Etiqueta: problem solving

Clasificación de los problemas propuestos en aulas de Educación Secundaria Obligatoria

  Por

Laura Conejo y Tomás Ortega

Abstract: This article describes a theoretical and practical study in which the practical activities carried out in the mathematics sessions at a school for a period of five weeks has been analyzed. The goal of this paper is to create a classification tool which allows, on the one hand, analyze if the activities proposed are appropriate for the learning and teaching process, and, on the other hand, select a good collection of mathematical activities by mathematical teachers. For that purpose, we have examined the conceptions of the terms “problem” and “problem solving” proposed by several authors and the classifications of these made by Borasi and Schoenfeld and a first classification of activities proposed to students of 3rd y 4th (14-16 years old) of Educación Secundaria Obligatoria. We conclude that both classifications were insufficient and we have, therefore, undertaken, firstly, a reformulation of both classifications and, secondly, a classification of the activities according to the new classifications.

Keywords: problem, problem solving, sorting, math, typology, structural elements.

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A proposal of using a Classroom Response System (CRS) to promote interactive Calculus lessons at the University

  Por

José Ignacio Barragués, Adolfo Morais, María Juncal Manterola
y Jenaro Guisasola

Abstract: The current conception of what means to teach and to learn Mathematics holds that students must learn constructing actively new meanings from experience and previous knowledge. This conception demands a follow-up of the learning and of the completed tasks, to develop in the classroom activities that allow putting in practice key concepts in practical problems, etc. In this context, the Classroom Response System (CRS) is being investigated by its potential to improve the communication between the teacher and the students. This study describes the educational strategies put in practice at the UPV/EHU (Spain), for the education of Calculus in Engineering studies, using a CRS to facilitate the 64 Educación Matem ática, vol. 25, núm. 1, abril de 2013 Una propuesta de uso de un Classroom Response System … interaction with large groups of students. The results show that students valued positively the received education. In addition, it was observed a significantly superior average normalized gain in the learning to that obtained by a group of students that received a conventional education.

Key words: Clickers, CRS, Classroom Response System, significant learning, peer instruction, calculus, problem solving, PBL.

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The area of the straight pyramid: design and implementation of a geometry activity

  Por

Nora E. Herrera
Stella M. Soto
Verónica A. Quiroga
Ana E. Puzzella
Marcel D. Pochulú

Abstract:In this paper, we present the design of a task of geometric in order to make emerge the concept of right pyramid area from its development plan. The implementation took place in a course for Physics teachers at the National University of San Juan (Argentina), during the academic year 2014. To diagram and support the proposal, we use elements of Critical Mathematics Education, Theory of Didactic Situations and Onto-semiotic Focus of Knowledge and Mathematical Instruction. The purpose is to highlight some elements that serve to delineate math activities that can be done differently in the college class, moving them away from traditional models of teaching and encouraging students to construct their own
knowledge. To do this, we show the design criteria we use and how we made an a priori and a posteriori analysis of the mentioned task.

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Keywords: didactic proposal, task design criteria, problem solving, surface area of the right pyramid.

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Breaking the didactic contract in solving a geometry problem with high school students

  Por

Apolo Castañeda
Juan Arturo Hernández-Morales
Rosa Isela González-Polo

Abstract: This study reports the results of the implementation of an experimental design in a high school mathematics classroom (students 12-14 years old) aimed at the construction of triangles, given three segments. Within the experimental design, there is a problem of calculation of area and perimeter where the ruptura and establishment of didactical contract is analysed. For the design of the sequence, theoretical reflections on the concept of didactical contract of Brousseau were considered, as well as the problem solving model of (Lester, 2013: 258), this allowed the design of activities regarding triangles construction using paper strips. These activities served as a prelude to address a problem of calculation of area and perimeter of a triangle with wrong measures. The results show that students get into contradictions, because despite finding certain conditions for the measure of the segments of a triangle and working previously with unsolvable problems, they cannot recognize a triangle with wrong measures and even claim that it is possible to obtain the perimeter of three segments of a figure which is not closed.

Key words: Didactical Contract, problem solving, geometry, high school students.

