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Una nueva herramienta para evaluar la comprensión del cálculo confiando en la comprensión relacional e instrumental

  • Moosavi, Hojjat [1] ; Tehranian, Abolfazl [1] ; Doostie, Hossein [1] ; Shahvarani, Ahmad [1]
    1. [1] Islamic Azad University

      Islamic Azad University

      Irán

  • Localización: Educatio siglo XXI: Revista de la Facultad de Educación, ISSN 1699-2105, ISSN-e 1989-466X, Vol. 40, Nº 1, 2022, págs. 55-78
  • Idioma: español
  • DOI: 10.6018/educatio.432431
  • Títulos paralelos:
    • A New Tool for Assessing the Understanding of Calculus by Relying on Relational and Instrumental Understanding
  • Enlaces
  • Resumen
    • español

      Los cambios en los libros de matemáticas de la escuela secundaria en los últimos años han llevado a algunos cambios en el concepto de cálculo, y la mayoría de los estudiantes solían trabajar duro para memorizar en lugar de comprender. En los primeros años después de ingresar a la universidad, serán desafiados por los mismos conceptos y su aplicación en otras ciencias. La revisión de los estudios anteriores ha demostrado que hasta ahora no se ha desarrollado ningún instrumento de investigación para abordar tales desafíos. Luego, los investigadores del estudio desarrollaron y estandarizaron un instrumento. La población estaba compuesta por todos los estudiantes de primer año de pregrado de ingeniería y ciencias básicas de la Universidad de Teherán. Usando una técnica de muestreo intencional, se seleccionaron 162 estudiantes varones y mujeres. Todos los seleccionados habían pasado el curso de cálculo 1. Los investigadores consideraron algunos factores y desarrollaron un instrumento y finalmente lo validaron con base en esos componentes. Además, dado que no había herramientas disponibles para medir la comprensión relacional e instrumental de la derivada, se diseñaron y agregaron algunas preguntas sobre el concepto de definición de derivada al final del cuestionario. Finalmente, después de las investigaciones realizadas a través del análisis factorial exploratorio, se desarrolló e introdujo un instrumento de investigación para medir la comprensión del concepto de derivada y su comprensión instrumental y relacional.

    • English

      The changes in high school mathematics books in recent years have led to some changes in the concept of calculus, and majority of learners used to work hard on memorizing rather than understanding. In the early years after entering university, they will be challenged by the same concepts and their application in other sciences. Review of the previous studies have shown that no research instrument has been developed to address such challenges till now. Then, the researchers of the study developed and standardized an instrument. The population consisted of all first-year undergraduate students of engineering and basic sciences fields from of University in Tehran. Using purposeful sampling technique, 162 male and female students were selected. All of them selected had passed the course of calculus 1. The researchers considered some factors and developed an instrument and finally validated it based on those components. Moreover, since there were no available tools to measure the derivative’s relational and instrumental understanding, some questions regarding the concept of derivative definition were designed and added to the end of the questionnaire. Finally, after the investigations conducted through exploratory factor analysis, a research instrument was developed and introduced to measure the understanding of the concept of derivative and its instrumental and relational understanding.

