Preconcepciones de pendiente en estudiantes de Educación Secundaria

Martha Iris Rivera López, Crisólogo Dolores Flores

Resumen

En este artículo se reportan los resultados de una investigación cuyo objetivo fue identificar las preconcepciones de pendiente en estudiantes de Educación Secundaria. Se empleó una entrevista basada en tareas para la recolección de datos de 30 estudiantes de 10.º grado y el método de análisis temático para su respectivo análisis. Los resultados muestran que las preconcepciones de pendiente que manifiestan los estudiantes son la pendiente como la longitud de un segmento de recta, un objeto, una propiedad física, el valor del ángulo, la intersección de la recta con los ejes asociada a una expresión algebraica y el cociente de los valores de las intersecciones en el eje x e y. Aunque algunos estudiantes declararon una primera experiencia con el concepto, este conocimiento tuvo una mínima influencia en sus procedimientos y justificaciones.

Palabras clave

Pendiente; Preconcepciones; Entrevista basada en tareas; Análisis temático; Educación Secundaria

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Referencias

Abouchedid, K. y Nasser, R. (2000). The role of presentation and response format in understanding, preconceptions and alternative concepts in algebra problems. Obtenido de https://files.eric.ed.gov/fulltext/ED438174.pdf

Agudelo-Valderrama, C. y Martínez, D. (2016). In pursuit of a connected way of knowing: The case of one mathematics teacher. International Journal of Science and Mathematics Education, 14(4), 719-737.

Arias, M. (2000). Triangulación metodológica: sus principios, alcances y limitaciones. Investigación y Educación en Enfermería, 18(1), 13-26.

Ausubel, D. (1978). Psicología Educativa. Un punto de vista cognitivo. México: Trillas.

Batanero, C., Estepa, A., Godino, J. y Green, D. (1996). Intuitive strategies and preconceptions about association in contingency tables. Journal for Research in Mathematics Education, 27(2), 151-169.

Behar, R. y Ojeda, M. (2000). El proceso de aprendizaje de la estadística: ¿Qué puede estar fallando? Heurística, 10(1), 26-43.

Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. American Journal of Physics, 62(8), 750-762.

Biemans, H. y Simons, P. (1995). How to use preconceptions? The contact strategy dismantled. European Journal of Psychology of Education, 10(3), 243-259.

Billings, E. y Klanderman, D. (2000). Graphical representations of speed: obstacles preservice K‐8 teachers experience. School Science and Mathematics, 100(8), 440-450.

Birgin, O. (2012). Investigation of eighth-grade students’ understanding of the slope of the linear function. Bolema, 26(42a), 139-162. https://doi.org/10.1590/S0103-636X2012000100008

Braun, V. y Clarke, V. (2012). Thematic analysis. En H. Cooper (Ed.), Handbook of research methods in psychology (pp. 57-71). Washington (DC): American Psychological Association.

Bretones, A. (2003). Las preconcepciones del estudiante de profesorado: de la construcción y transmisión del conocimiento a la participación en el aula. Educar, 32(1), 25-54.

Bush, S. y Karp, K. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. The Journal of Mathematical Behavior, 32(3), 613-632. https://doi.org/10.1016/j.jmathb.2013.07.002

Byerley, C. y Thompson, P. (2017). Secondary mathematics teachers’ meanings for measure, slope, and rate of change. The Journal of Mathematical Behavior, 48(1), 168-193. https://doi.org/10.1016/j.jmathb.2017.09.003

Campanario, J. y Otero, J. (2000). Más allá de las ideas previas como dificultades de aprendizaje: las pautas de pensamiento, las concepciones epistemológicas y las estrategias metacognitivas de los alumnos de Ciencias. Enseñanza de las Ciencias, 18(2), 155-169.

Casey, S. y Nagle, C. (2016). Students’ use of slope conceptualizations when reasoning about the line of best fit. Educational Studies in Mathematics, 92(2), 163-177. https://doi.org/10.1007/s10649-015-9679-y

Cho, P. y Nagle, C. (2017). Procedural and conceptual difficulties with slope: An analysis of students’ mistakes on routine tasks. International Journal of Research in Education and Science, 3(1), 135-150.

