O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Convex analysis for minimizing and learning submodular set functions

The connections between convexity and submodularity are explored, for purposes of minimizing and learning submodular set functions.

First, we develop a novel method for minimizing a particular class of submodular functions, which can be expressed as a sum of concave functions composed with modular functions. The basic algorithm uses an accelerated first order method applied to a smoothed version of its convex extension. The smoothing algorithm is particularly novel as it allows us to treat general concave potentials without needing to construct a piecewise linear approximation as with graph-based techniques.

Second, we derive the general conditions under which it is possible to find a minimizer of a submodular function via a convex problem. This provides a framework for developing submodular minimization algorithms. The framework is then used to develop several algorithms that can be run in a distributed fashion. This is particularly useful for applications where the submodular objective function consists of a sum of many terms, each term dependent on a small part of a large data set.

Lastly, we approach the problem of learning set functions from an unorthodox perspective---sparse reconstruction. We demonstrate an explicit connection between the problem of learning set functions from random evaluations and that of sparse signals. Based on the observation that the Fourier transform for set functions satisfies exactly the conditions needed for sparse reconstruction algorithms to work, we examine some different function classes under which uniform reconstruction is possible.

Teaching and learning mathematics : a guide to research and its applications. 'Enseñando y aprendiendo matemáticas : una guía para el estudio y sus aplicaciones'.

El objetivo de esta obra es ofrecer una revisión de algunas de las investigaciones sobre la enseñanza de las matemáticas. En esta edición, se sintetizan las conclusiones de las investigaciones más recientes en diferentes partes del mundo. Abarca cuestiones tan diversas como el número y el cálculo; la forma y el espacio; probabilidad y estadística; investigación en el aula. Se han añadido dos nuevos capítulos, uno sobre el uso de la tecnología en la enseñanza de las matemáticas y otro en la solución de problemas. Cada capítulo ofrece una visión general de las investigaciones más recientes y un análisis detallado de los hallazgos más importantes. La investigación está relacionada con cuestiones del progreso de los alumnos, la diferenciación de la enseñanza y el rol de género. Tiene una extensa bibliografía.

Learning mathematics : issues, theory and classroom practice.

Recurso para profesores de matemáticas de primaria y secundaria. El texto considera las cuestiones relativas a cómo los estudiantes aprenden matemáticas. Cada uno de los once capítulos trata un tema particular que ilustra la interacción entre la teoría y la práctica. Esta edición cuenta con dos nuevos capítulos: uno relacionado con la cognición y la transferencia del aprendizaje, y otro que examina la importancia del modelo de aprendizaje en las matemáticas.

Inclusive approaches to teaching and learning mathematics

This chapter explores the role of mentors in supporting pre-service teachers to include all children in mathematics teaching, no matter what their individual needs.

Students' conflicting attitudes towards games as a vehicle for learning mathematics : a methodological dilemma

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This article reports on the methodological dilemma of resultant conflicting attitudinal data related to game- playing. Concerns arising from the divergence in the results are raised in this article. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.

Developing guidelines for teachers helping students experiencing difficulty in learning mathematics

As part of an ongoing project, we have developed a model of planning and teaching that is designed to assist teachers to help students overcome barriers they might experience in learning mathematics. The following is a discussion of one aspect of the model that we term “enabling prompts”. These refer to the directions, invitations, or questions that a teacher offers when interacting one-on-one with students experiencing difficulties. We argue that teachers should plan to pose subsidiary questions in the first instance, rather than, for example, offering further explanations. We outline our overall planning and teaching model, we present some examples of enabling prompts used by our project teachers, and we propose some considerations for teachers when structuring their own enabling prompts.

Young children learning mathematics: a guide for educators and families

Can young children learn mathematics before school? What ideas and concepts are they capable of learning? How can adults develop a child's mathematical thinking from birth to five years? Early learning plays a critical role in laying a foundation for later success in schooling. This book explores the possibilities and potential for early childhood educators, parents and carers to stimulate young children's mathematical thinking. Drawing on the authors' significant research, it answers frequently asked questions about early childhood mathematics, discusses the experiences, activities and conversations that could lead to mathematics learning, and provides simple, easy-to-follow guidelines on introducing and building on the mathematical concepts underpinning play and activity in young children aged from birth to five.

Beyond deficit models of learning mathematics : Socio-cultural directions for change and research

Major paradigmatic changes in mathematics education research are drawing attention to new perspectives on learning. Whereas deficit models were previously in the foreground of research designs, these have been replaced by a wide variety of theoretical directions for studying diverse approaches to learning mathematics. There is now an acceptance of the need for richness and variety in research practices so that approaches can be studied, compared and mutually applied and improved. Psychological and quantitative approaches and methods are now increasingly complemented, or even replaced, by new directions that rely on social and anthropological theories and methods. Rather than reviving ideas about deficit research in mathematics education, the aim of this chapter is to present some socio-cultural perspectives of mathematics learning, and to show how these perspectives go beyond the deficit model of learning. Framing the main traditional markers of discrimination in school mathematics—gender, social class and ethnicity—in a perspective of social justice, the chapter concludes with a reflection on equality in terms of the democratic principle of meritocracy in mathematics education.