Secondary School Calculus: Preparation or Pitfall in the Study of College Calculus?

Abstract

This study investigated the effects of various levels of secondary school calculus experience on performance in first-year college calculus, with focus on student performance on conceptual and procedural exam items. Analysis of covariance, with mathematics SAT score as a covariate, was employed to explore differences among four groups of students. Students who had a year of secondary school calculus, advanced placement or otherwise, differed significantly in performance from students who had either no calculus or a brief introduction to calculus prior to college. A brief secondary school introduction to calculus, in comparison with no secondary school calculus, provided an initial advantage in the college course. This slight advantage reappeared on the final exam and on the procedural subscale of the final exam. Students who had studied a full year of secondary school calculus performed significantly better than other groups throughout the first-semester course. The advantage was revealed more strongly in procedural than in conceptual items. There were no significant differences among the four groups of students on outcome measures in the second-semester course. Students with more secondary school calculus background were more likely to continue into the second semester of college calculus.

¿Qué hacen y qué entienden los estudiantes y profesores de física cuando usan expresiones diferenciales?

“…En efecto, los resultados de distintos trabajos han puesto de manifi esto la pobre comprensión conceptual de los estudiantes en la asignatura de cálculo (Artigue y Viennot, 1987;Ferrini-Mundy y Gaudard, 1992;Ferrini-Mundy y Geuther, 1991;Labraña, 2001;Orton, 1983aOrton, , 1983bPorter y Masingila, 2000;Schneider, 1991Schneider, , 1992Tall, 1985Tall, y 1992Thompson, 1994) y señalan el enfoque meramente algorítmico de la enseñanza como el origen de esas deficiencias. No en vano, un amplio sector del profesorado de matemáticas y de educación matemática asumen de forma explícita una visión instrumentalista de la matemática (Moreno, 2001;Mura, 1993Mura, , 1995, visión que trasladan a sus alumnos, quienes llegan a pensar que hacer matemáticas se reduce a realizar operaciones puntuales sobre símbolos sin signifi cado (Porter y Masingila, 2000).…”

La diferencial no es un incremento inifinitesimal. Evolución del concepto de diferencial y su clarificación en la enseñanza de la física

“…En contraste con esta importancia, las conclusiones de distintos trabajos, realizados generalmente en el ámbito de la enseñanza de las matemáticas, han puesto de manifiesto la existencia de serias deficiencias entre estudiantes, e incluso entre profesores, en relación con la comprensión de las ideas fundamentales del cálculo (Azcárate, 1990;Breitenberger, 1992;Ferrini-Mundy y Gaudard, 1992;Ferrini-Mundy y Geuther, 1991, Orton, 1983a, 1983b) y, más concretamente, en relación con el concepto de diferencial (Alibert et al, 1987;Artigue y Viennot, 1987). Por nuestra parte, hemos comprobado el bajo porcentaje de estudiantes de física de COU y primeros cursos de carreras científico-técnicas que usan el cálculo diferencial en la física sabiendo por qué y para qué hacen lo que hacen.…”

“…En estas condiciones, resulta lógico que el uso del cálculo diferencial, en lugar de constituir una ayuda para avanzar en la comprensión física, sea percibido por los estudiantes como un obstáculo y una fuente de rechazo hacia la física, generador de inseguridad y ansiedad (Aghadiuno, 1992;Lavaly, 1990;Martin y Coleman, 1994;Monk, 1994). Distintos trabajos coinciden en señalar que las deficiencias y dificultades encontradas en el uso del cálculo diferencial tienen su origen, principalmente, en una enseñanza inadecuada, caracterizada por un enfoque meramente algorítmico (Artigue y Viennot, 1987;Ferrini-Mundy y Gaudard, 1992;Ferrini-Mundy y Geuther, 1991;López, 1991;Nagy et al, 1991;Orton, 1983aOrton, y 1983bSchneider, 1991;Thompson, 1994;Thompson y Thompson, 1994). A veces se justifica dicho enfoque algorítmico como un primer paso, adecuado para la iniciación.…”

Unlocking the Gate to Calculus Success: Pre-Calculus for Engineers - An Assertive Approach to Readying Underprepared Students

“…Many institutions give credit for students' high school calculus accomplishments when AP exam scores are earned of at least 3 or 4 (varies by institution), and higher AP scores correlate to better grades in the first semester calculus course 5 . Greater success was also noted for students who took yearlong calculus courses in high school, even if not APbased 6 . A relationship exists between the highest levels of math course completed in high school to college course placement 7 .Calculus readiness is correlated to high school GPA 8 , which suggests that most engineering students, who tend to be near the top of their high school classes, Page 23.1285.3 should be successful in calculus I.…”

“…A relationship exists between the highest levels of math course completed in high school to college course placement 7 .Calculus readiness is correlated to high school GPA 8 , which suggests that most engineering students, who tend to be near the top of their high school classes, Page 23.1285.3 should be successful in calculus I. Yet an overall, high failure rate for calculus I takers persists; more than 35%-40% of students do not pass the course 6,9,10 .…”