Confrey, J. (1990). Chapter 1: A review of the research on student conceptions in mathematics, science and programming. Review of Research in Education, 16(1), 3-56.

Dolores, C., Alarcón, G. y Albarrán, D. (2002). Concepciones alternativas sobre las gráficas cartesianas del movimiento: el caso de la velocidad y la trayectoria. RELIME, 5(3), 225-250.

Dolores, C., García, J. y Gálvez, A. (2017). Estabilidad y cambio conceptual acerca de las razones de cambio en situación escolar. Educación Matemática, 29(2), 125-158. https://doi.org/10.24844/em2902.05

Dolores, C., Rivera, M. I. y García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematical Education in Science and Technology, 50(3), 369-389. https://doi.org/10.1080/0020739X.2018.1507050

Dolores, C., Rivera, M. I. y Moore‐Russo, D. (2020). Conceptualizations of slope in Mexican intended curriculum. School Science and Mathematics, 120(2), 104-115. https://doi.org/10.1111/ssm.12389

Dündar, S. (2015). Knowledge of mathematics teacher-candidates about the concept of slope. Journal of Theory and Practice in Education, 11(2), 673-693.

Goldin, G. (1997). Chapter 4: Observing Mathematical Problem Solving through Task-Based Interviews. Journal for Research in Mathematics Education. Monograph, 9, 40-177.

Hoffman, W. (2015). Concept image of slope: Understanding middle school mathematics teachers' perspective through task-based interviews (tesis doctoral). The University Of North Carolina At Charlotte.

Kambouri, M. (2016). Investigating early years teachers’ understanding and response to children's preconceptions. European Early Childhood Education Research Journal, 24(6), 907-927. https://doi.org/10.1080/1350293X.2014.970857

Kambouri, M., Briggs, M. y Cassidy, M. (2011). Children’s misconceptions and the teaching of early years science: A case study. Journal of Emergent Science, 2(2), 7-16.

Koichu, B. y Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65(3), 349-365.

Korpershoek, H., Kuyper, H., Bosker, R. y Van der Werf, G. (2013). Students’ preconceptions and perceptions of science-oriented studies. International Journal of Science Education, 35(14), 2356-2375. https://doi.org/10.1080/09500693.2012.679324

Lobato, J. y Thanheiser, E. (2002). Developing understanding of ratio-as-measure as a foundation for slope. En B. Litwiller y G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 162-175). Reston, VA: National Council of Teachers of Mathematics.

Mahmud, M. y Gutiérrez, O. (2010). Estrategia de enseñanza basada en el cambio conceptual para la transformación de ideas previas en el aprendizaje de las ciencias. Formación Universitaria, 3(1), 11-20. http://dx.doi.org/10.4067/S0718-50062010000100003

Matz, M. (1980). Towards a computational theory of algebraic competence. The Journal of Mathematical Behavior, 3, 93-166.

McDermott, L., Rosenquist, M. y Van Zee, E. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics, 55(6), 503-513.

Mhlolo, M. y Schafer, M. (2013). Consistencies far beyond chance: an analysis of learner preconceptions of reflective symmetry. South African Journal of Education, 33(2), 1-17. http://dx.doi.org/10.15700/saje.v33n2a686

Moore-Russo, D., Conner, A. y Rugg, K. (2011). Can slope be negative in 3-space? Studying concept image of slope through collective definition construction. Educational Studies in Mathematics, 76(1), 3-21. https://doi.org/10.1007/s10649-010-9277-y

Moschkovich, J. (1990). Students’ interpretations of linear equations and their graphs. En G. Booker, P. Cobb y T. de Mendicuti (Eds.), Proceedings of the 14th Annual Meeting of the International Group for the Psychology of Mathematics Education (pp. 109-116). México: PME-NA.

Mudaly, V. y Moore-Russo, D. (2011). South African teachers’ conceptualisations of gradient: A study of historically disadvantaged teachers in an Advanced Certificate in Education programmed. Pythagoras, 32(1), 27-33.

