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.

Interview with Barbara Comber in "Chapter 3 : Critical Literacy" of "Making Literacy Real : Theories and Practices for Learning and Teaching [2nd. Ed.]"

One of the so-called ‘wicked problems’ confronting most nations is poverty, or the unequal distribution of resources. This problem is perennial, but how, where and with which physical, psychological, social and educational effects, and for which students (and their teachers), needs continual scrutiny. Poverty is relative. Entire populations may be poor or groups of people and individuals within nations may be poor. Poverty results from injustice. Not only the un- and under-employed are living in poverty, but also the ‘working poor’. Now we see affluent societies with growing pockets of persistent poverty. While there are those who dispute the statistics on the rise of poverty because different nations use different measures (for example see Biddle, 2013; http://theconversation.com/factcheck-is-poverty-on-the-rise-in-australia-17512), there seems to be little dispute that the gaps between the richest and the poorest are increasing (see http://www.stanford.edu/group/scspi/sotu/SOTU_2014_CPI.pdf)...

Mathematics knowledge for teaching and the classroom environment

This study investigated the classroom environment in an underperforming mathematics classroom. The objectives were: (1) to investigate the classroom environment and identify influences upon it, and (2) to further explore those influences (i.e., teacher knowledge). This was completed using a diachronic case study approach in which data were gathered during lesson observations and coaching sessions. These data were analysed to describe and exemplify the classroom environment, then further described against forms of teacher knowledge. Conjectures regarding the importance of teacher knowledge of content were made which formed a base for developing a model of teacher planning and pedagogy.

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.

Designing and using historical vignettes in science teaching : a personal account

Historical vignettes are interesting short stories which encapsulate a brief period of scientific history. They can be useful tools for teaching the nature of science, demonstrating the practices of science and making science fun. Historical vignettes illustrate the role of people and social processes in science. In this paper I describe my experience with writing and presenting an historical vignette during a Biology unit. Included is a copy of the vignette and I have identified some possible improvements that might lead to better outcomes. This may be helpful for other teachers who wish to try this strategy for themselves.

Understanding preservice teachers’ development of pedagogical knowledge practices when co-teaching primary science to peers

Preservice teachers articulate the need for more teaching experiences for developing their practices, however, extending beyond existing school arrangements may present difficulties. Thus, it is important to understand preservice teachers’ development of pedagogical knowledge practices when in the university setting. This mixed-method study investigated 48 second-year preservice teachers’ development of pedagogical knowledge practices as a result of co-teaching primary science to peers. Data were collected through a survey, video-recorded lessons, extended written responses and researcher observations. The study showed how these preservice teachers demonstrated 9 of 11 pedagogical knowledge practices within the co-teaching arrangement. However, research is needed to determine the level of development on each pedagogical knowledge practice and how these practices can be transferred into authentic primary classroom settings.

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.

The spatialized practices of teaching writing in Australian elementary schools : diverse students shaping discoursal selves

This paper discusses the teaching of writing within the competing and often contradictory spaces of high-stakes testing and the practices and priorities around writing pedagogy in diverse school communities. It uses socio-spatial theory to examine the real-and-imagined spaces (Soja, 1996) that influence and are influenced by teachers’ pedagogical priorities for writing in two linguistically diverse elementary school case studies. Methods of critical discourse analysis are used to examine rich data sets to make visible the discourses and power relations at play in the case schools. Findings show that when teachers’ practices focus on the teaching of structure and skills alongside identity building and voice, students with diverse linguistic backgrounds can produce dramatic, authoritative and resonant texts. The paper argues that “thirdspaces” can be forged that both attend to accountability requirements, yet also give the necessary attention to more complex aspects of writing necessary for students from diverse and multilingual backgrounds to invest in writing as a creative and critical form of communication for participation in society and the knowledge economy.

Robots, the internet and teaching history in the age of the NBN and the Australian curriculum

Have you ever wished you were Doctor Who and could pop yourself and your students into a Tardis and teleport them to an historical event or to meet a historical figure? We all know that unfortunately time travel is not (yet) possible, but maybe student and teacher teleportation just might be – sort of. Over the past few centuries and in lieu of time travel our communities have developed museums as a means of experiencing some of our history...

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.