netherlands.
Zazkis, R. and Liljeddahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379-402.
Zermelo, E. (1909). Sur les ensembles finis et le principe de l’induction complète. Acta Mathematica, 32, 185-193.
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2008). References. A Deep Sea of Luminescent Ideas. In: Educational Algebra. Mathematics Education Library, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71254-3_11
Download citation
DOI: https://doi.org/10.1007/978-0-387-71254-3_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-71253-6
Online ISBN: 978-0-387-71254-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)