Los procesos de pensamiento de los estudiantes al usar los manipulativos Algeblocks y la Politabla Dreyfous en álgebra elemental
Portada Pedagogía, 37(1)
PDF

Palabras clave

manipulativos
álgebra
desarrollo cognoscitivo
representaciones mentales de conceptos
factorización de positivos

Cómo citar

Villafañe-Cepeda, W., & Fernández, L. M. (2021). Los procesos de pensamiento de los estudiantes al usar los manipulativos Algeblocks y la Politabla Dreyfous en álgebra elemental. Revista De Educación De Puerto Rico (REduca), 37(1), 99–122. Recuperado a partir de https://revistas.upr.edu/index.php/educacion/article/view/19303

Resumen

Cómo citar:

Villafañe-Cepeda, W. & Fernández, L. M. (2004). Los procesos de pensamiento de los estudiantes al usar los manipulativos Algeblocks y la Politabla Dreyfous en álgebra elemental. Pedagogía, 37(1), 99-122.

PDF

Citas

Alfred, S. A. (1999). An analysis of students‘ cognitive strategies employed in a learning experience from chaos theory (Disertación doctoral, Rutgers, The State University of New Jersey, 1999).

Anthony, G. (1996). Active learning in a constructivist framework. Educational Studies in Mathematics, 31, 349-369.

Barb, C. M. (1997). An investigation of the development of mathematical beliefs and problem-solving processes of preservice elementary teachers in a constructivist environment (Disertación doctoral, Kent State University, 1997). Dissertation Abstract lnternational, 58, A03.

Baroody, A. J. (1989). Manipulatives don't come with guarantees. Arithmetic Teacher, 37(2), 4.

Baroody, A. J., y Ginsburg, H. P. (1990). Children's mathematical learning: A cognitive view. En R. B. Davis, C. A. Maher, y N. Noddings (Eds.), Constructivist view on the teaching and learning of mathematics, Monograph No. 4 of the Journal for Research in Mathematics Education (pp. 51-64). Reston, VA: National Council of Teachers of Mathematics.

Benítez Cotto, A. (1997). Investigando y aprendiendo con manipulativos. En Z. Orengo Rohena, y A. Aponte Moreno (Eds.), Investigación en matemática educativa en Puerto Rico: Tres años del instituto de matemáticas (pp. 303-307). San Juan, PR: UPR.

Berman, B., y Friederwitzer, F. (1989). Algebra can be elementary... when it's concrete. Arithmetic Teacher, 36(8), 21-24.

Bermúdez, N. M. (1997). Uso de manipulativos y tecnología para motivar a los estudiantes en geometría, disminuir el ausentismo y aumentar el aprovechamiento académico. En Z. Orengo Rohena, y A. Aponte Moreno (Eds.), Investigación en matemática educativa en Puerto Rico: Tres años del instituto de matemáticas (pp. 258-260). San Juan, PR: UPR.

Blais, D. M. (1988). Constructivism: A theoretical revolution for algebra. Mathematics Teacher, 81, 624-631.

Bogdan, R. C., y Biklen, S. K. (1998). Qualitative research for education: An introduction to theory and methods. Boston, MA: Allyn y Bacon.

Bohan, H. J., y Shawaker, P. B. (1994). Using manipulatives effectively: A drive down rounding road. Arithmetic Teacher, 41, 246- 248.

Bright, G. W. (1986). Using manipulatives. Arithmetic Teacher, 33(6), 4.

Brown, C. A., y Smith, M.S. (1997). Supporting the development of mathematical pedagogy. The Mathematics Teacher, 90, 138- 143.

Bums, M. (1996). How to make the most of math manipulatives. Instructor, 105(7), 45 -51.

Burton, G. M. (1992). Young children's choices of manipulatives and strategies for solving whole number division problems. Focus on Learning Problems in Mathematics, 14(2), 2-17.

Bush, J. A. (1998). An exploratory study of two students' understanding of group theory concepts prerequisite to the concept of quotient group (Disertación doctoral, University of Northem Colorado, 1998).

Capps, L. R., y Pickreign, J. (1993). Language connections in mathematics: A critical part of mathematics instruction. Arithmetic Teacher, 41(1), 8-12.

Chen, S. H. (1992). An examination of the relationship between achievement in solving process problems and cognitive levels of development in third-grade students (Tesis de maestría, San José State University, 1992). Master Abstract International, 31, 04.

Chester, J. (1991). Math manipulatives uses and math achievement of third-grade students. (ERIC Document Reproduction Service No. ED339591).

Cobb, P. (1995). Cultural tools and mathematical learning: A case study. Journal for Research in Mathematics Education, 26, 362-385.

