Proyecto investigador
Tipo de documento
Autores
Lista de autores
Molina, Marta
Resumen
Proyecto investigador sobre el Estudio de componentes de la competencia algebraica que se sustentan en conocimiento de la estructura de la Aritmética y el Álgebra, enmarcado en la línea “Didáctica de la Matemática. Pensamiento Numérico. Enseñanza y Aprendizaje del Álgebra”. Documento elaborado para optar a la plaza de Profesor Titular de Universidad, código 6/1/2012, adscrita al área de Didáctica de la Matemática, Departamento de Didáctica de la Matemática de la Facultad de Ciencias de la Educación de la Universidad de Granada [Resolución de 27 de febrero de 2012, de la Universidad de Granada, BOE 65, 24233-24187].
Fecha
2012
Tipo de fecha
Estado publicación
Términos clave
Álgebra | Aprendizaje | Relaciones numéricas | Representaciones
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Lugar (no publicado)
Institución (no publicado)
Referencias
Arcavi, A. (1994). Symbol sense: informal sense–making in formal mathematics. For the Learning of Mathematics, 1(3), 24-35. Arcavi, A. (2006). El desarrollo y el uso del sentido de los símbolos. En I. Vale, T. Pimentel, A. Barbosa, L. Fonseca, L. Santos y P. Canavarro (Eds.), Números y álgebra na aprendizagem da matemática e na formaçâo de profesores (pp. 29-47). Caminha, Portugal: Sociedade Portugesa de Ciências de Eduacaçâo. Arzarello, F. (1996). The role of natural language in prealgebraic and algebraic thinking. En H. Steinbring, M .G. Bartolini Bussi y A. Sierspinska (Eds.), Language and communication in the mathematics classroom (pp. 249-261). Reston, VA: NCTM. Arzarello, F., Bazzini, L. y Chiappini, G. (2001). A model for analysing algebraic processes of thinking. En R. Sutherland, T. Rojano, A. Bell y R. Lins (Eds.), Perspectives on school algebra (pp. 61-81). Dordrecht, Los Países Bajos: Kluwer. Banerjee, R. (2008). Developing a learning sequence for transiting from arithmetic to elementary algebra. Tesis doctoral, Homi Bhabha Centre for Science Education, Mumbai, India. Banerjee, R. (2011). Is arithmetic useful for the teaching and learning of algebra? Contemporary education dialogue, 8(2), 137-159. Baroody, A. J. y Coslick, R. T. (1998). Fostering children’s mathematical power. Mahwah, NJ: Laurence Erlbaum Associates. Bastable, V. y Schifter, D. (2007). Classroom stories: examples of elementary students engaged in early algebra. En J. Kaput, D. W. Carraher y M. L. Blanton (Eds.), Algebra in the early grades (pp. 165-184). Mahwah, NJ: Lawrence Erlbaum Associates. Bednarz, N., Kieran, C. y Lee, L. (1996). Approaches to algebra. Perspectives for Seeing. Harmondsworth, Middlesex: BBC y Penguin Books Ltd. Bell, A. (1988). Algebra choices in curriculum design. En A. Borbas (Ed.), Proceedings of the 12th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 147-153). Veszprém, Hungary: Ferenc Genzwein OOK. Bell, A. (1995). Purpose in school algebra. Journal of Mathematical Behavior, 14, 41-74. Blanton, M. L. y Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446. Boero, P. (1994). About the role of algebraic language in mathematics and related difficulties. Rendiconti del Seminario Matematico, 52(2), 161-194. Boero, P. (2001). Transformation and anticipation as key processes in algebraic problem solving. En R. Sutherland, T. Rojano, A. Bell y R. Lins (Eds.), Perspectives on school algebra (pp. 99-119). Dordrecht, Los Países Bajos: Kluwer Academic Publishers. Boero, P., Dauek, N. y Ferrari, P. L. (2002). Developing mastery of natural language. Approaches to some theoretical aspects of mathematics. En L. D. English (Ed.), Handbook of international research in mathematics education (pp. 262-295). Routledge. Booth, L. R (1982). Ordering your operations. Mathematics in School, 11(3), 5-6. Booth, L. R. (1989). A question of structure or a reaction