Um estudo de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

Pursuing excellence : a study of U.S. eighth-grade mathematics and science teaching, learning, curriculum, and achievement in international context /

Mode of access: Internet.

Sharing best practices in introducing and teaching ethics principles to public administration employees : research report

O projeto, financiado pelo Programa Aprendizagem ao Longo da Vida, decorreu entre 1 de agosto de 2011 e 31 de julho de 2013 e foi coordenado pelo Instituto de Administração Pública de Praga, tendo como parceiros a Escola de Economia e Direito de Berlim, a Escola Nacional de Administração Pública da Polónia e o INA, de Portugal. A coordenação portuguesa do estudo esteve a cargo da Prof. Doutora Helena Rato e da Dra. Matilde Gago, com a colaboração do Prof. Doutor César Madureira e da Dra. Margarida Quintela, ex investigadores do INA, atualmente na DGAEP.

Depleting the curriculum: teaching digital platforms and curricular impoverishment

The paper aims at showing how curricular complexity tends to be depleted by the use of digital platforms based on the SCORM (Sharable Content Object Reference Model) standard, which was created with the main purpose of recycling content as it is supposed to be independent both from the context of learning and the supporting technology also deemed to be neutral, all surrounded by a rhetoric of innovation and “pedagogical” innovation. The starting point of the discussion is García Perez’s model of Traditional Didactics as a simple tool to show almost graphically that any ancient didactic model is far richer in terms of complexity than the linearity, in disguise most of the times but still visible under a not so sophisticated critical lens, of the interaction human-(reusable) content that is the basis of the SCORM standard. The paper also addresses some of the more common deliberate mix-ups related to those digital platforms, such as learning and teaching, content and learning object, systems of automatic teaching and learning management systems.

EXAMINING SECONDARY MATHEMATICS TEACHER CANDIDATES’ LEARNING AND ENACTMENT OF MATHEMATICS TEACHING PRACTICES: A MULTIPLE CASE STUDY

This qualitative case study explored three teacher candidates’ learning and enactment of discourse-focused mathematics teaching practices. Using audio and video recordings of their teaching practice this study aimed to identify the shifts in the way in which the teacher candidates enacted the following discourse practices: elicited and used evidence of student thinking, posed purposeful questions, and facilitated meaningful mathematical discourse. The teacher candidates’ written reflections from their practice-based coursework as well as interviews were examined to see how two mathematics methods courses influenced their learning and enactment of the three discourse focused mathematics teaching practices. These data sources were also used to identify tensions the teacher candidates encountered. All three candidates in the study were able to successfully enact and reflect on these discourse-focused mathematics teaching practices at various time points in their preparation programs. Consistency of use and areas of improvement differed, however, depending on various tensions experienced by each candidate. Access to quality curriculum materials as well as time to formulate and enact thoughtful lesson plans that supported classroom discourse were tensions for these teacher candidates. This study shows that teacher candidates are capable of enacting discourse-focused teaching practices early in their field placements and with the support of practice-based coursework they can analyze and reflect on their practice for improvement. This study also reveals the importance of assisting teacher candidates in accessing rich mathematical tasks and collaborating during lesson planning. More research needs to be explored to identify how specific aspects of the learning cycle impact individual teachers and how this can be used to improve practice-based teacher education courses.

Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

Sociedade, cultura, matemática e seu ensino

One of the effects of the globalized world is a strong tendency to eliminate differences, promoting a planetary culture. Education systems are particularly affected, undergoing strong pressure from international studies and evaluations, inevitably comparative, and sadly competitive. As a result, one observes the gradual elimination of cultural components in the definition of education systems. The constitution of new social imaginaries becomes clear; imaginaries empty of historical, geographical and temporal referents, characterized by a strong presence of the culture of the image. The criteria of classification establish an inappropriate reference that has as its consequence the definition of practices and even of education systems. On the other hand, resistance mechanisms, often unconscious, are activated seeking to safeguard and recover the identifying features of a culture, such as its traditions, cuisine, languages, artistic manifestations in general, and, in doing so, to contribute to cultural diversity, an essential factor to encourage creativity. In this article, the sociocultural basis of mathematics and of its teaching are examined, and also the consequences of globalization and its effects on multicultural education. The concept of culture is discussed, as well as issues related to culture dynamics, resulting in the proposition of a theory of transdisciplinar and transcultural knowledge. Upon such basis the Ethnomathematics Program is presented. A critique is also made of the curriculum presently used, which is in its conception and detailing, obsolete, uninteresting and of little use. A different concept of curriculum is proposed, based on the communicative (literacy), analytical (matheracy), and material (technoracy) instruments.