Colón Rodríguez, M. (2000). El efecto del uso de los manipulativos en el aprovechamiento de estudiantes del nivel intermedio en la solución de ecuaciones lineales en una variable. Tesis de maestría no publicada, Universidad de Puerto Rico, Río Piedras, Puerto Rico.

Colón Soto, S. (1996). Efectividad del uso del laboratorio con manipulativos para minimizar las destrezas rezagadas y actitudes. Investigación no publicada, Universidad de Puerto Rico en Río Piedras.

Creswell, J. W. (1994). Research design: Qualitative and quantitative approaches. Thousand Oaks, CA: Sage.

Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, CA: Sage.

Davis, R. B. (1989). Research studies in how humans think about algebra. En S. Wagner, y C. Kieran (Eds.), Research agenda for mathematics education: Research issues in the learning and teaching of algebra: Vol. 4 (pp. 266-274). Reston, VA: National Council of Teachers of Mathematics y Lawrence Erlbaum Associate.

Davis, R. B., y Maher, C. A. (1990). What do we do when we "do mathematics"? En R. B. Davis, C. A. Maher, y N. Noddings (Eds.), Constructivist view on the teaching and learning of mathematics, Monograph No. 4 of the Journal for Research in Mathematics Education (pp. 65-78). Reston, VA: National Council of Teachers of Mathematics.

Davis, R. B., Maher, C. A., y Noddings, N. (1990). Suggestions for the improvement of mathematics education. En R. B. Davis, C. A. Maher, y N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics, Monograph No. 4 of the Journal for Research in Mathematics Education (pp. 187-191). Reston, VA: National Council of Teachers of Mathematics.

Days, H. C., Wheatley, G. H., y Kulm, G. (1979). Problem structure, cognitive level, and problem-solving performance. Journal for Research in Mathematics Education, 10, 135-146.

Drew, C. J., Hardman, M. L., y Weaver Hart, A. (1996). Designing and conducting research: Inquiry in education and social science (2nd ed.). Boston, MA: Allyn and Bacon.

Edwards, T. G. (1994). Current reform efforts in mathematics education. (ERIC Document Reproduction Service No. ED372969).

Ernest, P. S. (1994, noviembre). Evaluation of the effectiveness and implementation of math manipulatives project. Conferencia presentada en la convención anual de la Mid-South Educational Research Association, Nashville, TN.

Fontana, A., y Frey, J. H. (2000). Interview: From structured questions to negotiated text. En N. K. Denzin y Y. S. Lincoln (Eds.), Handbook of qualitative research (2nd ed., pp. 645-672). Thousand Oaks, CA: Sage.

Foster, P. (1996). Observational researcher. En R. Sapsford y V. Jupp (Eds.), Data collection and analysis. (pp. 57-93). Thousand Oaks, CA: Sage.

Fraenkel, J. R., y Wallen, N. E. (1996). How to design and evaluate research in education (3rd ed.). New York: McGraw-Hill.

Gadanidis, G. (1994). Deconstructing constructivism. Mathematics Teacher, 87, 91 -97.

Gall, J. P., Gall, M. D., y Borg, W. R. (1999). Applying educational research: A practical guide (4th ed.). New York: Longman.

Goldsby, D. S. (1997). The effect of algebra tile use on the polynomial factoring ability of algebra I students. (Disertación doctoral, University of New Orleans, 1997). Dissertation Abstract International, 5 7, A08.

Greenes, C. (1995). Mathematics learning and knowing: A cognitive process. Journal of Education, 177 (1), 85-106.

Greeno, J. G., Collins, A. M., y Resnick, L. B. (1996). Cognition and learning. En D. C. Berliner, y R. C. Calfee (Eds.), Handbook of educational psychology (pp.15 -46). New York: Macmillan.

Hartshorn, R., y Boren, S. (1990). Experiential learning of mathematics: Using manipulatives. (ERIC Document Reproduction Service No. ED32 l 967).

Heddens, J. W. (1986). Bridging the gap between the concrete and the abstract. Arithmetic Teacher, 33(6), 14-17.

Hercovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. En S. Wagner, y C. Kieran (Eds.), Research agenda for mathematics education: Research issues in the learning and teaching of algebra: Vol. 4 (pp. 60- 86). Reston, VA: National Council of Teachers of Mathematics y Lawrence Erlbaum Associate.

Hinzman, K. P. (1997). Use of the manipulatives in mathematics at the middle school level and their effects on students‘ grades and attitudes. Tesis de maestría no publicada, Universidad de Salem-Teikyo, West Virginia.

Howen, H. (1986). The role of manipulatives in learning mathematics. Insights into Open Education, 19(1), 2-11.

Hsieh, D. A. (1995). A comparison of the thinking processes of mathematically advanced and average students, age 10 to 11, engaged in mathematics problem-solving. (Disertación doctoral, University of Northern Colorado, 1995). Dissertation Abstract International, 57, A02.

