Developing mathematical modelling competence: conceptual clarification and educational planning

Teaching and Learning Mathematical Modelling: Approaches and Developments from German Speaking Countries

“…The effectiveness of two different approaches (a holistic as well as an atomistic approach; see Blomhøj and Jensen 2003) was tested against each other in the following way: The participating 15 ninth grade classes were divided into two groups. Each group was assigned five modelling problems that had the same context, but students' work on the problems differed: Whereas the students of the atomistic group only had to work on one step of the modelling cycle, the students of the holistic group had to go through the whole modelling process for every problem.…”

Professional modellers’ conceptions of the notion of mathematical modelling: ideas for education

“…What is expressed by the modellers in this study resembles the type of dichotomy between reality and mathematics that is underlying the conception of the modelling cycle. While a comparison of the descriptions of modelling by our participants with Blomhøj and Højgaard Jensen's (2003) framework indicates some similarities as well as some discrepancies, our participants did not talk about modelling in terms of a cyclic process. Modelling cycles have been characterised as "normative" and seen as "an ideal way of modelling" (Borromeo Ferri 2006, p. 89), and are sometimes referred to in teaching "realistic or applied modelling" .…”

“…In the other approaches the organisation and goals of the mathematics courses vary in terms of their focus on pure mathematics, applied mathematics and problem solving. To some extent, these categorisations relate to the idea of holistic and atomistic approaches to mathematical modelling (Blomhøj and Højgaard Jensen 2003). Of these "extreme positions" (p. 128) along a continuum, the holistic approach emphasises mathematical modelling as an entire process including a set of sub-processes (for example, validation) that all need to be considered in modelling work.…”

Competencia de modelización en interpretación de gráficas funcionales

“…La propuesta de Penrose (1978; extraído de Houston, 2007) es una de las pioneras que describe los pasos en el proceso de modelización. Posteriormente han seguido propuestas con la misma base pero que destacan otros aspectos, como el modelo de la situación real (Maaß, 2006) y la relación entre la teoría y los datos en el proceso de modelización (Blomhøj y Højgaard, 2003). Desde un enfoque evaluativo Houston (2007) caracteriza criterios para evaluar las fases de la modelización en los estudiantes.…”