Konkret material i matematikundervisningen – bekymmer och motsättningar : En systematisk litteraturstudie om laborativ matematik

Laborativt arbete med konkret material är en arbetsform inom matematiken som på en del håll åter fått uppsving i ett försök att råda bot på svenska elevers försämrade prestationer i och intresse för matematik. Denna litteraturstudies syfte är att undersöka vilka faktorer som kan påverka negativt vid laborativt arbete med konkret material i matematikundervisningen. I resultatet av litteraturstudien synliggörs huvudsakligen två faktorer som är av större betydelse för undervisningens utfall samt en faktor av mindre betydelse, elevernas ålder. Den första faktorn behandlar valet av material och materialets utformning, vilket kan inverka på elevernas förståelse. Om det konkreta materialet är mycket likt de föremål elever möter i sin vardag, såsom pizzaslices eller pengar, kan denna likhet störa elevernas matematiska förståelse genom att för stor uppmärksamhet riktas mot igenkännandet och att se föremålen som potentiella leksaker, istället för att se dem som konkreta symboler för abstrakt matematik. Detta tycks inte åldersbetingat, utan förekommer i olika årskurser. Den andra faktorn som uppmärksammats är lärarens vägledande roll. Läraren behöver adekvat kompetensutveckling och professionellt stöd i arbetet med konkret material för att öka chanserna att arbetssättet får ett så gynnsamt utfall som möjligt. Läraren spelar en stor roll i både valet av konkret material och i hur instruktioner samt vägledning ges. Det är också viktigt att läraren i undervisningen bjuder in till interaktion och kommunikation om elevernas funna resultat och lösningsförslag för att stärka elevernas förståelse. Sökandet efter relevant litteratur genomfördes i AABRI, ERIC, Google Scholar, Libris, och Summon.

Understanding Teacher and Student Learning Situated in a School-wide Implementation of Fractions Instruction

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

Problem solving competency and the mathematical kangaroo

The goal of the study was to investigate differences in how two groups of students activated mathematical competencies in the mathematical kangaroo (MK). The two groups, group 1 and 2, were identified from a sample of 264 students (grade 7, age 13) through high achievement (top 20 %) in only one of the tests: the MK or a curriculum bounded test (CT). Analysis of mathematical competencies showed that the high achievers in the MK, activated the problem solving competency to a greater extent than the high achievers in the CT, when doing the MK. The results indicate the importance of using non-traditional tests in the assessment process of students to be able to find students that might possess good mathematical competencies although they do not show it on curriculum bounded tests.

Educação matemática: pesquisas e possibilidades

This book presents a current overview of themes that entangle research in Mathematics Education, which were produced in conjunction with professors who act in the Mathematics Education field at PPGECM (Science and Mathematics Post-graduation Program), that counts with professors from many universities, especially UFPR (Paraná's Federal University), UTFPR (Paraná's Technological Federal University) and UDESC (Santa Catarina's Federal University).The set of texts brings some areas of interest, studies that are in development and research that have been completed. It is expected that the chapters present the program, aspects of its production, interests and theoretical/methodological relations, contributing to the strengthening of Mathematics Education as a research field and familiarization and deepening of the topics discussed.

Didactic transposition: an example in the educative system in Costa Rica

This paper includes some fundamental ideas about the theory of didactic transposition of Yve Chevallard (1980), from which it is made an analysis of the knowledge transformation suffers from the mathematical level to the scholastic level. To demonstrate this transformation, it is analyzed the theme of integers, which is included in the seventh- grade curriculum of the educational system of Costa Rica.

Diseño de un modelo de situación problema, con la unidad facilitadora solidaria llamada Belisol, para fortalecer el pensamiento numérico y variacional, en los estudiantes de la Institución Educativa Rural Benigno Mena González

Al analizar los resultados deficientes de las Pruebas Saber, del PTA ( Programa Todos a Aprender del MEN), y la participación en las Olimpiadas del Conocimiento, de los estudiantes de la Institución Educativa Rural Benigno Mena González del municipio de San Jerónimo, se consideró implementar un proyecto pedagógico, como plan de mejoramiento para la enseñanza y aprendizaje de las matemáticas, que sirviera como una iniciativa para fortalecer los pensamientos numérico y variacional en los estudiantes de secundaria de la Institución; se buscaba, con la implementación de esta propuesta, desarrollar habilidades en dominio, comprensión y solución de situaciones problemas cotidianas dentro del contexto escolar y desde la innovación de nuevas prácticas metodológicas en los procesos educativos. Desde esta perspectiva, nace el interrogante: ¿Cómo modelar una situación problema, teniendo como motivo la unidad facilitadora solidaria denominada Belisol, para fortalecer el pensamiento numérico y variacional, en los estudiantes de la Institución Educativa Rural Benigno Mena González del municipio de San Jerónimo?, para dar tránsito a una propuesta de investigación innovadora. Ahora bien, para intervenir y reflexionar sobre este interrogante, se propuso el método de Investigación Acción Participación (IAP), el cual se aplica a estudios que se interesan sobre realidades humanas y problemáticas cotidianas o sociales, que además, sean reales, de la acción, y de constante participación de los sujetos, entidades o comunidades involucradas; aquí cabe la posibilidad de un aprendizaje cooperativo, colectivo, y por supuesto, colaborativo donde se ha planteado como motivo de la situación problema planteada la unidad financiera llamada Belisol con el fin de exteriorizar los fundamentos de una acción formativa, orientada a la incursión en el ámbito de la educación matemática económica financiera, a través del ejercicio del ahorro escolar y el trueque, promoviendo de esta manera el espíritu solidario en la comunidad Benigniana.

