Keywords
cognition
metacognition
problem solving
How to Cite
Abstract
This paper presents the results of a phenomenological study about mathematical problem solving. Eight pre-service mathematics teachers participated: six were studying to become teachers at elementary school level —4th to 6th grades— and two at high school —7th to 12th grades—. The data was obtained through long interviews, thinking out loud problem solving sessions and retrospective interviews that took place immediately after the problem solving sessions. The objective of the long interview was to determine the participants‘ beliefs and declarative knowledge about this topic. The objective of the problem solving sessions was to determine the type of representation, strategies, and control processes that the participants use when solving problems. During the retrospective interview, the participants had the opportunity to reflect about their performance. These techniques allowed the investigators to contrast the beliefs of the participants against their execution.
How to cite:
Hernández-Rodríguez, O., & Villafañe-Cepeda, W. (2009). Creencias de los candidatos a maestros sobre la solución de problemas en matemáticas. Cuaderno de Investigación en la Educación, 24, 165-181. Retrieved from https://revistas.upr.edu/index.php/educacion/article/view/13554
References
Ball, D. L. (1988). Understanding to teach mathematics. For the learning of mathematics, 8 (1), 40–48.
Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449–467.
Cadenas, R. (2007). Carencias, dificultades y errores en los conocimientos matemáticos en alumnos del primer semestre de la escuela de educación de la Universidad de los Andes. ORBIS, Revista Científica Ciencias Humanas, 2(6), 68–84.
Chapman, O. (2005). Constructing pedagogical knowledge of problem solving: Preservice mathematics teacher. 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. 2 (pp.225 – 232). Melbourne: PME.
Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers‘ practices. Educational Studies in Mathematics, 52, 243–270.
De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner, & R. C. Calfee(Eds.), Handbook of Educational Psychology (pp. 491-549). New York: Macmillan.
Departamento de Educación (2007). Estándares de contenido y expectativas de grado. San Juan, P.R.: Autor.
Departamento de Educación (2003). Marco curricular del programa de matemáticas. San Juan, P.R.: Autor.
Departamento deEducación de Puerto Rico (2000). Estándares: Programa de matemáticas. San Juan, P.R.: Autor.
Feiman-Memser, S., McDiarmid, W., Melnick, S., and Parker, M. (1987). Changing beginning teachers‘conceptions: A description of an introductory teacher education course. Paper presented at the annual meeting of the American Education Research Association. Washington,D.C.
Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. Resnick (Ed.), The nature of intelligence (pp. 231-236). Hillsdale, NJ: Erlbaum.
Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163-176.
Greeno, J. G., Collins, A.M., & Resnick, L. B. (1996). Cognition and learning. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 15-46). New York:Macmillan Library Reference.
Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30, 229-260.
Green, T. F. (1971). The activities of teaching. New York, NY: McGraw-Hill Book.
Grows, D., & Good, T. L. (2002). Issues in problem-solving instruction. In D. L. Chambers (Ed.), Putting research into practice in the elementary grades: Readings from Journals of the National Council of Teachers of Mathematics (pp. 60-62). Reston, VA: NCTM.
Hernández Rodríguez, O. (2002). Procesos cognoscitivos y metacognoscitivos en estudiantes universitarios puertorriqueños en la solución de problemas matemáticos no típicos: Disertación doctoral no publicada, Universidad de Puerto Rico, Río Piedras, Puerto Rico.
Kulik, S. y Rudnick, J. (1980). Problem solving: A handbook for teachers. Boston, MA: Allyn and Bacon.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 25(1), 29-63.
Leikin, R. (2003). Problem-solving preferences of mathematics teachers: Focusing on symmetry. Journal of Mathematics Teacher Education, 6, 297–329.
Leonard, J., y Joergensen, P. (2002). Empowering all elementary preservice teachers to teach children mathematics. (ERIC Document Reproduction Service No. ED469957).
Lester, F. K., Jr. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25 (6), 660-675.
Liljedahl, P. (2005). Aha!: The effect and affect of mathematics discovery on undergraduate mathematics students. International Journal of Mathematics Education Science and Technology, 36(2/3), 219-236.
Liljedahl, P., Rolka, K., and Rösken, B. (2007). Affecting affect: The reeducation of preservice tearchers‘ beliefs about mathematics and mathematics learning and teaching. In G. W. Martin, M. E. Strutchens, and P. C.Elliott (Eds.), The learning om athematics (pp. 319-330). Reston, VA:NCTM.
Maqsud, M. (1997). Effects of metacognitive skills and nonverbal ability on academic achievement of high school pupils. Educational Psychology, 17, 387-398.
Mewborn, D. S.,& Cross, D. I. (2007). Mathematics teachers‘ beliefs about mathematics and links to students‘ learning. In W. G. Martin, M. E. Strutchens, & P. C. Elliot (Eds.), The learning of mathematics (pp. 259-269). Reston, VA: NCTM.
National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics of the 1980's. Reston, VA: Author.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation: Standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
Santos Trigo, M. L. (1995). ¿Qué significa elaprender matemáticas? Una experienciacon estudiantes de cálculo. Educación Matemática, 7(1), 46-61.
Schoenfeld, A. H. (1987). What‘s all thefuss about metacognition? In A. H.Schoenfeld (Ed.), Cognitive science and mathematics education (pp.189-215). New Jersey: Erlbaum.
Schoenfeld, A.H. (1989). Explorations of students‘ mathematical beliefand behavior. Journal for Research in Mathematics Education, 20, 338-355.
Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition and sensemaking in mathematics. In D. A. Grouws(Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). NY: Macmillan.
Swanson, H. L. (1990). Influence of metacognitive knowledge and aptitude on problem solving. Journal of Educational Psychology, 82, 306-314.
Swanson, H. L.(1992). The relationship between metacognition and problem solving in gifted children. Roeper Review, 15(1), 43-49.
Törner, G., & Grigutsch, S. (1994). Mathematics Weltbilder bei studienanfanger-eine erhebung. Journal fur Mathematikdidaktik,15(3/4), 211-252.
Van Dooren, W., Verschaffel, L., & Onghena, P. (2003). Preservice teachers' preferred strategies for solving Arithmetic and Algebra word problems. Journal of Mathematics Teachers Education, 6(1), 27 - 52.
The contents published in the Puerto Rico Journal of Education is freely distributed under open access practices, in accordance with the Creative Commons license, Attribution-NonCommercial 4.0 International (CC BY-NC 4.0). Through these principles, the journal and its authors allow readers to access, reproduce and share articles in full text. Users should give credit to authors in a reasonable way without suggesting they have their support. Under no circumstances, readers may make use of the contents for commercial purposes. The authors retain copyright on their works.