to: “the early learning algebra: a structural perspective”. En S. Wagner y C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Vol. 4, pp. 57-59). Reston, VA: Lawrence Erlbaum Associates y NCTM. Boulton–Lewis, G. M., Cooper, T., Atweh, B., Pillay, H. y Wills, L. (2000). Pre–Algebra: a cognitive perspective. En A. Olivier y K. Newstead (Eds.), Proceedings of the 22nd International Group for the Psychology of Mathematics Education (Vol. 2, pp. 144-151). Stellenbosch, Sudáfrica: Program Committee for PME22. Brizuela, B. M. y Lara-Roth, S. (2001). Additive relations and function tables. En H. Chick, K. Stacey, J. Vincent y J. Vincent (Eds.), Proceedings of the 12th ICMI study conference. The future of the teaching and learning of algebra (pp. 110-119). Melbourne, Australia: University of Melbourne. Cai, J. y Knuth, E. (2011). Early algebraization. A global dialogue from multiple perspectives. Berlín, Alemania: Springer-Verlag. Carpenter, T. P. y Franke, M. L. (2001). Developing algebraic reasoning in the elementary school: generalization and proof. En H. Chick, K. Stacey, J. Vincent y J. Vincent (Eds.), Proceedings of the 12th ICMI study conference. The future of the teaching and learning of algebra (pp.155-162). Melbourne, Australia: University of Melbourne. Carpenter, T. P., Franke, M. L. y Levi, L. (2003). Thinking mathematically: integrating arithmetic y algebra in elementary school. Portsmouth, Reino Unido: Heinemann. Carpenter, T. P. y Moser, J. M. (1984). The acquisition of addition and subtraction concepts. En R. Lesh y M. Landau (Eds.), Acquisition of mathematics: concepts and processes (pp. 7-44). New York, NY: Academic Press. Carraher, D. W., Schliemann, A. D. y Brizuela, B. M. (2001). Can young students operate on unknowns? En M. van der Heuvel-Panhuizen (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education (Vol. 1, pp. 130-140). Utrecht, Los Países Bajos: Freudenthal Institute. Carraher, D. W., Schliemann, A. D., Brizuela, B. M. y Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87-115. Carraher, D. W. y Schliemann, A. D. (2007). Early algebra and algebraic reasoning. En F. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (Vol. 2., pp. 669-705). Charlotte, NC: Information Age Publishing. Castro, E. y Molina, M. (2007). Desarrollo de pensamiento relacional mediante trabajo con igualdades numéricas en aritmética básica. Educación Matemática, 19(2), 67-94. Castro E., Rico, L. y Romero, I. (1997). Sistemas de representación y aprendizaje de estructuras numéricas. Enseñanza de las Ciencias, 15(3), 361-371 Cerulli, M. y Mariotti, M. A. (2001). Arithmetic and algebra, continuity or cognitive break? The case of Francesca. En M. Heuvel–Penhuizen (Ed.), Proceedings of the 25th International Group for the Psychology of Mathematics Education (Vol. 2, 225- 231). Utrecht, Los Países Bajos: Freudenthal Institute. Chazan, D. y Yerushalmy, M. (2003). On appreciating the cognitive complexity of school algebra: Research on algebra learning and directions o curricular change. En J. Kilpatrick, W. G. Martin y D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 123-135). Reston, VA: NCTM. Davis, R. B. (1975). Cognitive processes involved in solving simple algebraic equations. Journal of Children´s Mathematical Behavior, 1(3), 7-35. Demby, A. (1997). Algebraic procedures used by 13-to 15- years old. Educational Studies in Mathematics, 33, 45-70. Drijvers, P., Goddijn, A. y Kindt, M. (2011). Algebra education: exploring topics and themes. En P. Drijvers (Eds.), Secondary algebra education (pp. 5-26). Rotterdam, Los Países Bajos: Sense Publishers. Drijvers, P. y Hendrikus, M. (2003). Learning algebra in a computer algebra environment: Design research on the understanding of the concept of parameter. Tesis doctoral no publicada. Utrecht, Los Países Bajos: Utrecht University. Drouhard‚ J.