  • Referencias bibliográficas
    • Aksoy, Y. (2007). The effect of computer algebra systems on the teaching of derivative concept. Ph.D. Thesis. Gazi University, Ankara.
    • Ayebo, A., Ukkelberg, S., & Assuah, C. (2017). Success in introductory calculus: The role of high school and pre-calculus preparation,...
    • Bahar, E. E., Rahman, A., & Minggi, I. (2012). Analisis Pemahaman Mahasiswa Terhadap Konsep Limit Fungsi di Satu Titik (Studi Kasus pada...
    • Balcı, M. (2012). Genel matematik-1. İzmir: Sürat Üniversite Yayınları.
    • Bingölbali, E. (2010). Türev kavramına ilişkin öğrenme zorlukları ve kavramsal anlama için öneriler. M.F. Özmantar, E. Bingölbali ve H. Akkoç...
    • Berresford, G. & Rockett, A. (2015). Brief applied calculus. Nelson Education.
    • Bruner, J. (1966). Toward a Theory of Instruction. Cambridge, MA: Belknap Press.
    • Brown, J.S., & VanLenhn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive science, (4), 399-426.
    • Denbel, D.G. (2015). Some Conceptual Difficulties of Students on Derivation. Journal of Educational and Management Studies, 5(4), 211-214.
    • Desfitri, R. (2016). In-Service Teachers’ Understanding on the Concept of Limits and Derivatives and the Way They Deliver the Concepts to...
    • Fuentealba, C., Badillo, E., Sánchez-Matamoros, G., Cárcamo, A. (2019). The Understanding of the Derivative Concept in Higher Education. EURASIA...
    • Gür, H., & Barak, B. (2007). Ortaöğretim 11. sınıf öğrencilerinin türev konusundaki hata örnekleri. Educational Sciences: Theory &...
    • Haapasalo, L. & Zimmermann, B. (2015). Investigating mathematical beliefs by using a framework from the history of mathematics. In: C....
    • Hӓhkiöniemi, M. (2005). Is there a lımıt in the derıvatıve? – exploring students’ understanding of the limit of the difference quotient. In...
    • Hoffmann, L.D. & Bradley, G.L. (2010). Calculus for Business, Economics, and the Social and Life Sciences, Claremont McKenna College.
    • Jaworski, B. (2015). Mathematics meaning-making and its relation to design of teaching. PNA, 9 (4), 261–272.
    • Karadeniz, A. A. (2003). Yüksek matematik cilt-1 diferansiyel ve integral hesap. Çağlayan Basımevi. İstanbul. 13. Baskı.
    • Kilpatrick, J. Swafford, J. & Findell, B., eds. (2001). Adding it up: Helping children learn mathematics, Washington DC: National Research...
    • Laridon, P., Jawurek, A., Kitto, A., Pike, M., Myburgh, M., Rhodes-Houghton, R., Sasman, M., Scheiber, J., Sigabi, M., & Van Rooyen, R....
    • Maharaj, A., & Ntuli, M. (2018). Students’ Ability to Correctly Apply Differentiation Rules to Structurally Different Functions. S Afr...
    • NCTM (National Council of Teachers of Mathematics). (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
    • Özkan, E.M. & Ünal, H. (2009). Misconception in Calculus-I: Engineering students’ misconceptions in the process of finding domain of functions....
    • Pino-Fan, L. R., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective...
    • Roundy, D. Dray, T. Manogue, C. A. Wagner, J. & Weber, E. (2015). An extended theoretical framework for the concept of the derivative....
    • Rohde, U. L. Jain, G. C. Poddar, A. K. & Ghosh, A. K. (2012). Introduction to differential calculus: systematic studies with engineering...
    • Sahin, A., Cavlazoglu, B., & Zeytuncu, Y.E. (2015). Flipping a college calculus course: A Case study. Journal of Educational Technology...
    • Sahin, Z., Yenmez, A.A., & Erbas, A. (2015). Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case...
    • Skemp, R. R. (1976). Relational understanding and instrumental understanding, Mathematics Teaching, 77, 20–26.
    • Skemp, R.R. (1978). Relational understanding and Instrumental understanding. Arithmetic Teacher, 26(3), 9-15.
    • Star, J. R. & Stylianides, G. J. (2013). Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality....
    • Thomas, G.B. D. Weir, M., & Hass, J. (1988). Thomas’ Calculus, 11th Edition, Massachusetts.
    • Tierney, W. G., & Garcia, L. D. (2008). Preparing Underprepared Students for College: Remedial Education and Early Assessment Programs....
    • Van Engen, H. (1953). The formation of concepts. In H.F. Fehe (Ed.), The learning of mathematics: Its theory and practice, 21st yearbook of...
    • Watson, A, & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh, & T. Wood (Eds), Tools and resources in...
    • Widada, W., Sunardi, H., Herawaty, D., Boby, E., & Syefriani, D. (2018). Abstract Level Characteristics in SOLO Taxonomy during Ethnomathematics...
    • Woods, R.G. & Barrow, R.C. (1975). An introduction to philosophy of education. London: Methuen.
    • Yoong, W.KH. (1984). Aspects of mathematical understanding, Singapore Journal of Education, 8(2), 45-55.
    • Fuentealba, C., Badillo, E., Sánchez-Matamoros, G. (2019). Identificación y caracter-ización de los subniveles de desarrollo del esquema de...
    • Lee, J. (2018). An Analysis of University Students’ Representational Fluency About the Derivative Concept. The journal of educational research...
    • Sánchez-Matamoros-Garcia, G., García Blanco, M.M. y Llinares Ciscar, S. (2008). La comprensión de la derivada como objeto de investigación...
    • Smith, S. R. (2015). Incomplete understanding of concepts: The case of the derivative. Mind, 124(496), 1163-1199
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