Hynes, M. C. (1986). Selection criteria. Arithmetic Teacher, 33 (6), 11-13.

Inhelder, B. y Piaget, J. (1955). De la lógica del niño a la lógica del adolescente. Buenos Aires: Paidós.

Joyner, J. M. (1990). Using manipulatives successfully. Arithmetic Teacher, 38(2), 6-7.

Kennedy, L. M. (1986). A rationale. Arithmetic Teacher, 33(6), 6-7, 32.

Kerka, S. (1986). On second thought: Using new cognitive research in vocational education. (ERIC Document Reproduction Service No. ED272699).

Kerka, S. (1997). Constructivism, workplace learning, and vocational education. (ERIC Document Reproduction Service No. ED407573).

Land, W. A., y Edwards, K. (1994, noviembre). Teaching mathematics to attention deficit disorder students. Conferencia presentada en la convención anual de la Mid-South Educational Research Association, Nashville, TN.

Lapp, D. A. (1999). Multiple representation for pattern exploration with the graphing calculator and manipulatives. The Mathematics Teacher, 92, 109-113.

Leinebach, M., y Raymond, A. M. (1996, julio). A two-year collaborative action research study on the effects of a "hands-on" approach to learning algebra. Conferencia presentada en la convención anual de la North American Chapter of the International Group for the Psychology of Mathematics Education, Panama City, FL.

Lester, F. K., Garofalo, J., y Kroll, D. (1989). The role of metacognition in mathematical problem solving: A study of two grade seven classes. A Final report of the Mathematics Education Development Center, Indiana University. (ERIC Document Reproduction Service No. ED3 l 4255).

Marquis, J. (1988). Common mistakes in algebra. En A. F. Coxford y A. P. Shulte (Eds.), The ideas of algebra, K -12, 1988 Yearbook (pp.204- 205). Reston, VA: National Council of Teachers of Mathematics.

Martelly, D. I. (1998). Effects of using manipulative materials to teach remedial algebra to community college students on achievement and altitudes toward mathematics (Disertación doctoral, Florida Intemational University, 1998).

Martínez López, M. (1997). El impacto de los manipulativos y la tecnología en la enseñanza del álgebra. En Z. Orengo Rohena, y A. Aponte Moreno (Eds.), Investigación en matemática educativa en Puerto Rico: Tres años del instituto de matemáticas (pp. 308-311). San Juan, PR: UPR.

Matos Quintana, E. I. (1997). La efectividad del uso de manipulativos, tecnología y aprendizaje cooperativo en el álgebra. En Z. Orengo Rohena, y A. Aponte Moreno (Eds.), Investigación en matemática educativa en Puerto Rico: Tres años del instituto de matemáticas (pp. 261 -279). San Juan, PR: UPR.

McClung, L. W. (1998). A study on the use of manipulatives and their effect on student achievement in a high school algebra I class. Tesis de maestría no publicada, Universidad de Salem-Teikyo, West Virginia.

Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco, CA: Jossey-Bass.

Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco, CA: Jossey-Bass.

Mertz, D. L. (1990). Cognitive analysis of individual differences in arithmetic performance by postsecondary students (Disertación doctoral, University of California Santa Barbara, 1990). Dissertation Abstract International, 51, Al2.

Moser, J. M. (1986). Curricular issues. Arithmetic Teacher, 33(6), 8-10.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Nickerson, R. S., Perkins, D.N., y Smith, E. E. (1990). Enseñar a pensar: Aspectos de la aptitud intelectual (2nd ed.). Barcelona, España: Paidós.

Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Beverly Hills, CA: Sage.

Peterson, P. L., y Knapp, N. F. (1998). Inventing and reinventing ideas: Constructivist teaching and learning mathematics. En G. Cawelti (Ed.), Challenges and achievements of American education. The 1998 ASCD Yearbook (pp. 134-157). Alexandria, VA: Association for Supervision and Curriculum Development.

Phillips, D. C., y Soltis, J. F. (1985). Perspectives on learning. New York: Teachers College.

Piaget, J. (1964). Development and learning. En R. E. Ripple, y V. N. Rockcastle (Eds.), Piaget rediscovered (pp. 25-33). Ithaca, NY: Cornell University.

Piaget, J. (1972). Psychology and epistemology: Towards a theory of knowledge. Harmonsworth, England: Penguin Books.

Piaget, J. (1973). To understand is to invent. New York: Grossman.

Piaget, J. (1977). The role of action in the development of thinking. En W. F. Overton, y J. McCarthy Gallagher (Eds.), Knowledge and development: Advances in research and theory (pp. 17-42). New York: Plenum.

Pogrow, S. (1994). Helping students who "just don't understand". Educational Leadership, 52(3), 62- 66.