Le développement d’une séquence d’enseignement/apprentissage basée sur l’histoire de la numération pour des élèves du troisième cycle du primaire

Notre contexte pratique — nous enseignons à des élèves doués de cinquième année suivant le programme international — a grandement influencé la présente recherche. En effet, le Programme primaire international (Organisation du Baccalauréat International, 2007) propose un enseignement par thèmes transdisciplinaires, dont un s’intitulant Où nous nous situons dans l’espace et le temps. Aussi, nos élèves sont tenus de suivre le Programme de formation de l’école québécoise (MÉLS Ministère de l'Éducation du Loisir et du Sport, 2001) avec le développement, notamment, de la compétence Résoudre une situation-problème et l’introduction d’une nouveauté : les repères culturels. Après une revue de la littérature, l’histoire des mathématiques nous semble tout indiquée. Toutefois, il existe peu de ressources pédagogiques pour les enseignants du primaire. Nous proposons donc d’en créer, nous appuyant sur l’approche constructiviste, approche prônée par nos deux programmes d’études (OBI et MÉLS). Nous relevons donc les avantages à intégrer l’histoire des mathématiques pour les élèves (intérêt et motivation accrus, changement dans leur façon de percevoir les mathématiques et amélioration de leurs apprentissages et de leur compréhension des mathématiques). Nous soulignons également les difficultés à introduire une approche historique à l’enseignement des mathématiques et proposons diverses façons de le faire. Puis, les concepts mathématiques à l’étude, à savoir l’arithmétique, et la numération, sont définis et nous voyons leur importance dans le programme de mathématiques du primaire. Nous décrivons ensuite les six systèmes de numération retenus (sumérien, égyptien, babylonien, chinois, romain et maya) ainsi que notre système actuel : le système indo-arabe. Enfin, nous abordons les difficultés que certaines pratiques des enseignants ou des manuels scolaires posent aux élèves en numération. Nous situons ensuite notre étude au sein de la recherche en sciences de l’éducation en nous attardant à la recherche appliquée ou dite pédagogique et plus particulièrement aux apports des recherches menées par des praticiens (un rapprochement entre la recherche et la pratique, une amélioration de l’enseignement et/ou de l’apprentissage, une réflexion de l’intérieur sur la pratique enseignante et une meilleure connaissance du milieu). Aussi, nous exposons les risques de biais qu’il est possible de rencontrer dans une recherche pédagogique, et ce, pour mieux les éviter. Nous enchaînons avec une description de nos outils de collecte de données et rappelons les exigences de la rigueur scientifique. Ce n’est qu’ensuite que nous décrivons notre séquence d’enseignement/apprentissage en détaillant chacune des activités. Ces activités consistent notamment à découvrir comment différents systèmes de numération fonctionnent (à l’aide de feuilles de travail et de notations anciennes), puis comment ces mêmes peuples effectuaient leurs additions et leurs soustractions et finalement, comment ils effectuaient les multiplications et les divisions. Enfin, nous analysons nos données à partir de notre journal de bord quotidien bonifié par les enregistrements vidéo, les affiches des élèves, les réponses aux tests de compréhension et au questionnaire d’appréciation. Notre étude nous amène à conclure à la pertinence de cette séquence pour notre milieu : l’intérêt et la motivation suscités, la perception des mathématiques et les apprentissages réalisés. Nous revenons également sur le constructivisme et une dimension non prévue : le développement de la communication mathématique.

Teaching Mathematics in English to Swedish Speaking Students : A systematic review of strategies for teaching mathematics to second language learners

The Swedish government has authorised the teaching of mathematics in English to Swedish speaking students. Much of that teaching is performed by foreign trained native English speaking teachers lacking training in second language learners. This systematic review summarises international studies from the last ten years that deal with the teaching of mathematics to second language learners. The review shows that second language students working in a bilingual environment achieve higher rates of content and language knowledge than learners in a monolingual environment. This study also summarises some of the teacher practices that are effective for teaching mathematics in English to second language learners.

Crafting a Third Space: Teacher Beliefs and Practices in Curriculum Reform for Multicultural Education

Thesis (Ph.D.)--University of Washington, 2016-06

A comparison of content-based and context-based teaching on ninth-grade mathematics achievement

The purpose of this study was to determine if an experimental context-based delivery format for mathematics would be more effective than a traditional model for increasing the performance in mathematics of at-risk students in a public high school of choice, as evidenced by significant gains in achievement on the standards-based Mathematics subtest of the FCAT and final academic grades in Algebra I. The guiding rationale for this approach is captured in the Secretary's Commission on Achieving Necessary Skills (SCANS) report of 1992 that resulted in school-to-work initiatives (United States Department of Labor). Also, the charge for educational reform has been codified at the state level as Educational Accountability Act of 1971 (Florida Statutes, 1995) and at the national level as embodied in the No Child Left Behind Act of 2001. A particular focus of educational reform is low performing, at-risk students. ^ This dissertation explored the effects of a context-based curricular reform designed to enhance the content of Algebra I content utilizing a research design consisting of two delivery models: a traditional content-based course; and, a thematically structured, content-based course. In this case, the thematic element was business education as there are many advocates in career education who assert that this format engages students who are often otherwise disinterested in mathematics in a relevant, SCANS skills setting. The subjects in each supplementary course were ninth grade students who were both low performers in eighth grade mathematics and who had not passed the eighth grade administration of the standards-based FCAT Mathematics subtest. The sample size was limited to two groups of 25 students and two teachers. The site for this study was a public charter school. Student-generated performance data were analyzed using descriptive statistics. ^ Results indicated that contrary to the beliefs held by many, contextual presentation of content did not cause significant gains in either academic performance or test performance for those in the experimental treatment group. Further, results indicated that there was no meaningful difference in performance between the two groups. ^