Adaptation model for PCMAT – Mathematics collaborative learning platform

The aim of this paper is to present an adaptation model for an Adaptive Educational Hypermedia System, PCMAT. The adaptation of the application is based on progressive self-assessment (exercises, tasks, and so on) and applies the constructivist learning theory and the learning styles theory. Our objective is the creation of a better, more adequate adaptation model that takes into account the complexities of different users.

Evolutionarily stable learning schedules and cumulative culture in discrete generation models.

Individual learning (e.g., trial-and-error) and social learning (e.g., imitation) are alternative ways of acquiring and expressing the appropriate phenotype in an environment. The optimal choice between using individual learning and/or social learning may be dictated by the life-stage or age of an organism. Of special interest is a learning schedule in which social learning precedes individual learning, because such a schedule is apparently a necessary condition for cumulative culture. Assuming two obligatory learning stages per discrete generation, we obtain the evolutionarily stable learning schedules for the three situations where the environment is constant, fluctuates between generations, or fluctuates within generations. During each learning stage, we assume that an organism may target the optimal phenotype in the current environment by individual learning, and/or the mature phenotype of the previous generation by oblique social learning. In the absence of exogenous costs to learning, the evolutionarily stable learning schedules are predicted to be either pure social learning followed by pure individual learning ("bang-bang" control) or pure individual learning at both stages ("flat" control). Moreover, we find for each situation that the evolutionarily stable learning schedule is also the one that optimizes the learned phenotype at equilibrium.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

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 to teach mathematics in the secondary school : a companion to school experience.

En su segunda edición, este recurso ha sido actualizado para incorporar las recientes iniciativas de la Estrategia Nacional de Aritmética e incluye otros temas: la naturaleza de las matemáticas como asignatura; las matemáticas en el currículo nacional; el aprendizaje de los alumnos; uso de las TIC; la comunicación de las matemáticas; la evaluación y los exámenes públicos; la enseñanza de la matemática después de los dieciséis años; el desarrollo profesional. Tiene bibliografía e índice alfabético.

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.

Dyscalculia : action plans for successful learning in mathematics.

Recurso basado en observaciones de niños con dificultades matemáticas y en métodos probados para ayudarlos. Pone ejemplos de problemas que los niños pueden encontrar con la manipulación de los números. Proporciona a los profesores orientación sobre cómo evitar la confusión de los alumnos y cómo guiarlos a través del currículo de matemáticas más complejas.

Learning to teach mathematics in the secondary schools : a companion to school experience.

Recurso que proporciona asesoramiento y orientación básica para todos los profesores en formación y prácticas de matemáticas en la escuela secundaria. Trata sobre cuál es el papel de las matemáticas en las aulas de secundaria, lo que se espera de un profesor de matemáticas, cómo se enseñan y aprenden mejor las matemáticas, el papel de las TIC, comunicación con las matemáticas, planificación de clases de matemáticas, integración de alumnos con necesidades especiales, enseñar matemáticas a los estudiantes de más de dieciséis años, desarrollo profesional. Tiene glosario, direcciones de recursos y organizaciones.

Toward a methodology for exploring Mathematics preservice teachers' learning from a sociocultural perspective. 'Hacia una metodología para explorar el aprendizaje de futuros profesores de Matemáticas desde una perspectiva sociocultural'.

Resumen basado en el de la publicación

Quality of learning support for mathematics in transition to University

Resumen basado en el de la publicaci??n

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.

Don’t aim too high for your kids: parental over-aspiration undermines students’ learning in mathematics

Previous research has suggested that parents’ aspirations for their children’s academic attainment can have a positive influence on children’s actual academic performance. Possible negative effects of parental over-aspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German schoolchildren and their parents (N = 3,530; grades 5 to 10), we showed that parental aspiration and children’s mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., over-aspiration) had negative reciprocal relations with children’s mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children’s gender, age, intelligence, school type, and family SES. The results were also replicated with an independent sample of US parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children’s achievement.