-P. (2001). Research in language aspects of algebra: a turning point? En H. Chick‚ K. Stacey‚ J. Vincent y J. Vincent (Eds.)‚ The future of the teaching and learning of algebra (pp. 238-242). Melbourne‚ Australia: The University of Melbourne. Drouhard, J.-P. y Teppo A. R. (2004). Symbols and language. En K. Stacey, H. Chick, y M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12th ICMI study (227-264). New York, NY: Kluwer. Empson, S. B., Levi, L. y Carpenter, T. (2011). The algebraic nature of fractions: developing relational thinking in elementary school. En J. Cai y E. Knuth (Eds.), Early algebraization. A global dialogue from multiple perspectives (pp. 409-428). Berlín, Alemania: Springer-Verlag. Esty, W. W. (1992). Language concepts of mathematics. Focus on Learning Problems in Mathematics, 14(4), 31-53. Foxman, D. y Beishuizen, M. (1999). Untaught mental calculation methods used by 11-year-olds. Mathematics in School, 28(5), 5-7. Freiman, V. y Lee, L. (2004). Tracking primary students' understanding of the equal sign. En M. Johnsen y A. Berit (Eds.), Proceedings of the 28th International Group for the Psychology of Mathematics Education (Vol. 2, pp. 415-422). Bergen, Noruega: Bergen University College. Fujii, T. y Stephens, M. (2001). Fostering an understanding of algebraic generalization through numerical expressions: the role of quasi-variables. En H. Chick, K. Stacey, J. Vincent y J. Vincent (Eds.), Proceedings of the 12th ICMI study conference (pp. 258-264). Melbourne, Australia: University of Melbourne. Furinghetti, F. y Paola, D. (1994). Parameters, unknowns and variables: a little difference? En J. P. da Ponte y J. F. Matos (Eds.), Proceedings of the XVIII International Conference for the Psychology of Mathematics (Vol. 2, 368-375). Lisboa, Portugal: Universidad de Lisboa. Gómez, B. (1994). Los métodos de cálculo mental: Un análisis en la formación de profesores. Tesis doctoral, Universidad de Valencia, Valencia. Gray, E. y Tall, D. (1992). Success and failure in mathematics: the flexible meaning of symbols as process and concept. Mathematics Teaching, 14, 6-10. Gray, E. y Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26(2), 115–141. Greeno, J. G. (1982, marzo). A cognitive learning analysis of algebra. Paper presented at the annual meeting of the American Educational Research Association, Boston, MA. Harper, E. (1987). Ghosts of Diophantus. Educational Studies in Mathematics, 18, 75-90. Heid, M. K. (1996). A technology-intensive functional approach to the emergence of algebraic thinking. En A. Bednarz, C. Kieran y L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 239-255). Dordrecht, Los Países Bajos: Kluwer Academic Publishers. Herscovics, N. y Linchevski, L. (1994). Cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78. Hewitt, D. (1998). Approaching arithmetic algebraically. Mathematics Teaching, 163, 19-29. Hoch, M. (2003). Structure sense. En M. A. Mariotti (Ed.), Proceedings of the 3rd Conference for European Research in Mathematics Education (CD). Bellaria, Italia: ERME. Hoch, M. y Dreyfus, T. (2004). Structure sense in high school algebra: The effect of brackets. En M. J. Høines y A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol.3, pp. 49-56). Bergen, Norway: Bergen University College. Hoch, M. y Dreyfus, T. (2005). Students’ difficulties with applying a familiar formula in an unfamiliar context. En H. L. Chick y J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 145-152). Melbourne, Australia: University of Melbourne. Hoch, M. y Dreyfus, T. (2006). Structure sense versus manipulation skills: an unexpected result. En J. Novotná, H. Moraová, M. Krátká y N. Stehlíková (Eds.), Proceedings of the 30th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 305-312). Praga, República Checa: Faculty of Education, Charles University in Prague. Hotz, H. G. (1918). First-year algebra scales. Contributions to education, 90. Kaput, J. (1998). Teaching and learning a new algebra with understanding. Dartmouth, MA: National Center for Improving Student Learning and Achievement in Mathematics and Science. Kaput, J. (1999). Teaching and learning a new algebra. En E. Fennema y T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Lawrence Erlbaum Associates Kaput, J. (2000). