On the need to enhance physical insight via mathematical reasoning
S. Rojas
Departamento de Física, Universidad Simón Bolívar, Venezuela, e–mail: srojas@usb.ve
Recibido el 13 de agosto de 2007
Aceptado el 4 de septiembre de 2007
Abstract
It is becoming common to hear teaching advice about spending more time on the "physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics problems. Based on this type of justification, mathematical skills such as the ability to compute moments of inertia, center of mass, or gravitational fields from mass distributions, and electrical fields from charge distributions are considered "distracting mathematics" and therefore receive less attention. Based on published cited research on the subject, we'll argue a) that this approach can have a negative influence on student reasoning when dealing with questions of rotational dynamics, a highly non–intuitive subject where even instructors may fail to provide correct answers, and b) that exposure of students to mathematical reasoning and to a wide range of computational techniques to obtain the moment of inertia of different mass distributions will make students more comfortable with the subject of rotational dynamics, thus improving their physical insight on the topic.
Keywords: Physical intuition; physics learning; teaching of physics; mathematical reasoning; student performance.
Resumen
Se está haciendo común escuchar sobre estrategias de enseñanza en los cursos de física que hacen enfasis en la "física del problema", justificandose en la esperanza que de esa forma los estudiantes obtendrían mejor intuición física y desarrollarían mejor sus capacidades al pensar en problemas de ciencias e ingenierías. De acuerdo con estas estrategias de enseñanza, habilidades matemáticas como por ejemplo la capacidad de calcular e interpretar momentos de inercia, centro de masa, campos gravitacionales de distribuciones de masa o campos eléctricos de distribuciones de carga se consideran como "matemáticas que distraen" y por lo tanto han de recibir menos atención. Con apoyo en estudios reportados en la literatura que referenciamos, en este trabajo discutimos a) que estas estrategias de enseñanza influyen negativamente en el razonamiento de los estudiantes cuando intentan describir aspectos relacionados con la dinámica rotacional, un tema altamente no–intuitivo donde incluso instructores con amplia experiencia enseñando la temática pueden no poder proporcionar respuestas correctas a problemas relacionados con el tema y b) que una exposicion de los estudiantes al razonamiento matemático que les permita discernir con certeza cuantitativa y cualitativa sobre la dependencia de la inercia rotacional de distribución de masa referente al eje de rotación les permitiría sentir más confianza, no solo cuando tratan del tema de la dinámica rotacional, sino también de otros temas afines de estudios en los cursos introductorios de física.
Descriptores: Intuición en física; aprendizaje en física; enseñanza de la física; razonamiento matemática; rendimiento estudiantil.
PACS: 01.40.gb; 01.40.Ha; 01.40.Fk
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Acknowledgments
We are grateful to Dr. Cheryl Pahaham, who kindly provided useful comments on improving this article.
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