0000000000076215
AUTHOR
Irene Ferrando
Pre-service teachers’ flexibility and performance in solving Fermi problems
AbstractFermi problems are real-context estimation tasks that are suitable for introducing open-ended problems in primary school education. To ensure their effective introduction in the classroom, teachers must have adequate proficiency to deal with them. One of the key aspects of problem-solving proficiency is flexibility, but there are few studies on flexibility in solving real-context problems. This study, based on an analysis of the errors made by 224 prospective teachers when solving a Fermi problem sequence, establishes performance levels. In addition, we define levels of flexibility in using multiple solutions across the sequence, which allows us to address the main objective: to stu…
Analysis of the Relationship Between Context and Solution Plan in Modelling Tasks Involving Estimations
In this chapter we analyse students’ written solution plan of a sequence of modelling tasks involving estimations. Our research objective is to statistically analyse whether there is a relation between the solution plan and the characteristics of the context of the real estimation task. From previous work, we have identified some task variables that are directly related to the context. In this study we have designed a sequence of modelling tasks and we have analysed the productions of N = 224 Spanish pre-service primary school teachers. The results show that there is a relationship between the variables of the task and the solution plan used by the students in each case. From the results of…
Una propuesta para trabajar la proporción desde el arte
[EN] We present a proposal addressed to students of the first courses of ESO. Through these activities, pupils will work concepts related with proportionality. Our proposal is developed along art history, the students will acquire skills related with proportionality through the uses the artists have done throughout history. Through a route beginning in ancient Egypt and ending in today Athens, students will act as the artists, architects or even tour guides to deal with technical problems and solve them mathematically. Some of the activities have been already implemented in the project Estalmat CV (a mathematic stimulation program for talented students) and later adapted to a conventional c…
Computer Animation to teach interpolation
<div data-canvas-width="460.953206963072">Aunque las asignaturas de matemáticas son un tema básico en los estudios de una ingeniería, a menudo son considerados por los estudiantes como una asignatura difícil. En este trabajo presentamos una experiencia de aprendizaje basada en la animación por ordenador mediante el uso de la modelización matemática. Nuestro objetivo es proporcionar a los estudiantes un contexto que motive el estudio de la interpolación de funciones. Presentamos un planteamiento del problema que se pretende resolver mediante</div><div data-canvas-width="460.9542195018301">el Ciclo de Modelización. Se presentan y discuten tanto desarrollo de la actividad com…
La observación de aula como herramienta de desarrollo profesional: el caso del OCDE Global Teaching InSights
Se presenta el proyecto Global Teaching InSights Video Study, de la Organización para la Cooperación y el Desarrollo Económicos [OCDE], cuyo objetivo es potenciar la grabación y el análisis de sesiones de clases como herramienta de desarrollo profesional y de formación de docentes de matemáticas. Se describe el trabajo llevado a cabo por los autores coordinando grupos de trabajo que se encargaron de diseñar un estudio de caso basado en un vídeo de una clase real. La difusión pública de los vídeos producidos permite, además, abordar el diseño de investigaciones centradas en observación guiada de la práctica de la enseñanza de las matemáticas.
Avances de investigación en educación matemática
El fomento de la flexibilidad y adaptabilidad en resolución de problemas matemáticos favorece el desarrollo de la competencia matemática. En este estudio se describe y justifica el diseño de una secuencia de tareas de modelización que permite analizar la flexibilidad inter-tarea en los estudiantes. El objetivo central del estudio es analizar si los estudiantes son capaces de adaptar sus planes de resolución según aspectos relativos al contexto de la tarea, cambiando de estrategia de una tarea a otra, si estos aspectos varían. En el estudio han participado 110 estudiantes del grado de Maestro/a en Educación Primaria; los resultados permiten conocer en qué medida son flexibles los estudiantes…
Supporting mathematical modelling by upscaling real context in a sequence of tasks
AbstractCreating and developing mathematical models to solve real-world problems is a complex task and students often have difficulties in tackling it successfully. The design and implementation of sequences that help students autonomously develop their ability to solve modelling tasks could be a useful scaffolding tool to foster modelling learning. In this paper we present a sequence of estimation tasks in a real context based on what we have called the upscaling technique, which consists of scaling the accessibility and knowledge of the context used. A study with two samples of grade 10 students, experimental and control, has allowed us to find out whether this sequence promotes success i…
Studying and improving Mathematics instruction in secondary schools in Spain study group (grupo de estudio SiMiS1 )
El objetivo de este artículo es presentar y justificar el diseño de POEMat.ES, una pauta de observación de acciones del profesor de matemáticas en clase. POEMat.ES ha sido desarrollado por un grupo de investigadores con perfiles diversos en cuanto a experiencia docente e investigadora, a fin de sistematizar la observación de la práctica de enseñanza para entender e interpretar con precisión el proceso de enseñanza de matemáticas en educación secundaria en el contexto español. El diseño de POEMat.ES se ha basado en modelos específicos del conocimiento del profesor de matemáticas. La construcción del instrumento se aborda desde dos aproximaciones complementarias: se proponen categorías de obs…
Análisis de los modelos matemáticos producidos durante la resolución de problemas de Fermi
[EN] In this paper, we present an analysis of written productions of 16 year-old students while solving Estimation Problems involving Big Numbers (EPiBN). This kind of problems is a particular type of Fermi problems and allows us to introduce modelling processes in Secondary school classrooms. Our analysis supports on the characterization of mathematical models developed by students based on the model definition of Lesh and Harel. The results show that, through the analysis of EPiBN resolutions, differentiating aspects can be distinguished between the models produced by students without modelling experience of those produced by students with prior experience, especially in the concepts and …
Difficulties in Teaching Modelling: A French-Spanish Exploration
An exploratory research study based on an online questionnaire in order to better understand difficulties encountered in teaching of mathematical modelling in France and Spain is presented. This questionnaire takes into account biographical variables, mathematics and modelling conceptions of pre-service teachers, teachers, researchers and education inspectors, from primary to tertiary education. Regarding difficulties, heterogeneous conceptions are revealed, and the analysis constructs four clusters, from positive and confident conceptions to negative and lacking confidence. In some cases, the roles of some biographical variables are indicated such as country, age, gender or school level th…
Design and Implementation of a Tool for Analysing Student Products When They Solve Fermi Problems
In this chapter, we present a tool for analysing the work of secondary-level students from two different schools when they solve a type of Fermi problem. The tool is based on the characterisation of the concepts, procedures and language used to construct the models. Our results show that the proposed tool is useful to describe the models and to distinguish different aspects between the models produced by students without any previous modelling experience and those obtained by students who were already acquainted with working on modelling activities.