Investigating problem-based learning in Saudi Arabian mathematics education: a TIMSS-related study

The aim of this study is to investigate the effectiveness of problem-based learning (PBL) on students’ mathematical performance. This includes mathematics achievement and students’ attitudes towards mathematics for third and eighth grade students in Saudi Arabia. Mathematics achievement includes, knowing, applying, and reasoning domains, while students’ attitudes towards mathematics covers, ‘Like learning mathematics’, ‘value mathematics’, and ‘a confidence to learn mathematics’. This study goes deeper to examine the interaction of a PBL teaching strategy, with trained face-to-face and self-directed learning teachers, on students’ performance (mathematics achievement and attitudes towards mathematics). It also examines the interaction between different ability levels of students (high and low levels) with a PBL teaching strategy (with trained face-to-face or self-directed learning teachers) on students’ performance. It draws upon findings and techniques of the TIMSS international benchmarking studies. Mixed methods are used to analyse the quasi-experimental study data. One -way ANOVA, Mixed ANOVA, and paired t-tests models are used to analyse quantitative data, while a semi-structured interview with teachers, and author’s observations are used to enrich understanding of PBL and mathematical performance. The findings show that the PBL teaching strategy significantly improves students’ knowledge application, and is better than the traditional teaching methods among third grade students. This improvement, however, occurred only with the trained face-to-face teacher’s group. Furthermore, there is robust evidence that using a PBL teaching strategy could raise significantly students’ liking of learning mathematics, and confidence to learn mathematics, more than traditional teaching methods among third grade students. Howe ver, there was no evidence that PBL could improve students’ performance (mathematics achievement and attitudes towards mathematics), more than traditional teaching methods, among eighth grade students. In 8th grade, the findings for low achieving students show significant improvement compared to high achieving students, whether PBL is applied or not. However, for 3th grade students, no significant difference in mathematical achievement between high and low achieving students was found. The results were not expected for high achieving students and this is also discussed. The implications of these findings for mathematics education in Saudi Arabia are considered.

Guía didáctica de rúbricas de evaluación para el bloque uno de números y funciones, dirigida a docentes de matemáticas de segundo año de bachillerato

El presente trabajo titulado “Guía Didáctica de Rúbricas de Evaluación para el Bloque Uno de Números y Funciones, dirigida a docentes de matemática de Segundo Año de Bachillerato” ha sido diseñado con la intención de fortalecer el proceso de evaluación a través de la utilización de un nuevo instrumento, la rúbrica; con el objetivo de facilitarla tarea evaluadora del docente. En el primer capítulo, se da a conocer de manera general los cambios que ha sufrido la educación en los últimos años, la necesidad de conocer y relacionar las corrientes pedagógicas innovadoras como el constructivismo y la teoría del aprendizaje significativo con la evaluación del proceso educativo, la didáctica en el ámbito de la matemática, y la implementación de guías didácticas y rúbricas como instrumentos de apoyo para el docente. En el segundo capítulo se busca dar sustento a la propuesta mediante la aplicación de una encuesta, en la cual se evidenciala falta de instrumentos de evaluación que rompan el estigma de la utilización únicamente de pruebas en este proceso, además la factibilidad del uso de una guía didáctica de rúbricas para la matemática. Finalmente, en el tercer capítulo se presentan20 modelos de rúbricas holísticas y analíticas desarrolladas por cada actividad, referidas al Bloque Uno de “Números y Funciones” en base a las Destrezas con Criterio de Desempeño de acuerdo a lo que se establece en el Currículo del sistema educativo ecuatoriano.

The pedagogical content knowledge of Danish geography teachers in a changing schooling context

This study examines the self-reported, topic-specific professional knowledge (TSPK) of Danish geography teachers seen as an aspect of their pedagogical content knowledge (PCK) when teaching weather formation and climate change. This topic is considered representative of geography teaching in Denmark. In the last ten years Danish primary and lower-secondary schooling has undergone several significant changes, including the introduction of a final multiple-choice exam in geography in 2007, and a fundamental reconstruction of the curriculum in 2014. These changes are expected to influence the TSPK of geography teachers in ways that potentially have an impact on their classroom practice. Teachers´ responses to specific questions relating to their choice of learning goals and the content and organisation of their lessons show that geography teachers take into account not only the knowledge aspects which point to the final multiple-choice exam, but also the ‘bildung’ perspectives of the subject equipping students to develop their own opinions when dealing with socio-scientific issues (SSI).

Steps to success : family-friendly guide for fourth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fourth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for third grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting third grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for fifth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fifth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Fundamentos teóricos de la Educación Universitaria, sus artífices e incidencias en el currículo promovido

Recibido 21 de agosto de 2008 • Aceptado 29 de abril de 2009 • Corregido 23 de junio de 2009   Es posible pensar que al igual que la política nutre el currículo, la pedagogía, en su arte práctica, supone ser su abono para el cultivo de aprendizajes en la vida. Esto significa que el docente con formación pedagógica puede estar en capacidad de transformar su conocimiento disciplinar en un aprendizaje de conocimiento entendible, práctico y con sentido, por cuanto recurre a la pedagogía como el instrumento que le facilita viabilizar la política curricular en aras de convertir el proceso educativo en uno de calidad. Asimismo, se considera que gran parte de la profesionalización docente podría radicar en la continuidad de la formación del profesorado o formación permanente, cuyo resultado es el desarrollo profesional del profesorado y, consecuentemente, del alumnado, para que, de este proceso, se geste, “conocimiento al servicio de la vida, del elevamiento de la calidad de vida” (Flores, 1994, p. XXV), es decir, aprendizajes significativos producto de modelos de enseñanza acordes con lo que dicta y busca la propuesta curricular promovida.

A estimulação da inteligencia corporal cinestesica no contexto na educação fisica escolar

Universidade Estadual de Campinas. Faculdade de Educação Física

A Análise Matemática no Ensino Universitário Brasileiro: a contribuição de Omar Catunda

The goal of this paper is to show the diffusion, reception, and utilization of Omar Catunda's book Course of Mathematical Analysis for mathematics and engineering teaching in Brazilian universities, e. g., University of Sao Paulo and the University of Bahia from 1950 to 1976. We used interviews of some ex-alumni or users of his book. We also present some signs of the influence of his book and of Catunda himself at University of Rio Grande do Sul. We argue that Catunda and his book were important agents of process of modernizing the teaching of calculus and analysis, through his classes as well as his book.

O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

On the asymptotic enumeration of accessible automata

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bell-man-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (< X, M > models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called < X, R > models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example. (c) 2007 Elsevier Inc. All rights reserved.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

A modified epidemiological model for computer viruses

Since the computer viruses pose a serious problem to individual and corporative computer systems, a lot of effort has been dedicated to study how to avoid their deleterious actions, trying to create anti-virus programs acting as vaccines in personal computers or in strategic network nodes. Another way to combat viruses propagation is to establish preventive policies based on the whole operation of a system that can be modeled with population models, similar to those that are used in epidemiological studies. Here, a modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained. Then, disease-free and endemic equilibrium points are calculated, stability and bifurcation conditions are derived and some numerical simulations are shown. The relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks. (C) 2009 Elsevier Inc. All rights reserved.