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. Dartmouth, MA: National Center for Improving Student Learning and Achievement in Mathematics and Science. Kaput, J., Carraher, D. W. y Blanton, M. L. (2008). Algebra in the early grades. Londres, Reino Unido: Routlege. Kieran, C. (1989). The early learning of algebra: A structural perspective. En S. Wanger y C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Vol. 4, pp. 33–59). Reston, VA: Lawrence Erlbaum Associates y NCTM. Kieran, C. (1990). Cognitive processes involved in learning school algebra. En P. Nesher y J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 96-112). New York, NY: Cambridge University Press. Kieran, C. (1991). A procedural–structural perspective on algebra research. En F. Furinghetti (Ed), Proceedings of the Fifteenth International Conference for the Psychology of Mathematics Education (Vol. 2, pp. 245-253). Assisi, Italia: PME Program Committee. Kieran, C. (1992). The learning and teaching of school algebra. En D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). Reston, VA: National Council of Teachers of Mathematics. Kieran, C. (1996). The changing face of school algebra. En C. Alsina, J. Álvarez, B. Hodgson, C. Laborde y A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271-290). Sevilla, España: S.A.E.M. Thales Kieran, C. (2006). Research on the learning and teaching of algebra. A broadening of sources of meaning. En A. Gutiérrez y P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 11-49). Róterdan, Países Bajos: Sense Publishers. Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–62). Charlotte, NC: Information Age Publishing. Kilpatrick, J., Swafford, J. O. y Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy. Kirshner‚ D. (1987). Linguistic analysis of symbolic elementary algebra. Tesis doctoral‚ University of British Columbia, Canada. Kirshner, D. (1989). The visual syntax of algebra. Journal for Research in Mathematics Education, 20(3), 274-287. Kirshner, D. y Awtry, T. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35(4), 224–257. Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A. y Stephens, A. C. (2005). Middle School Students’ understanding of core algebraic concepts: equivalence & variable. Zentralblatt für Didaktik der Mathematik [International Reviews on Mathematics Education], 37(1), 68-76. Koedinger, K. R. y Nathan, M. J. (2004). The real story behind story problems: effects of representations on quantitative reasoning. Journal of the Learning Sciences, 13(2), 129-164. Koehler, J. (2002). Algebraic reasoning in the elementary grades: Developing an understanding of the equal sign as a relational symbol. Tesis de máster no publicada, Universidad de Wisconsin–Madison, Wisconsin. Liebenberg, R., Sasman, M. y Olivier, A. (1999, Julio). From numerical equivalence to algebraic equivalence. Mathematics learning and teaching initiative (MALATI). Presentado en el V congreso anual de la Asociación de Educación Matemática de Sur África (AMESA), Puerto Elizabeth. Descargado el 15 de Febrero de 2005 de http://www.wcape.school.za/malati/Files/Structure992.pdf. Linchevski, L. y Herscovics, D. (1994). Cognitives obstacles in pre-algebra. En J. P. Ponte y J. F. Martos (Eds), Proceedings of the 18th International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 176-183). Lisboa: Universidad de Lisboa. Linchevski, L. y