Rivera Orsini, Y. (1996). Efectividad del uso de los manipulativos en álgebra elemental para estudiantes con rezago académico. Investigación no publicada, Universidad de Puerto Rico en Río Piedras.

Roberts, V. A. (1990). Relationships among processing behavior mode, cognitive development level and mathematics achievement in black metropolitan high school students (Disertación doctoral, Howard University, 1990). Dissertation Abstract International, 51, B 10.

Rodríguez, J. (1998). Informe final del Proyecto Manipulativos y Tecnología para un Aprendizaje Activo (Ma Te A2). San Juan, PR: Author.

Rosa Carrasquillo, C. L. (1997). La efectividad del uso de manipulativos, la computadora y el aprendizaje cooperativo en el aprovechamiento académico e interés del estudiante en la unidad de fracciones. En Z. Orengo Rohena, y A. Aponte Moreno (Eds.), Investigación en matemática educativa en Puerto Rico: Tres años del instituto de matemáticas (pp. 295-302). San Juan, PR: UPR.

Santiago, I. I. (1997). Uso de manipulativos en el desarrollo de conceptos de álgebra. En Z. Orengo Rohena, y A. Aponte Moreno (Eds. ), Investigación en matemática educativa en Puerto Rico: Tres años del instituto de matemáticas (pp. 63-70). San Juan, PR: UPR.

Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, Fl: Academic Press.

Schoenfeld, A. H. (1987). Cognitive science and mathematics education: An overview. En A. H. Schoenfeld (Eds.), Cognitive science and mathematics education (pp. 1-31). Hillsdale, NJ: Lawrence Erlbaum.

Sharp, J. M. (1995, octubre). Results of using algebra tiles as meaningful representation of algebra concepts. Conferencia presentada en la convención anual de Mid-Western Educational Research Association, Chicago, IL.

Sherman, H. W. (1990). A comparison of three methods of teaching rational number concepts to preservice teachers. Educational Research Quarterly, 14(4), 48-55.

Sloan, S. C. (1993). The effect of cognitive processes on the learning of mathematics by pre-service elementary teachers (Disertación doctoral, University of Minnesota, 1993). DissertationAbstract International, 54, A05.

Sobol A. J. (1998). A formative and summative evaluation study classroom interactions and student/teacher effects when implementing algebra tile manipulatives with junior high school. (Disertación doctoral, St. John's University, 1998).

Sowell, E. J. (1989). Effects of manipulatives materials in mathematics instruction. Journal for Research in Mathematics Education, 20, 498- 505.

Stake, R. E. (2000). Case studies. En N. K. Denzin y Y. S. Lincoln (Eds.), Handbook of qualitative research (2nd ed., pp. 435-454). Thousand Oaks, CA: Sage.

Steele, D. F. (1993, abril). What mathematics students can teach us about educational engagement: Lessons from the middle school. Conferencia presentada en la convención anual de la American Educational Research Association, Atlanta, GA.

Steele, D. F. (1994, abril). Helping preservice teachers confront their conceptions about mathematics and mathematics teaching and learning. Conferencia presentada en la convención anual de la American Educational Research Association, New Orleans, LA.

Tang, E. P., y Ginsburg, H. P. (1999). Young children's mathematical reasoning: A psychological view. En LV. Stiff, y F. R. Curcio (Eds.), Developing mathematical reasoning in grades k-12: 1999 Yearbook (pp. 45-61).

Reston, VA: National Council of Teachers of Mathematics.

Thompson, G. J. (1986). An investigation of thought processes used by community college students solving verbal algebra problems (Disertación doctoral, Northern Arizona University, 1986).

Tooke, D. J. (1992). Why aren't manipulatives used in every middle school mathematics classroom? Middle School Journal, 24 (2), 61-62.

Tsao, P. D. (1995). Conceptual development for learning to solve linear equations in one variable (Disertación doctoral, University of Georgia, 1995). Dissertation Abstract International, 56, A 10.

Vockell, E. L., Asher, J. W. (1995). Educational research (2nd ed.). Englewood Cliffs, NJ: Merril.

Von Glasersfeld, E. (1990). An exposition of constructivism: Why some like it radical. En R. B. Davis, C. A. Maher, y N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 19-29). Reston, VA: National Council of Teachers of Mathematics.

Webb, N. L. (1979). Processes, conceptual knowledge, and mathematical problem-solving ability. Journal for Research in Mathematics Education, 10, 83-93.

Wiersma, W. (1995). Research methods in education: An introduction (6th ed.). Boston, MA: Allyn and Bacon.

Yin, R. K. (1993). Applications of case study research: Design and methods. Newbury Park, CA: Sage.

Yin, R. K. (1994). Case study research (2nd ed.). Thousand Oaks, CA: Sage.

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.

Descargas

Los datos de descargas todavía no están disponibles.