Nagle, C. y Moore-Russo, D. (2014). Slope across the curriculum: Principles and standards for school mathematics and common core state standards. Mathematics Educator, 23(2), 40-59.

Newton, X. y Poon, R. (2015). Pre-service STEM majors understanding of slope according to common core mathematics standards: An exploratory study. Global Journal of Human-Social Science Research, 15(7), 1-17.

Oyarbide, M. (2004). Estilos cognitivos, desarrollo operatorio y preconcepciones. Revista Internacional de Psicología, 5(1), 1-23.

Planinic, M., Milin-Sipus, Z., Katic, H., Susac, A. y Ivanjek, L. (2012). Comparison of student understanding of line graph slope in physics and mathematics. International Journal of Science and Mathematics Education, 10(6), 1393-1414. https://doi.org/10.1007/s10763-012-9344-1

Pozo, J. y Carretero, M. (1987). Del pensamiento formal a las concepciones espontáneas: ¿Qué cambia en la enseñanza de la ciencia? Infancia y Aprendizaje, 38, 35-52.

Rivera, M. I., Salgado, G. y Dolores, C. (2019). Explorando las Conceptualizaciones de la Pendiente en Estudiantes Universitarios. Bolema, 33(65), 1027-1046. http://dx.doi.org/10.1590/1980-4415v33n65a03

Rodríguez, P. (2017). Ideas previas de estudiantes de décimo grado respecto al concepto de ecosistemas. Enseñanza de las Ciencias, (Extra), 4157-4162.

Salgado, G., Rivera, M. I. y Dolores, C. (2019). Conceptualizaciones de pendiente: Contenido que enseñan los profesores del Bachillerato. UNIÓN-Revista Iberoamericana de Educación Matemática, 15(57), 41-56.

Simons, P. (1999). Transfer of learning: Paradoxes for learners. International Journal of Educational Research, 31(7), 577-589.

Sirotic, N. y Zaskis, R. (2007). Irrational numbers: The gap between formal and intuitive knowledge. Educational Studies in Mathematics, 65(1), 49-76. https://doi.org/10.1007/s10649-006-9041-5

Stanton, M. y Moore‐Russo, D. (2012). Conceptualizations of slope: A review of state standards. School Science and Mathematics, 112(5), 270-277. https://doi.org/10.1111/j.1949-8594.2012.00135.x

Stump, S. (1999). Secondary mathematics teachers’ knowledge of slope. Mathematics Education Research Journal, 11(2), 124-144. https://doi.org/10.1007/BF03217065

Stump, S. (2001). High school precalculus students’ understanding of slope as measure. School Science and Mathematics, 101(2), 81-89. https://doi.org/10.1111/j.1949-8594.2001.tb18009.x

Teuscher, D. y Reys, R. (2012). Rate of change: AP calculus students’ understandings and misconceptions after completing different curricular paths. School Science and Mathematics, 112(6), 359-376. https://doi.org/10.1111/j.1949-8594.2012.00150.x

Thacker, I. (2019). An embodied design for grounding the mathematics of slope in middle school students’ perceptions of steepness. Research in Mathematics Education, 1-25. https://doi.org/10.1080/14794802.2019.1692061

Tovar, J., Castillo, H. y Marín, M. (2007). Preconcepciones de estudiantes de la Pontificia Universidad Javeriana Cali sobre el curso de Estadística. Pensamiento Psicológico, 3(9), 61-78.

Wilhelm, J. y Confrey, J. (2003). Projecting rate of change in the context of motion onto the context of money. International Journal of Mathematical Education in Science and Technology, 34(6), 887-904. https://doi.org/10.1080/00207390310001606660

Yanik, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78(2), 231-260. https://doi.org/10.1007/s10649-011-9324-3

Yerushalmy, M. (1997). Designing representations: Reasoning about functions of two variables. Journal for Research in Mathematics Education, 28(4), 431-466.

Yip, D. (1998). Identification of misconceptions in novice biology teachers and remedial strategies for improving biology learning. International Journal of Science Education, 20(4), 461-477.https://doi.org/10.1080/0950069980200406

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