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Teaching and Learning of Calculus

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319329741 9783319329758 Year: Pages: 37 DOI: 10.1007/978-3-319-32975-8 Language: English
Publisher: Springer
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-24 17:52:35
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This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.

Problem Solving in Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319407296 9783319407302 Year: Pages: 39 DOI: 10.1007/978-3-319-40730-2 Language: English
Publisher: Springer
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-30 17:39:59
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This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches – why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches – what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts – what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled.

Teaching and Learning Mathematical Modelling: Approaches and Developments from German Speaking Countries

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319450032 9783319450049 Year: Pages: 42 DOI: 10.1007/978-3-319-45004-9 Language: English
Publisher: Springer
Subject: Mathematics --- Education
Added to DOAB on : 2017-02-06 18:21:56
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This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established.

Teaching and Learning About Whole Numbers in Primary School

Authors: --- --- ---
Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319451121 9783319451138 Year: Pages: 50 DOI: 10.1007/978-3-319-45113-8 Language: English
Publisher: Springer
Subject: Mathematics --- Education
Added to DOAB on : 2017-02-10 14:36:17
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This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future.The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319442716 9783319442723 Year: Pages: 50 DOI: 10.1007/978-3-319-44272-3 Language: English
Publisher: Springer
Subject: Education --- Mathematics
Added to DOAB on : 2017-02-21 14:42:35
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This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental issues. Further, it discusses various topics, including curriculum studies and implementation, spatial abilities and geometric reasoning, as well as the psychological roots of geometrical thinking and teacher preparation in geometry education. It considers these issues from historical, epistemological, cognitive semiotic and educational points of view in the context of students' difficulties and the design of teaching and curricula.

Instructional Scaffolding in STEM Education: Strategies and Efficacy Evidence

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ISBN: 9783319025643 9783319025650 Year: Pages: 144 DOI: 10.1007/978-3-319-02565-0 Language: English
Publisher: Springer
Subject: Science (General) --- Education
Added to DOAB on : 2017-02-21 15:16:55
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This book uses meta-analysis to synthesize research on scaffolding and scaffolding-related interventions in STEM (science, technology, engineering, and mathematics) education. Specifically, the volume examines the extent to which study quality, assessment type, and scaffolding characteristics (strategy, intended outcome, fading schedule, scaffolding intervention, and paired intervention) influence cognitive student outcomes. It includes detailed descriptions of the theoretical foundations of scaffolding, scaffolding strategies that have been proposed to meet different intended learning outcomes in STEM, and associated efficacy information. Furthermore, the book describes assessment strategies and study designs which can be used to evaluate the influence of scaffolding, and suggests new fields in which scaffolding strategies that have proven efficacious may be used.

Chapter: 'Future Research Directions for Innovating Pedagogy' from book: Adaptive and Adaptable Learning:11th European Conference on Technology Enhanced Learning, EC-TEL 2016, Lyon, France, September 13-16, 2016, Proceedings (Book chapter)

Authors: --- --- ---
Book Series: Lecture Notes in Computer Science ISSN: 0302-9743 / 1611-3349 ISBN: 9783319451527 9783319451534 Year: Pages: 3 DOI: https://doi.org/10.1007/978-3-319-45153-4_83 Language: English
Publisher: Springer
Subject: Education
Added to DOAB on : 2017-11-27 16:46:41
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A series of reports on Innovating Pedagogy were launched in 2012 to look at the trends that show how practitioners may engage in innovation in pedagogy. This paper looks at the latest set of trends, and highlights four 2015 trends that seem particularly rich for researchers to explore in the next five years.

Tra insegnamento e ricerca. Entre enseignement et recherche: La storia della Rivoluzione francese. L’histoire de la Révolution française

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Book Series: Clio: Saggi di scienze storiche, archeologiche e storico-artistiche ISSN: 2532-4608 ISBN: 9788888904207 Year: Volume: 15 Pages: 444 DOI: 10.6093/978-88-88904-20-7 Language: Italian
Publisher: FedOA - Federico II University Press
Subject: History
Added to DOAB on : 2018-06-05 17:19:21
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What is the place of the French Revolution in teaching history? What are the ideological trends and pedagogic messages that are used in school textbooks? Are these textbooks simple "national autobiographies" or the faithful reflection of historical research on the topic? The contributions collected in this volume seek to answer some of these questions, taking into account different countries, from France to Russia, from the United States to China. In a time like ours, where much is said about the public use of history, the relationship between historical research, teaching and dissemination remains a fundamental theme.

Research on Teaching and Learning Probability

Authors: --- --- --- --- et al.
Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319316246 9783319316253 Year: Pages: 33 DOI: 10.1007/978-3-319-31625-3 Language: English
Publisher: Springer
Subject: Education
Added to DOAB on : 2016-12-20 13:01:35
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This book summarizes the vast amount of research related to teaching and learning probability that has been conducted for more than 50 years in a variety of disciplines. It begins with a synthesis of the most important probability interpretations throughout history: intuitive, classical, frequentist, subjective, logical propensity and axiomatic views. It discusses their possible applications, philosophical problems, as well as their potential and the level of interest they enjoy at different educational levels. Next, the book describes the main features of probabilistic thinking and reasoning, including the contrast to classical logic, probability language features, the role of intuitions, as well as paradoxes and the relevance of modeling. It presents an analysis of the differences between conditioning and causation, the variability expression in data as a sum of random and causal variations, as well as those of probabilistic versus statistical thinking. This is followed by an analysis of probability’s role and main presence in school curricula and an outline of the central expectations in recent curricular guidelines at the primary, secondary and high school level in several countries. This book classifies and discusses in detail the three different research periods on students’ and people’s intuitions and difficulties concerning probability: early research focused on cognitive development, a period of heuristics and biases programs, and the current period marked by a multitude of foci, approaches and theoretical frameworks.

International Comparative Studies in Mathematics: Lessons for Improving Students’ Learning

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319424132 9783319424149 Year: Pages: 36 DOI: 10.1007/978-3-319-42414-9 Language: English
Publisher: Springer
Subject: Education --- Mathematics
Added to DOAB on : 2017-02-06 14:38:40
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This open access book examines the cultural and educational factors that influence how successfully students learn mathematics; focuses on international comparative studies as a means of generating theories and improving students’ learning; and discusses four valuable lessons that can be learned from international comparative studies with regard to improving students’ learning.

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