Livneh, D. (1999). Structure sense: the relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173-196. Linchevski, L. y Livneh, D. (2002). The competition between numbers and structure: Why expressions with identical algebraic structures trigger different interpretations. Focus on Learning Problems in Mathematic, 24(2), 20-35. Lins, R. y Kaput, J. (2004). The early development of algebraic reasoning: the current state of the field. En K. Stacey, H. Chick y M. Kendal (Eds.), The teaching and learning of algebra. The 12th ICMI Study (pp. 47-70). Norwell, MA: Kluwer Academic Publishers. Ma, L. (1999/2010). Conocimiento y enseñanza de las matemáticas elementales. La comprensión de las matemáticas fundamentales que tienen los profesores en China y los EE.UU. (Trad. Paula Micheli). Santiago de Chile: Academia Chilena de Ciencias. MacGregor, M. (1996). Aspectos curriculares en las materias aritmética y álgebra. UNO Revista de Didáctica de las Matemáticas, 9, 65-69. MacGregor, M. y Stacey, K. (1997). Students´ understanding of algebraic notation: 11-15. Educational studies in mathematics, 33, 1-19. Mason, J. (1996). Expressing generality and roots of algebra. En N. Bednarz, C. Kieran y L. Lee (Eds.), Approaches to algebra. Perspectives for research and teaching (pp. 65-86). Londres: Kluwer Academic Publishers. Mason, J., Drury, H. y Bills, E. (2007). Explorations in the zone of proximal awareness. En J. Watson y K. Beswick (Eds.), Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 42-58). Adelaida, Australia: MERGA. Mason, J., Graham, A. y Johnston-Wilder, S. (2005). Developing thinking in algebra. Londres, Reino Unido: The Open University. Molina, M. (2006). Desarrollo de Pensamiento Relacional y Comprensión del Signo igual por Alumnos de Tercero de Educación Primaria. Tesis doctoral, Universidad de Granada, Granada. Molina, M. (2009). Una propuesta de cambio curricular: integración del pensamiento algebraico en educación primaria. PNA, 3(3), 135-156. Molina, M. (2010). Una visión estructural del trabajo con expresiones aritméticas y algebraicas. Suma, 65, 7-15. Molina, M. y Ambrose, R. (2008). From an operational to a relational conception of the equal sign. Thirds graders’ developing algebraic thinking. Focus on Learning Problems in Mathematics, 30(1), 61–80. Molina, M., Castro, E. y Castro, E. (2009). Elementary students´ understanding of the equal sign in number sentences. Electronic Journal of Research in Educational, 17, 7(1), 341-368. Molina, M., Castro, E., Molina, J. L. y Castro, E. (2011). Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza. Enseñanza de las Ciencias, 29(1), 75–88. Molina, M. y Mason, J. (2009). Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic. Canadian Journal of Science, Mathematics and Technology Education, 9(4), 224-242. Nathan, M. J. y Koedinger, K. R. (2000). Teachers' and researchers' beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168-190. Novotná, J. y Hoch, M. (2008). How structure sense for algebraic expression or equations is related to structure sense for abstract algebra. Mathematics Education Research Journal, 20(2), 93-104 Palarea, M. M. (1998). La adquisición del lenguaje algebraico y la detención de errores comunes cometidos en álgebra por los alumnos de 12 a 14 años. Tesis doctoral. Universidad de la Laguna, Tenerife. Consultado el 10 de febrero de 2011 en http://www.colombiaaprende.edu.co/html/mediateca/1607/articles-106509_archivo.pdf Peltier, M. (2003). Problemas aritméticos. Articulación, significados y procedimiento de resolución. Educación Matemática, 15(3), 29-55. Piccioto, H. (1998). Operation sense, tool–based pedagogy, curricular breadth: A proposal. Descargado el 20 de Diciembre de 2005 de http://www.picciotto.org /math–ed/early-math/early. html Pirie, S. y Martin, L. (1997). The equation, the whole equation