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How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
This book brings together texts that involve research covering various topics. The main objective of this work is to highlight the plurality of methodologies, bibliographic sources and objects of study that circulate in the most diverse countries in the postgraduate area.
The premise of the 15th ICMI Study is that teachers are key to students' opportunities to learn mathematics. What teachers of mathematics know, care about, and do is a product of their experiences and socialization, together with the impact of their professional education. The Professional Education and Development of Teachers of Mathematics assembles important new international work- development, research, theory and practice - concerning the professional education of teachers of mathematics. As it examines critical areas to reveal what is known and what significant questions and problems warrant collective attention, the volume also contributes to the strengthening of the international community of mathematics educators. The Professional Education and Development of Teachers of Mathematics is of interest to the mathematics education community as well as to other researchers, practitioners and policy makers concerned with the professional education of teachers.
O amor à poesia ressignifica os encontros. Sobretudo os encontros felizes em vida celebrada. Na singularidade poética de Marco Lucchesi, esses alcances parecem se dar naturalmente. Nascem da expansão de fronteiras idiomáticas e culturais próprias da atitude do poeta. Criador de geografias plurais da palavra. Traduções conectoras de longínquas terras em sedutora erudição. Aproximações entre mundos (im)possíveis. Este belo livro resulta de outro desses percursos nomadistas do poeta, incensado pelos aromas do Oriente dessa vez à luz da Índia. Ao longo de todo um cenário de encontros com alunos e importantes poetas e intelectuais representativos de suas respectivas línguas de ex...
Beliefs and Mathematics is a Festschrift honoring the contributions of Günter Törner to mathematics education and mathematics. Mathematics Education as a legitimate area of research emerged from the initiatives of well known mathematicians of the last century such as Felix Klein and Hans Freudenthal. Today there is an increasing schism between researchers in mathematics education and those in mathematics as evidenced in the Math wars in the U.S and other parts of the world. Günter Törner represents an international voice of reason, well respected and known in both groups, one who has successfully bridged and worked in both domains for three decades. His contributions in the domain of bel...
Este livro reúne as conferências apresentadas durante o I Colóquio Internacional Marco Lucchesi que ocorreu em Roma nos dias 15 e 16 de janeiro de 2024 na Embaixada do Brasil. As apresentações foram realizadas por palestrantes de diversos países e, por este motivo, nesta publicação, foram mantidas as línguas usadas por cada integrante do evento (português, italiano, francês, espanhol e inglês).
Nesta obra, Alexandre Marzullo nos presenteia com um caderno de ensaios filosóficos-poéticos que tem como tema central a escrita. "Estes fragmentos filosófico-poéticos debruçam-se – com ímpeto – sobre a escrita como tema. Mas à escrita não se restringem. Afinal, falar sobre uma coisa, em um esforço detido de reflexão, é saltar : falar sobre todas as outras coisas possíveis, na visão de sua correspondência com aquela primeira da qual se trata em origem. Porque tudo aquilo que se corresponde em um peito vivo deseja a voz desse peito mesmo que a carrega: quer ser ouvido por aquele mesmo que fala. O que significa que refletir sobre algo é, em última instância, falar sobre amor, mesmo não o sabendo; é falar sobre o que se perde e sobre o medo de perder – a experiência fulminante do amar."
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This book aims to contribute to debates in the fields of political geography, geopolitics and territorial management from the point of view of authors who work in Brazilian universities in the five regions of the country.