A operacionalização do programa de matemática em vigor no 1.º Ciclo do Ensino Básico pelos professores do concelho de Machico

Trabalho de projeto apresentado à Escola Superior de Educação de Paula Frassinetti para obtenção do grau de Mestre em Ciências da Educação Especialização em Supervisão Pedagógica

GeoGebraTUTOR : développement d’un système tutoriel autonome pour l’accompagnement d’élèves en situation de résolution de problèmes de démonstration en géométrie plane et genèse d’un espace de travail géométrique idoine

Travaux d'études doctorales réalisées conjointement avec les travaux de recherches doctorales de Nicolas Leduc, étudiant au doctorat en génie informatique à l'École Polytechnique de Montréal.

O currículo de matemática do 1º ciclo doensino secundário de Cabo Verde na perspectiva de professores

Este estudo tem por objetivo compreender a perspetiva de professores sobre o currículo de Matemática do 1º ciclo do Ensino Secundário cabo-verdiano e conhecer necessidades de formação que identificam, para um melhor desempenho na sua catividade profissional. As questões de estudo são: 1) Como se reveem os professores de Matemática no currículo do 1º ciclo do Ensino Secundário, enquanto agentes que interpretam e implementam esse currículo? 2) Que potencialidades e dificuldades reconhecem nesse currículo? 3) Que áreas consideram haver necessidade de formação, para a melhoria da sua prática docente, nesse nível de ensino? O desenvolvimento do referencial teórico integra duas áreas temáticas como eixos centrais: o currículo, o professor e o professor de Matemática. Foi feita uma análise de normativos cabo-verdianos para a educação, entre os quais se destacam a Lei de Bases do Sistema Educativo, o Plano de estudos para o ensino secundário e o Programa de Matemática do 1o ciclo do Ensino Secundário. A metodologia adotada na investigação segue uma abordagem interpretativa e descritiva, suportada por um design de estudo de caso. São estudados três casos, relativos a professores de Matemática cabo-verdianos do 1º ciclo do Ensino Secundário. A recolha de dados recorre a urna entrevista semiestruturada a cada professor, à observação de três aulas por professor participante e à recolha documental. A análise de dados foi feita utilizando principalmente a técnica de análise de conteúdos. Os professores revêem-se como executores de um currículo uniforme, de cumprimento obrigatório, normativo, emanado centralmente e do qual procuram interpretar as intenções. A sua visão de currículo é centrada nos conteúdos do programa, um dos motivos para que o enquadramento ao nível dos meios institucionais e as competências esperadas ao nível do saber fazer e ao nível do saber ser nem sempre serem conhecidas e/ou cumpridas. Em Acão, revêem-se como figuras centrais do currículo. Todos se reveem com mais competência na implementação curricular à medida que vão adquirindo experiência profissional. Concordam com os temas do programa e um deles sugere a inclusão de um tema. Consideram que os conteúdos nem sempre estão bem organizados e mostram a necessidade de a metodologia do programa ser mais detalhada, evidenciando claramente os seus propósitos. Eventualmente, podem não concordar com a estrutura de currículo em espiral do programa. Os professores identificam mais formação com melhor desempenho. As necessidades de formação são: Metodologia do Ensino da Matemática, Resolução de Problemas, Avaliação e a Geometria ligada à utilização de materiais pedagógicos. O estudo parece indicar que os professores não desenvolvem práticas diferentes por não terem essa vivência e aponta os professores mais jovens como mais abertos à mudança. ABSTRACT: The aim of this study is to understand the perspective of the teacher in relation to the Mathematics curriculum of the 1st cycle of Secondary School of Cape Verde (grades 7-8) and to learn about his/her training needs to develop better skills and performance in their professional activity. The key questions in this study are: 1) how do Mathematics teachers, acting in the capacity of agents who interpret and implement the 1st cycle of Secondary School curriculum, see themselves in this curriculum? 2) What potentialities and difficulties can they recognize in the curriculum? 3) What areas do they consider in need of training to improve teaching capacity within such education grade? The theoretical framework of this investigation integrates two main areas: the curriculum and the teacher. An analysis of Cape-Verdian normative texts for education has been made, including the Lei de Bases do Sistema Educativo (Basis Law of the Educational System), the Study plan for secondary school and the Mathematics program of the 1st cycle of secondary school. ln terms of methodology, we opted for an interpretative approach to our investigation, namely the case study. We looked at three case studies concerning the Cape-Verdian mathematics teacher of the 1st cycle of secondary school. The data collection uses a semi­structured interview for each teacher, the observation of three classes per participating teacher and the documental collection. Content analysis is the main technique used for analyzing the data. Teachers see themselves as practitioners of a uniform curriculum with mandatory compliance and delineated guidelines set by the administration, and they follow their own understanding of its intended purpose. Their vision of the curriculum is focused on program contents, one of the reasons why the expected skills at the level of "how to do" and "how to be" are not always known and/or done. ln their professional setting they see themselves with professional skills growing in tandem with professional experience. They all agree with the program contents but one of them suggests one content to add. ln their opinion the program is not always well organized and they suggest the need for a more comprehensive and detailed methodology of program contents. ln addition, they might not agree with the spiral structure of the program curriculum. They also identified the need for more elaborate professional training including: A Methodology for Mathematics Education, solving problems, Evaluation and the Geometry related to the utilization of pedagogical materials. The study seems to indicate that teachers refrain from developing different practices because of lack of experience but also demonstrates that younger teachers are more open to change.

