Designing Professional Learning Tasks for Mathematics Learning Trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project

Diseño de tareas de aprendizaje profesional para trayectorias de aprendizaje de matemáticas

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project.En este artículo, presentamos un conjunto emergente de conjeturas de aprendizaje y de principios de diseño para ser empleados en el desarrollo de tareas de aprendizaje profesional que apoyan el aprendizaje de trayectorias de aprendizaje de matemáticas de maestros de primaria. Describimos brevemente nuestra perspectiva teórica sobre el conocimiento del profesor acerca de trayectorias de aprendizaje; revisamos la literatura sobre tareas de aprendizaje profesional, presentamos un conjunto de conjeturas iniciales acerca del aprendizaje del profesor sobre trayectorias de aprendizaje; y articulamos un conjunto de principios para guiar el diseño de tareas. Concluimos con un ejemplo de una tarea de aprendizaje profesional que ha sido tomada de nuestro proyecto de investigación actual.The research reported is based upon work supported by the National Science Foundation under grant number DRL-1008364. Any opinions, findings, and conclusions or recommendations expressed in this report are those of the authors and do not necessarily reflect the views of the National Science Foundation

Designing professional learning tasks for mathematics learning trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project.Diseño de tareas de aprendizaje profesional para trayectorias de aprendizaje de matemáticasEn este artículo, presentamos un conjunto emergente de conjeturas de aprendizaje y de principios de diseño para ser empleados en el desarrollo de tareas de aprendizaje profesional que apoyan el aprendizaje de trayectorias de aprendizaje de matemáticas de maestros de primaria. Describimos brevemente nuestra perspectiva teórica sobre el conocimiento del profesor acerca de trayectorias de aprendizaje; revisamos la literatura sobre tareas de aprendizaje profesional, presentamos un conjunto de conjeturas iniciales acerca del aprendizaje del profesor sobre trayectorias de aprendizaje; y articulamos un conjunto de principios para guiar el diseño de tareas. Concluimos con un ejemplo de una tarea de aprendizaje profesional que ha sido tomada de nuestro proyecto de investigación actual.Handle: http://hdl.handle.net/10481/24791Nº de citas en WOS (2017): 3 (Citas de 2º orden, 2)Nº de citas en SCOPUS (2017): 3 (Citas de 2º orden, 1

Conceptualización del desarrollo profesional en matemáticas: Elementos de un modelo

This theoretical paper discusses the concept of models for mathematics professional development. After examining the related literature, we propose a definition of this concept that includes four elements: goals, theories, contexts, and structure. We present aspects of professional development that comprise each element.En este artículo teórico discutimos sobre el concepto de modelos para el desarrollo profesional en matemáticas. Después de examinar la literatura relacionada, proponemos una definición de este concepto que incluye cuatro elementos: metas, teorías, contextos y estructura. Presentamos los aspectos del desarrollo profesional que abarca cada elemento

Teachers’ conceptions of learning philosophies: discussing context and contextualising discussion

With the introduction of any new initiative into the mathematics classroom, there is often an assumption that it will produce visible and measurable effects in teaching approaches and pupil progress. Yet, there is a body of research that tempers such optimism, drawing attention to a series of mitigating factors, for example, the deep-seated nature of teachers’ practices, their implicit or stated beliefs and values, and their lack of detailed awareness of how they perform in the classroom. Rather than make associative links between these factors and the success of the initiative, our intention is to examine the ways in which teachers are trying to interpret what the new scheme requires of them and how in turn, engaging with it causes them to re-describe both their pedagogic understanding and classroom practices relationally to earlier approaches. Employing data from a small project, we seek to examine four teachers’ moves to grapple with this attempted shift from one teaching paradigm to another by considering how certain key terms serve to anchor the teachers’ conceptions of themselves during this transition and find that their responses can be idiosyncratic and varied depending on the approaches in which they have been previously embedded. By using theoretical ideas from some neo-Marxist writers we examine these discursive shifts and their relevance to conceiving curriculum change. We suggest that the individual’s teaching practice develops as a result of it being understood and enacted through a succession of ideological filters, each adding to the cumulative experience of the teacher

Designing Professional Learning Tasks for Mathematics Learning Trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers� learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project.En este artículo, presentamos un conjunto emergente de conjeturas de aprendizaje y de principios de diseño para ser empleados en el desarrollo de tareas de aprendizaje profesional que apoyan el aprendizaje de trayectorias de aprendizaje de matemáticas de maestros de primaria. Describimos brevemente nuestra perspectiva teórica sobre el conocimiento del profesor acerca de trayectorias de aprendizaje; revisamos la literatura sobre tareas de aprendizaje profesional, presentamos un conjunto de conjeturas iniciales acerca del aprendizaje del profesor sobre trayectorias de aprendizaje; y articulamos un conjunto de principios para guiar el diseño de tareas. Concluimos con un ejemplo de una tarea de aprendizaje profesional que ha sido tomada de nuestro proyecto de investigación actual

Designing Professional Learning Tasks for Mathematics Learning Trajectories (Diseño de tareas de aprendizaje profesional para trayectorias de aprendizaje de matemáticas)

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project. En este artículo, presentamos un conjunto emergente de conjeturas de aprendizaje y de principios de diseño para ser empleados en el desarrollo de tareas de aprendizaje profesional que apoyan el aprendizaje de trayectorias de aprendizaje de matemáticas de maestros de primaria. Describimos brevemente nuestra perspectiva teórica sobre el conocimiento del profesor acerca de trayectorias de aprendizaje; revisamos la literatura sobre tareas de aprendizaje profesional, presentamos un conjunto de conjeturas iniciales acerca del aprendizaje del profesor sobre trayectorias de aprendizaje; y articulamos un conjunto de principios para guiar el diseño de tareas. Concluimos con un ejemplo de una tarea de aprendizaje profesional que ha sido tomada de nuestro proyecto de investigación actual

PNA

Resumen basado en el de la publicaciónSe discute sobre el concepto de modelos para el desarrollo profesional en matemáticas. Tras examinar la literatura relacionada, se propone una definición de este concepto que incluye cuatro elementos: metas, teorías, contextos y estructura. Finalmente se presentan los aspectos del desarrollo profesional que abarca cada elemento.AndalucíaBiblioteca de Educación del Ministerio de Educación, Cultura y Deporte; Calle San Agustín, 5 - 3 Planta; 28014 Madrid; Tel. +34917748000; [email protected]

Principled teaching for deep progress: improving mathematical learning beyond methods and materials

This paper contributes to knowledge about principled action which makes a difference to learners attainment. We report on the Improving Attainment in Mathematics Project, a project focusing on low-attaining secondary students. The purpose of the project was to introduce innovations in practice through action research with 10 teachers over 2 years, and evaluate the effect on students learning using national test scores, teachers reports, non-routine tasks and other performance indicators. However, this is not a study which shows how certain methods lead to better results. While it was found that learning improved, the methods and strategies the teachers used were not always generalisable across the project, indeed some were contradictory. Continued searching led to the identification of common underlying principles of teaching which different teachers manifested in different ways. Overt methods were less important than the collection of beliefs and commitments which underpinned teachers choices. There was, however, a convergence of practice around a focus on long-term development, the process of becoming a learner of mathematics, rather than short-term gains. In addition, we had to deal with some of the realities of authentic collaborative research with practitioners