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The construction of tangent circumference. Theoretical study from a heuristic perspective

  Por

Liliana Siñeriz y Trinidad Quijano

Abstract:This paper describes a theoretical study of the process of solving an open situation, in the framework of a research focused on geometric constructions. On one hand, we intend to show the multiplicity of aspects inherent to posing and solving problems from it. On the other hand, our aim is to provide some guidelines or suggestions to organize how to teach, in order to rescue methods and heuristics that underlie when it is solved, and to promote the generation of new problems arising from processes to develop and test conjectures by means of exploration.

Keywords: constructions, problem solving, problem posing, heuristics methods,
phases.

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La construcción de circunferencias tangentes. Estudio teórico desde una perspectiva heurística

  Por

Liliana Siñeriz y Trinidad Quijano

Resumen:En este artículo describimos un estudio teórico del proceso de resolución de una situación abierta en el marco de una investigación centrada en las construcciones geométricas. Por un lado, nos proponemos mostrar la multiplicidad de aspectos inherentes al planteamiento y resolución de problemas a partir de ella. Por otro lado, pretendemos aportar algunas pautas o sugerencias al organizar la enseñanza que lleven a rescatar los métodos y heurísticas que subyacen al resolverla, y promover la generación de nuevos problemas desde procesos de elaboración y contrastación de conjeturas a través de la exploración.

Palabras clave: construcciones, resolución de problemas, planteamiento de problemas, métodos heurísticos, fases.

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Entre el diseño y la implementación de una actividad de geometría: el área de la pirámide recta

  Por

DOI 10.24844/EM2801.06

Nora E. Herrera
Stella M. Soto
Verónica A. Quiroga
Ana E. Puzzella
Marcel D. Pochulú

Resumen:En este trabajo presentamos el diseño de una tarea referida a geometría, con la finalidad de hacer emerger el concepto de área de la pirámide recta a partir de su desarrollo plano. La implementación tuvo lugar en un curso con alumnos del profesorado de Física en la Universidad Nacional de San Juan (Argentina) durante el año académico 2014. Para diagramar y fundamentar la propuesta usamos elementos de la Educación Matemática Crítica, Teoría de Situaciones Didácticas y Enfoque Onto-semiótico del Conocimiento e Instrucción Matemática.El propósito es poner de relieve algunos elementos para delinear actividades matemáticas que puedan realizarse de manera diferente en la clase universitaria, alejándolas de los modelos tradicionales de enseñanza y estimulando a los estudiantes para que construyan su propio conocimiento. Para ello, mostramos los
criterios de diseño que empleamos y el modo en que elaboramos un análisis a priori y a posteriori de la tarea mencionada.

Palabras clave: propuesta didáctica, criterios de diseño de tareas, resolución de problemas, área de la pirámide recta.

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Ruptura del contrato didáctico en la solución de un problema de geometría con estudiantes de secundaria

  Por

DOI 10.24844/EM2801.04

Apolo Castañeda
Juan Arturo Hernández-Morales
Rosa Isela González-Polo

Resumen:Se presentan los resultados de la implementación de un diseño didáctico con estudiantes de secundaria (12-14 años), relativos a la construcción de triángulos, dados tres segmentos, donde se analiza la ruptura e instauración del contrato didáctico en la solución de un problema de cálculo de área y perímetro. Para el diseño de la secuencia se consideraron las aportaciones teóricas sobre el
contrato didáctico de Brousseau, y el modelo de resolución de problemas de Lester (2013: 258), a partir de los cuales se plantearon actividades de construcción de triángulos con tiras de papel que sirvieron de preámbulo para abordar un problema de cálculo de área y perímetro de un triángulo con medidas erróneas. Los resultados muestran que los estudiantes entran en contradicciones, ya que a pesar de concluir ciertas condiciones para las medidas de los segmentos de un triángulo y trabajar previamente con problemas sin solución, no pueden reconocer un triángulo con medidas erróneas e incluso afirman que es posible obtener el perímetro de tres segmentos de una figura que no es cerrada.

Palabras clave: Contrato Didáctico, resolución de problemas, geometría, estudiantes de secundaria.

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