Obstacles to Mathematization in Physics: The Case of the Differential

Abstract

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Unpacking students’ use of mathematics in upper-division physics: where do we go from here?

“…This fits with the models and frameworks developed by physics education researchers who have argued that using mathematics in physics is quite different to simply using mathematics [26][27][28][29][30]. There are a number of instances in the literature where students demonstrate that they are quite successful manipulating and applying mathematical formulas but struggle to interpret or to generate these formulas [8,12,15,42].…”

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students’ mathematical performance

“…It may also negatively impact the students' fluency to combine the individual equations and simplify the resulting equation for the required variable. Previous studies have reported that students struggle with transferring and using their mathematical knowledge and skills in the physics context [1,24,25,28]. In our case, as mathematical complexity increases, the students may find it even more difficult to apply their mathematical knowledge in the physics domain.…”

Análisis de los significados del concepto de diferencial desde una perspectiva ontosemiótica

“…Respecto a la dimensión epistémica, autores como Artigue, Menigoux y Viennot (1990), Bos (1974), Kleiner (2012), López-Gay (2001), Pulido (1997), Tall (1981a), Taylor (1974) y Valdivé y Garbin (2008) analizan la evolución histórica del concepto de diferencial y su estrecha relación con nociones como cantidad infinitamente pequeña, infinitesimal, aproximación lineal, aproximación o estimación lineal del incremento, destacando sus implicaciones en los procesos de enseñanza y aprendizaje. Gómez (2019), Martínez-Torregrosa et al (2002) y López-Gay et al (2015) plantean que una de las dificultades de tipo cognitivo se produce por la diversidad de significados que se les presenta a los estudiantes, ya que hay que tener en cuenta las diferentes definiciones que se fueron presentando a lo largo del desarrollo del cálculo y su articulación con las diversas representaciones y contextos.…”