Os inéditos-viáveis na e da formação continuada de professores que ensinam matemática nos anos iniciais da educação de jovens e adultos

Tese (doutorado)—Universidade de Brasília, Faculdade de Educação, Programa de Pós-Graduação em Educação, 2016.

Knowledge Construction: individual or social?

For many years, battles raged between those who saw knowledge as perception of a given reality and those who saw it as being constructed through rational activity. More recently, epistemological debates have focused on that activity being essentially individual or social. Initially, the International Group for the Psychology of Mathematics Education (PME) was heavily influenced by the idea that mathematical knowledge is constructed by individuals, and particularly by von Glasersfeld’s “radical” constructivism. The social constructivist thesis that mathematics is a social construction challenged this dominant notion, but Steve Lerman critiqued the “shared consciousness” interpretation of social constructivism and articulated the sociocultural idea of the centrality of social interactions. His influence led a strong turn to the social, with a focus on intersubjectivity in mathematical knowledge and mathematics learning. Steve not only challenged individual people’s ideas but also drew PME into a position where sociocultural and other poststructural theories are in regular use.

Two of everything: developing functional thinking in the primary grades through children's literature

Traditionally algebra has been regarded as the domain of the secondary school years in Australia and many other countries. Non-mathematics teachers, parents and students often narrowly regard algebra as the manipulation of symbols adhering to tightly prescribed rules (Serow, Callingham & Muir, 2013). It is now recognised, however, that foundational ideas associated with algebraic thinking can, and should be, included in mathematics curricula in the pre-school and primary years (Bobis, Mulligan & Lowrie, 2009). This stance is reflected in the Australian Curriculum: Mathematics (Australian Curriculum Assessment & Reporting Authority, 2012) which extends key algebraic ideas to patterns and generalisations, and acknowledges that number and algebra are developed together as each enriches the study of the other. This article explores the concept of functional thinking and demonstrates how the story, ‘Two of Everything’ (Hong, 1993) is employed as a springboard for developing functional thinking with students from the early years through to upper primary schooling.

Primary teachers’ algebraic thinking: example from lesson study

Previous studies have reported on primary children’s algebraic thinking and generalising in a range of problem settings but there is little evidence of primary teachers’ knowledge of algebraic thinking. In this paper the development in algebraic thinking of one primary teacher who taught a research lesson in a Japanese Lesson Study project involving teachers from three primary schools is presented. The findings suggest the need for professional learning in algebra and reasoning and indicate the value of Lesson Study.

Transformations of teaching and learning through digital technologies

This chapter is a critical synthesis of research related to the transformations that take place when digital technologies are incorporated into teaching and learning practices. In developing this synthesis, research from all levels of education was reviewed with a focus on the opportunities digital technologies offer for cognitive, pedagogical, affective and professional change. The chapter is structured in alignment with Pierce and Stacey’s (Pierce and Stacey, Int J Comput Math Learn 15(1):1–20 2010) map of pedagogical opportunities in which three dimensions for educational transformation were identified: tasks, classroom, and subject. A discussion of future directions for research into technology enhanced mathematics education concludes the review.

Primary teachers notice the impact of language on children’s mathematical reasoning

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children’s mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise mathematical reasoning in children’s actions and words. As part of a larger study, we explored whether observation of educators conducting mathematics lessons can develop teachers’ sensitivity in noticing children’s reasoning and consideration of how to support reasoning. In the Mathematical Reasoning Professional Learning Research Program, demonstration lessons were conducted in Australian and Canadian primary classrooms. Data sources included post-lesson group discussions. Observation of demonstration lessons and engagement in post-lesson discussions proved to be effective vehicles for developing a professional eye for noticing children’s individual and whole-class reasoning. In particular, the teachers noticed that children struggled to employ mathematical language to communicate their reasoning and viewed limitations in language as a major barrier to increasing the use of mathematical reasoning in their classrooms. Given the focus of teachers’ noticing of the limitations in some types of mathematical language, it seems that targeted support is required for teachers to facilitate classroom discourse for reasoning.