Challenging inequity in mathematics education by making pedagogy more visible to learners

This paper reports on initial findings from the Visible Maths Pedagogy research project, a collaboration between an academic researcher and two teacher researchers (the paper’s authors). The aim of the project was to explore the effects of making pedagogy more visible on students’ success in school mathematics. We adopted a Participatory Action Research methodology to plan and evaluate five strategies used alongside ‘progressive’ teaching approaches to make the teacher’s pedagogical rationale more visible to learners. Our findings show that students, particularly those from disadvantaged backgrounds, were initially prone to misinterpret the intentions of the teacher. However, the five strategies helped students gain a greater appreciation of the teacher’s pedagogical rationale and how to respond appropriately. We discuss the implications of these findings for enabling all students to access the benefits of progressive teaching approaches and for opening up to scrutiny what it means to be a successful learner of mathematics

Visible mathematics pedagogy: A model for transforming classroom practice

This paper focuses on the development of a model of research and professional development which aims to bring about transformations in classroom practice in situations that have previously proved resistant to change. We explore reasons why conventional models have failed to address one such situation, the continuing predominance of teacher-centred pedagogies in mathematics classrooms. We draw on findings from the Visible Mathematics Pedagogy research project to highlight how a critical model of participatory action research can be refined to enhance its potential to bring about changes in classroom practice. We report on research tools and processes that were developed, distinct from those commonly used in research, including the organisation of research team meetings around participatory principles, the active involvement of teachers in designing and employing data collection tools, and in generating protocols associated with video-stimulated reflection. We demonstrate how these research tools and processes enhanced collaboration and teacher agency, the trustworthiness of the research findings and teachers’ critical reflection on existing practice. We argue that our refined model of participatory action research can inform and support teachers and researchers wishing to transform classroom practice, especially in situations analogous to many mathematics classrooms, in which conventional models have had limited impact

Progressive pedagogies made visible: Implications for equitable mathematics teaching

This paper makes a significant contribution to contemporary debates over the direction curriculum reforms should take. It challenges claims that progressive pedagogies can exclude disadvantaged learners from gaining access to powerful knowledge and argues that greater attention needs to be given to learner agency and subject didactics. It reports on the findings from the Visible Maths Pedagogy research project, which aimed to develop and evaluate strategies for making progressive pedagogies more visible to mathematics learners. Evidence collected from student surveys and interviews suggests that these novel strategies were successful in heightening students’ appreciation of the teacher’s pedagogic rationale for employing progressive teaching approaches. They appeared to have a positive impact on students’ mathematical engagement and awareness of how to achieve success in the secondary school mathematics classroom, particularly for those from disadvantaged backgrounds. The findings highlight the potential of progressive pedagogies made visible for establishing an alternative didactic situation based on socio-mathematical norms associated with ‘sense-making’, rather than ‘answer-getting’, which can help develop students’ individual and collective agency. We argue that such a didactic situation offers a pathway towards a more equitable mathematics curriculum, that enables wider access to powerful knowledge, and which forms an integral part of a school curriculum designed to address the environmental, economic and social challenges currently faced by our global society

Dissipative quantum systems modeled by a two level reservoir coupling

The coupling between a quantum dynamical system and a two-level system reservoir is analysed within the framework of the Feynman-Vernon theory. We stress the differences between this new reservoir and the well-known bath of oscillators and show that, in order to obtain the Langevin equation for the system of interest in the high temperature regime, we have to choose a spectral distribution function $J(\omega)$ which is finite for $\omega=0$.Comment: 6 pages, RevteX, preprint UNICAM

On digit frequencies in beta-expansions

We study the sets DF(β) of digit frequencies of β-expansions of numbers in [0,1]. We show that DF(β) is a compact convex set with countably many extreme points which varies continuously with β; that there is a full measure collection of non-trivial closed intervals on each of which DF(β) mode locks to a constant polytope with rational vertices; and that the generic digit frequency set has infinitely many extreme points, accumulating on a single non-rational extreme point whose components are rationally independent

Symbol ratio minimax sequences in the lexicographic order

Consider the space of sequences of letters ordered lexicographically. We study the set of all maximal sequences for which the asymptotic proportions of the letters are prescribed, where a sequence is said to be maximal if it is at least as great as all of its tails. The infimum of is called the -infimax sequence, or the -minimax sequence if the infimum is a minimum. We give an algorithm which yields all infimax sequences, and show that the infimax is not a minimax if and only if it is the -infimax for every in a simplex of dimension 1 or greater. These results have applications to the theory of rotation sets of beta-shifts and torus homeomorphisms

Detecção de Pepper yellow mosaic virus em Capsicum chinense no estado do Pará.

Capsicum chinense é cultivada em larga escala no estado do Pará, porém algumas doenças podem restringir a produção. Nos plantios localizados na região metropolitana de Belém é comum observar plantas com sintomas de viroses como clorose, redução do limbo foliar, nanismo e consequentemente redução da produção de frutos causados por Cucumber mosaic virus - CMV. Entretanto, em um plantio no município de Parauapebas, localizado na região sul do estado do Pará, foram observadas plantas de C. chinense com sintomas diferentes daqueles observados na região metropolitana de Belém como mosaico foliar forte e deformação foliar. Dessa forma, este trabalho teve o objetivo de identificar a espécie de vírus causador da doença que ocorre em Parauapebas. Amostras de folhas coletadas neste plantio foram preservadas por meio do congelamento à 80o C, dessecadas e armazenadas à -20o C e via enxertia em plantas de pimenta cv. Cheiro. A partir de folhas coletadas fezes a purificação parcial de vírus, extração de ácido nucleico viral, RT-PCR utilizando primers para detecção do CMV e Potyvirus e sequenciamento de DNA. Observou-se a amplificação de fragmentos de DNA de cerca de 800pb por RT-PCR quando se utilizou os primers específicos para Potyvirus. Após a análise do DNA sequenciado por meio dos programas Blast e ClustalW verificou-se que o agente causal do mosaico da pimenta de Parauapebas é o Potyvirus Pepper yellow mosaic virus - PepYMV. Este é o primeiro relato do PepYMV na região Amazônica

Análise sensorial de cereal matinal extrusado de mandioca enriquecido com concentrado protéico de soro de leite.

Objetivou-se neste trabalho, determinar o teor de proteína em sementes crioulas de seis feijões