and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics, 34(2), 159-181. Reeve, W. D. (1926). A diagnostic study of the teaching problems in high school mathematics. Boston, MA: Ginn. Resnick, L. B., Bill, V. y Lesgold, S. (1992). Development of thinking abilities in arithmetic class. En A. Demetriou, M. Shayer y A. Efklides (Eds.), Neo-piagetian theories of cognitive development: Implications and applications for education (pp. 210-230). Londres: Routledge. Rodríguez-Domingo, S. (2011). Traducción de enunciados algebraicos entre los sistemas de representación verbal y simbólico por estudiantes de secundaria. Trabajo de Fin de Máster, Universidad de Granada, Granada. Disponible en http://funes.uniandes.edu.co/1751/ Rodríguez-Domingo, S., Molina, M., Cañadas, M. C. y Castro, E. (2011). Errores en la traducción de enunciados algebraicos en la construcción de un dominó algebraico. Comunicación presentada en la reunión del grupo PNA dentro del XV seminario anual de la Sociedad Española de Investigación en Educación Matemática (SEIEM), Septiembre de 2011, Ciudad Real. Disponible en http://funes.uniandes.edu.co/1887/ Rojano, T. (1994). La matemática escolar como lenguaje. Nuevas perspectivas de investigación y enseñanza. Enseñanza de las ciencias, 12(l), 45-56. Ruano, R. M., Socas, M. M. y Palarea, M. M. (2008). Análisis y clasificación de errores cometidos por alumnos de secundaria en los procesos de sustitución formal, generalización y modelización en álgebra. PNA, 2(2), 61-74. Schifter, D. (1999). Reasoning about operations. Early algebraic thinking in grades K–6. En L. V. Stiff y F. R. Curcio (Eds.), Developing mathematical reasoning in grades K–12. NCTM Yearbook (pp. 62-81). Reston, VA: NCTM. Schliemann A. D., Carraher, D. W. y Brizuela, B. M. (2007). Bringing out the algebraic caracter of arithmetic. Londres: Lawrence Erlbaum Associates. Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36. Sfard, A. y Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26(2-3), 191-228 Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9-15. Socas, M. (1997). Dificultades, obstáculos y errores en el aprendizaje de las matemáticas en la educación secundaria. En Rico, L. (Eds.), La educación matemática en la enseñanza secundaria (pp. 125-154). Barcelona: Horsori. Stacey, K. y MacGregor, M. (2001) Curriculum Reform and Approaches to Algebra. En R. Sutherland, T. Rojano, A. Bell y R. Lins (Eds.), Perspectives on School Algebra (pp. 141-153). Dordrecht, Los Países Bajos: Kluwer Academic Publishers. Steinberg, R. M., Sleeman, D. H. y Ktorza, D. (1990). Algebra students’ knowledge of equivalence of equations. Journal for Research in Mathematics Education, 22(2), 112-121. Stephens, M. (2007). Students' emerging algebraic thinking in primary and middle school years. En J. Watson y K. Beswick (Eds.), Proceedings of the 30th Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 678-687). Adelaide, Australia: MERGA. Subramaniam, K. (2004, Julio). Naming practices that support reasoning about and with expressions. Presentado en the 10th International Congress on Mathematical Education, Copenhagen, Denmark. Sutherland, R. (2002). A comparative study of algebra curricula. Report prepared for the Qualifications and Curriculum Authority. Londres: QCA. Sutherland, R. (2008). A dramatic shift of attention: From arithmetic to algebraic thinking. En J. Kaput, D. Carraher y M. Blanton (Eds.), Algebra in the early grades. Mahwah, NJ: Lawrence Erlbaum Associates. Sutherland, R., Rojano, T., Bell, A. y Lins, R. (Eds.) (2001). Perspectives on school algebra. Dordrecht, Los Países Bajos: Kluwer Academic Publishers. Tall, D. y Thomas, M. (1991). Encouraging versatile thinking in algebra using the computer. Education Studies in Mathematics, 22, 125-147. Tall, D., Thomas, M., Davis, G., Gray E. y Simpson, A. