Issues and Problems of Research on the Teaching and Learning of Applications and Modelling

Niss, Mogens Allan

doi:10.1533/9780857099655.1.72

Cited by 34 publications

(30 citation statements)

References 21 publications

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“…2 The participants in the survey were enrolled on a voluntary basis and explicitly agreed to contribute to our study on the cognitive styles of elementary school student teachers. …”

Section: B Research Methodology and Samplementioning

confidence: 99%

“…When we refer to the ''modeling'' of a situation or phenomenon we mean the process of (i) finding the variables which may be relevant in the description of the phenomenon itself, (ii) giving a verbal and schematic description of the phenomenon, (iii) determining the existing relationships between the variables, (iv) representing these relationships through equations and/or rules that give the model a predictive value [1]. According to Niss [2], models can be used in science and mathematics teaching in order to help students analyze and assess a given situation, and to consolidate the analytical skills acquired during learning. The specific, scientific contexts in which models are constructed and discussed are also important.…”

Section: Introductionmentioning

confidence: 99%

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Prospective elementary teachers’ perceptions of the processes of modeling: A case study

Fazio

Paola

Guastella

2012

Phys. Rev. ST Phys. Educ. Res.

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“…2 The participants in the survey were enrolled on a voluntary basis and explicitly agreed to contribute to our study on the cognitive styles of elementary school student teachers. …”

Section: B Research Methodology and Samplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prospective elementary teachers’ perceptions of the processes of modeling: A case study

Fazio

Paola

Guastella

2012

Phys. Rev. ST Phys. Educ. Res.

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“…Frente a este problema, muchos autores como Niss (1989), Blum (2002), , Gómez (2003), Gómez y Fortuny (2002), Burkhardt (2006), entre otros, coinciden en proponer un enfoque más instrumental de las matemáticas como herramienta de modelización (Blum y Leiß, 2007), integrando así en el proceso de estudio la actividad de modelización matemática y las cuestiones extramatemáticas que la generan. Destacamos aquí, sin entrar en detalle (ver Barquero, 2009), la propuesta que hace la universidad danesa de Roskilde (Niss, 2001, Blomhøj y Kjeldsen, 2009) aportando una respuesta «mixta» al problema anterior en forma de una organización didáctica formada por dos tipos de cursos, unos de carácter «tradicional» en el que se exponen los contenidos matemáticos «elementales», junto con cursos dedicados a la «modelización matemática».…”

Section: El Papel De La Modelización Mate-mática En La Enseñanza De Lunclassified

Los recorridos de estudio e investigación y la modelización matemática en la enseñanza universitaria de las ciencias experimentales

2011

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Resumen. Este trabajo se centra en el papel de la modelización matemática en los primeros cursos universitarios de Ciencias Experimentales. Situándonos en el ámbito de la Teoría Antropológica de lo Didáctico, nuestra propuesta se basa en el diseño e implementación de los denominados «Recorridos de Estudio e Investigación» como nuevos dispositivos didácticos que tienen una doble función: integrar en el currículo las cuestiones a las que responden los contenidos matemáticos que los estudiantes deben aprender y articularlos mediante un proceso de modelización que permite «recubrir» el currículo considerado, dotándolo de una clara funcionalidad.Palabras clave. Modelización matemática, enseñanza universitaria, ciencias experimentales, recorridos de estudio e investigación, Teoría Antropológica de lo Didáctico. Study and research courses and mathematical modelling in the natural sciences university teachingSummary. This paper focuses on the role of mathematical modelling in first year courses of experimental sciences university degrees. Within the frame of the Anthropological Theory of the Didactic, we propose the design and implementation of «Study and Research Courses» as a new didactic device having a double purpose: making students aware of the rationale of the mathematical contents they have to learn, and connecting these contents through the study of open modelling questions that can «cover» the main contents of the official mathematical syllabi, giving a clear functionality to its contents.Keywords. Mathematical modelling, university teaching, natural sciences, study and research courses, Anthropological Theory the Didactics.El punto de partida de nuestra investigación se sitúa en el problema de la enseñanza de las matemáticas en el primer curso universitario de las facultades de Ciencias Experimentales (CCEE) que, como problema docente (en el sentido de Gascón, 1999), admite una formulación en los términos siguientes: ¿Qué tipo de matemáticas se deben enseñar en los primeros cursos de CCEE y cómo deben ser enseñadas? La respuesta espontánea de la «enseñanza tradicional» de las matemáticas para CCEE a este problema se puede resumir en un proceso que consta de dos etapas. Primero, se enseñan unos conocimientos elementales que se proporcionan a los estudiantes como instrumentos «ya construidos» sin especificar con claridad ni su origen, ni su razón de ser, ni su ámbito de aplicación. Posteriormente, los estudiantes deben aprender a utilizar o, mejor, a «apli-car» estos conocimientos elementales y generales a las EL PAPEL DE LA MODELIZACIÓN MATE-MÁTICA EN LA ENSEÑANZA DE LAS CIEN-CIAS EXPERIMENTALES

