A Stochastic Model for the Modelling Process

Voskoglou, Michael Gr.

doi:10.1533/9780857099419.3.149

Cited by 20 publications

(16 citation statements)

References 6 publications

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“…Voskoglou used Markov chains to model problem solving (1996), the process of learning (2009), and the process of mathematically modeling real world problems (2007). The state space of the model in Voskoglou (2009) appeared to be contiguous where learning occurred along a continuum of conceptual phases or 'steps.' A limitation of this study was that the state transitions and decision epochs of the model were unclear.…”

Section: Markov Chains In Education Modelingmentioning

confidence: 99%

“…Three challenges persist: defining mutually exclusive states, describing how the states change over time according to time-dependent probability distributions, and securing access to statistically significant sample sizes. As indicated by Perdikaris (1992) and Voskoglou (2009), much of the research in this area relies on anecdotal evidence based on one or two classrooms, making it difficult to generalize the results to a larger population. While models of the undergraduate engineering education system have emerged in the past decade (Klingbeil, Mercer, Rattan, Raymer, & Reynolds, 2005;Pinar-Yildirim et al, 2007;Shah & Burke, 1999), it appears that longitudinal Markovian models of the K-8 mathematics education system have not been developed.…”

Section: Markov Chains In Education Modelingmentioning

confidence: 99%

See 1 more Smart Citation

Understanding the evolution of mathematics performance in primary education and the implications for STEM learning: A Markovian approach

Reamer

Ivy

Vila-Parrish

et al. 2015

Computers in Human Behavior

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Section: Markov Chains In Education Modelingmentioning

confidence: 99%

Section: Markov Chains In Education Modelingmentioning

confidence: 99%

Understanding the evolution of mathematics performance in primary education and the implications for STEM learning: A Markovian approach

Reamer

Ivy

Vila-Parrish

et al. 2015

Computers in Human Behavior

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“…Based on our calculations we can conclude that the first group demonstrated a significantly better performance at the stages of analysis/mathematization and of solution, but performed identically with the second one at the stage of validation/implementation. Remark: In earlier papers ( [11], [13]) we have also developed a stochastic model for the representation of the MM process by applying a Markov chain on its stages. However, our stochastic model is self restricted to give quantitative information only for the MM process through the description of the ideal behavior of a group of modelers (i.e.…”

Section: Applications Of the Model For MMmentioning

confidence: 99%

A Study on Fuzzy Systems

Voskoglou¹

2012

AJCAM

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In the present paper we use principles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainty. For this, the main stages of the corresponding process are represented as fuzzy subsets of a set of linguistic labels characterizing the system's performance at each stage. We also introduce three alternative measures of a fuzzy system's effectiveness connected to our general model. These measures include the system's total possibilistic uncertainty, the Shannon's entropy properly modified for use in a fuzzy environment and the "centroid" method in which the coordinates of the center of mass of the graph of the membership function involved provide an alternative measure of the system's performance. The advantages and disadvantages of the above measures are discussed and a combined use of them is suggested for achieving a worthy of credit mathematical analysis of the corresponding situation. An application is also developed for the Mathematical Modelling process illustrating the use of our results in practice.

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“…Algunas de ellas se definen de acuerdo con lo que se propone en otros ciclos conocidos (Voskoglou, 2007;Blum & Leiβ, 2007;Borromeo, 2007). Las primeras de estas acciones corresponde a las dos primeras fases del ciclo propuesto por Blum & Leiβ en la que los alumnos deben mostrar su capacidad para plantear una cuestión asociada a una situación real, habiendo comprendido la complejidad de esta situación.…”

Section: Ciclo Y Ruta De Modelizaciónunclassified

Trayectorias modelizadoras en la ESO

Sol¹,

Giménez

Rosich

2011

Model. sci. educ. learn.

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Se presentan los resultados de una investigación sobre las competencias modelizadoras de alumnos de la ESO con dificultades de aprendizaje de las matemáticas. Para ello se analizan las memorias escritas de sus actividades de modelización que hemos denominado Proyectos Matemáticos Realísticos. En especial se estudian las acciones que realizan los alumnos en la ejecución de su proyecto. La secuencia de todas las acciones que llevan a cabo los escolares lo hemos denominado "Ruta Modelizadora". Para su analisi hemos establecido una ruta hipotética que los alumnos de la ESO, como modelizadores no expertos, pueden llevar a cabo en un proceso de modelización completo. Esta ruta hipotética, formada por 16 acciones, la hemos utilizado como un instrumento de análisis. Los resultados de la investigación muestran que todos los alumnos son capaces de llevar a cabo sus proyectos matemáticos aunque se observan diferencias en los procesos que siguen.We present the results of our research about ESO student low attainers' modelling competencies. We have analyzed their papers (dossiers) about the modelling activities they carried out. These modelling activities have been called Realistic modelling Project (RMP). We have studied specially the set of actions that students do when they carry out their projects. The sequence of all the actions has been called 'Modelling Route". In order to analyse it we have set out a hypothetical modelling route that ESO students, as non-expert modellers, can perform a whole modelling process. This hypothetical route, consists of 16 actions, which we have used as an instrument of analysis. Research results show that all students are able to carry out their mathematical projects but there are differences in the processes followed.

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A Stochastic Model for the Modelling Process

Cited by 20 publications

References 6 publications

Understanding the evolution of mathematics performance in primary education and the implications for STEM learning: A Markovian approach

Understanding the evolution of mathematics performance in primary education and the implications for STEM learning: A Markovian approach

A Study on Fuzzy Systems

Trayectorias modelizadoras en la ESO

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