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behavior, 18(2), 1-19. Thompson, P. y Thompson, A. (1987). Computer presentations of structure in algebra. En J. Bergeron, N. Herscovics, y C. Kieran (Eds.), Proceedings of the 11th annual meeting of the International Group for the Psychology of Mathematics Education (Vol. 1, 248-254). Montreal, Canadá: PME. Disponible a 4/5/2012 en http://pat-thompson.net/PDFversions/1987StrucInAlg.pdf Thorndike, E. L., Coob, M. V., Orleans, J. S., Symonds, P. M., Wald, E. y Woodyard E. (1923). The psychology of algebra. New York, NY: Macmillan. Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. En A. Coxford (Ed.), The ideas of algebra K–12 (pp. 8-19). Reston, VA: National Council of Teachers of Mathematics. Usiskin, Z. (1995). Why is algebra important to learn? American educator, 19(1), 30-37 Vega-Castro, D. C. (2010). Sentido estructural manifestado por alumnos de 1º de bachillerato en tareas que involucran igualdades notables. Trabajo fin de máster, Universidad de Granada, Granada. Vega-Castro, D. C., Molina, M. y Castro, E. (2011). Estudio exploratorio sobre el sentido estructural en tareas de simplificación de fracciones algebraicas. En M. Marín, G. Fernández y J. Blanco (Eds.), Investigación en educación matemática XV (pp. 575-586). Ciudad Real: Sociedad Española de Investigación en Educación Matemática. Vega-Castro, D. C., Molina, M. y Castro, E. (2012). Reproduction of algebraic structures by 16-18 year old students. Comunicación aceptada para su presentación en el 12th International Congress on Mathematical Education a celebrarse en Seúl del 8 al 14 de Julio de 2012. Vega-Castro, D. C., Molina, M. y Castro, E. (en prensa). Sentido estructural de estudiantes de Bachillerato en tareas de simplificación de fracciones algebraicas que involucran igualdades notables. Relime. Vergnaud, G. (1988). Long terme et court terme dans l’apprentissage de l’algebre. En C. Laborde (Ed.), Actes du premier colloque franco-allemand de didactique des mathematiques et de l’informatique (pp. 189-199). Paris: La Pensée Sauvage. Vergnaud, G. (1989). L’obstacle des nombres négatifs et l’introduction á l’algébre. Construction des savoirs. Colloque International Obstacle Epistémologique et conflict Socio – cognitif, CIRADE, Montreal. Vergnaud, G. (1997). The nature of mathematical concepts. En T. Nuñes y P. Bryant (Eds.), Learning and teaching mathematics – an international perspective (pp. 5-28). East Sussex, Reino Unido: Psychology Press. Warren, E. (2001). Algebraic understanding and the importance of operation sense. En M. Heuvel–Penhuizen (Ed.), Proceedings of the 25th International Group for the Psychology of Mathematics Education (Vol. 4, pp. 399-406). Utrecht, Los Países Bajos: Freudenthal Institute. Warren, E. (2004). Generalizing arithmetic: supporting the process in the early years. En M. Johnsen y A. Berit (Eds.), Proceedings of the 28th International Group for the Psychology of Mathematics Education (Vol. 4, pp. 417-424). Bergen, Noruega: Bergen University College. Wagner, S. y Kieran, C. (1989). Research issues in the learning and teaching of algebra. Reston, VA: National Council of Teachers of Mathematics. Wagner, S. y Parker, S. (1999). Advancing algebra. En B. Moses (Ed.), Algebraic thinking, grades k-12. Readings from NCTM´s school-based journals and other publications (pp. 328-340). Reston, VA: National Council of Teachers of Mathematics. Wagner, S., Rachlin, S. L. y Jensen, R. J. (1984). Algebra learning project: Final report. Atenas: Department of Mathematics, University of Georgia. Wheeler, D. (l989). Contexts for research on the teaching and learning of algebra. En S. Wagner, y C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 278–287). Reston, VA: Lawrence Erlbaum Associates.
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