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“…An approach to integration of mathematical and applied contents proposed by Niss [1989] and Alsina [1998] was accepted. Accordingly, in the integrated curriculum, calculus topics were considered as dominant and were studied in their conventional order, as presented in Table 1.…”

Section: Application Oriented Curriculummentioning

confidence: 99%

The Effect of Integrating Design Problems on Learning Mathematics in an Architecture College

Verner

Maor

2003

Nexus Netw J

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A number of universities and colleges have developed mathematics courses based on the relationship between architecture and mathematics. Igor Verner and Sarah Maor report on a study of learning mathematics in professional context in one of the architecture colleges in Israel, with a focus on assessment and educational research. This paper considers in detail applied contents and learning activities in the course and our way forward in order to discuss them with the NEXUS community. IntroductionThe past decade has been a period of increasing research and debate on the interaction between architecture and mathematics. The mutual contributions of architectural and mathematical thinking [Salingaros 1999;Aroni 1999] have been emphasized and illustrated by numerous examples in:Geometrical analysis of architectural objects, e.g., calculating dimensions, proportions, surfaces, and volumes as well as positioning and performing spatial transformations [Kappraff 1991;March 1998];Formal description and interpretation of architectural concepts and symbols such as incidence, infinity, symmetry and multi-scaling [Williams 1998;Bovill 1996]; Mathematical background concerning science and engineering aspects of architectural design and construction [Salvadori 1968;Rajchman 1998].A number of universities and colleges have developed mathematics courses based on the relationship between subjects such as the course described by Jay Kappraff [1991]. However, only minimal information is available on the educational aspects of these courses [Banerjee and De Graaf 1996]. There is a need for a comprehensive survey and empirical studies of mathematics curricula for architecture education. This would help to reduce a gap between supporters and detractors of mathematics education in architecture. This paper reports a study of learning mathematics in professional context in one of the architecture colleges in Israel. The effect of integrating architectural and structure design problems in the calculus curriculum on students' achievements and attitudes was examined. A previous paper of ours [2001] presented results of the study with focus on assessment and educational research. Here we will consider in more detail applied contents and learning activities in the course, and our way forward in order to discuss them with the NEXUS community. Case Study FrameworkArchitecture education in Israel is offered at university and college levels. The Ministry of Labour coordinates the architecture programme in colleges and certifies the graduates as practical architects for designing certain types of buildings. As part of this programme, the mathematics curriculum comprises basic concepts in algebra, geometry and trigonometry. IGOR M. VERNER and SARAH MAOR -The Effect of Integrating Design Problems on Learning MathematicsThe shortcomings of the curriculum were found through the long-term experience of teaching it in one of the architecture colleges. First, the curriculum provided only partial knowledge of that required for other disciplines and design a...

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Issues and Problems of Research on the Teaching and Learning of Applications and Modelling

Cited by 34 publications

References 21 publications

Prospective elementary teachers’ perceptions of the processes of modeling: A case study

Prospective elementary teachers’ perceptions of the processes of modeling: A case study

Los recorridos de estudio e investigación y la modelización matemática en la enseñanza universitaria de las ciencias experimentales

The Effect of Integrating Design Problems on Learning Mathematics in an Architecture College

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