scholarly journals Unfolding the Educational and Practical Resources Inherent in Mathematics for Teaching Mathematics

2020 ◽  
pp. 1-24
Author(s):  
Erich Christian Wittmann
Keyword(s):  
Learning Environments ◽  
Mathematics Teaching ◽  
Teaching Model ◽  
Main Role ◽  
The Common ◽  
Mathematics For Teaching ◽  
Didactical Situations ◽  
Natural Way ◽  
Theory Of Didactical Situations

AbstractThe objective of this introductory chapter is to explain the common rationale behind the papers of this volume. The structure is as follows. The first section shows that learning environments are a natural way to address teachers in their main role, teaching, and that therefore this approach is promising for improving mathematics teaching in an effective way. The section ends with a teaching model based on Guy Brousseau’s theory of didactical situations.

Towards a Problématique for Research on Mathematics Teaching

1990 ◽  
Vol 21 (4) ◽  
pp. 258-272
Author(s):  
Nicolas Balacheff
Keyword(s):  
Key Words ◽  
Mathematics Teaching ◽  
Theoretical Framework ◽  
Its Analysis ◽  
Didactique Des Mathématiques ◽  
Didactical Situation ◽  
Didactical Situations ◽  
Theory Of Didactical Situations

This article presents the main features of the theoretical framework of French research known as recherches en didactique des mathématiques. The foundation of this approach consists mainly of the relationships between two hypotheses and two constraints, which are presented together with some specific key words. Outlines are given of Brousseau's théorie des situations didactiques (theory of didactical situations). An example is given that presents in some detail the rationale for the construction of a didactical situation and its analysis. This article ends with some questions addressed to research on mathematics teaching.

scholarly journals Didactical situations to treat Lorentz and Galileo transformations in theoretical physics

2021 ◽  
Vol 19 (1 Jan-Jun) ◽  
Author(s):  
S. A. De Souza Farias ◽  
Damiao Pedro Meira Filho ◽  
J. K. Santos Kamassury
Keyword(s):  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Special Theory ◽  
Theoretical Physics ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Didactical Situations ◽  
Mathematical Relations ◽  
Physical Principles ◽  
Theory Of Didactical Situations

Notions of Electromagnetism and Special Theory of Relativity (STR) require important mathematical knowledge applied to theoretical physics. Recognizing pedagogical difficulties in the teaching of theoretical physics, the Theory of Didactical Situations (TDS), which consists of a set of practices that aim to contribute to the improvement of mathematics teaching. In this context, the present work is motivated to present a set of practices based on TDS with a focus on teaching Electromagnetism and STR, where problems that require an understanding of the transformations of Galileo and Lorentz. Specifically, the didactic situation is constructed by means of four problem proposals, while in the adidatic situation, the student is invited to understand the roles of these transformations in the study of these problems. Ultimately, the relevance of the educator in the institutionalization situation is reinforced, a moment when it must be clarified how all mathematical relations are strongly related to physical principles.

SUB-LOGARITHMIC ALGORITHMS FOR THE LARGEST EMPTY RECTANGLE PROBLEM

1993 ◽  
Vol 03 (01) ◽  
pp. 79-85
Author(s):  
STEPHAN OLARIU ◽  
WENHUI SHEN ◽  
LARRY WILSON
Keyword(s):  
Parallel Algorithms ◽  
Erew Pram ◽  
Pram Model ◽  
The Common ◽  
Crcw Pram ◽  
Natural Way

We show that the Largest Empty Rectangle problem can be solved by reducing it, in a natural way, to the All Nearest Smaller Values problem. We provide two classes of algorithms: the first one assumes that the input points are available sorted by x (resp. y) coordinate. Our algorithm corresponding to this case runs in O(log log n) time using [Formula: see text] processors in the Common-CRCW-PRAM model. For unsorted input, we present algorithms that run in [Formula: see text] time using [Formula: see text] processors in the Common-CRCW-PRAM, or in O( log n) time using [Formula: see text] processors in the EREW-PRAM model. No sub-logarithmic time parallel algorithms have been previously reported for this problem.

Building on and Extending the Characteristics of Gifted Learners: Implementing the Real Engagement in Active Problem Solving (REAPS) Teaching Model

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
June Maker ◽  
◽  
Randy Pease ◽  
Keyword(s):  
Problem Solving ◽  
Learning Environments ◽  
Fidelity Of Implementation ◽  
Teaching Model ◽  
Evidence Based ◽  
Gifted Learners ◽  
Real World Problem ◽  
Talented Students ◽  
High Level ◽  
Evidence Based Model

Real Engagement in Active Problem Solving (REAPS) is an evidence-based model for building on and extending the characteristics of gifted learners, enabling them to develop their exceptional talents. The purposes of this study were to (a) identify teachers who implemented the method at a high level of fidelity and (b) describe their ways of applying principles for talent development in content, processes, products, and learning environments. Fidelity of Implementation was high, ranging from 3.0 to 5.8, with a mean of 4.7 on a scale from 0 to 6. Teachers used methods identified as important for exceptionally talented students: engagement, challenge, interest, and relevance. Administrators enabled this high level of implementation. Because the study was conducted in one school, we recommend extending the research to other schools and contexts, and to consider the importance of real-world problem solving in developing the understanding and values needed to use exceptional talents wisely.

Introduction

2012 ◽  
Author(s):  
Jamie Terence Kelly
Keyword(s):  
Common Good ◽  
Democratic Theory ◽  
Framing Effects ◽  
Behavioral Approach ◽  
Empirical Psychology ◽  
Collective Interest ◽  
Individual Preferences ◽  
Electoral Outcomes ◽  
The Common

This introductory chapter first sets out the book's purpose, which is to argue that, just as in economics and law, normative democratic theory must begin to pay attention to the picture of human choice described by empirical psychology. Thus, it develops a behavioral approach to normative democratic theory. The book focuses on judgment-based theories—those that construe votes as judgments about the common good (or collective interest), rather than as individual preferences over electoral outcomes. It also focuses on framing effects, which occur when different but equivalent formulations of a problem result in substantively different decisions being made. An overview of the subsequent chapters is also presented.

Introduction

2007 ◽  
Author(s):  
MICHAEL AYERS
Keyword(s):  
Early Modern ◽  
Common Ground ◽  
Rene Descartes ◽  
Philosophical Theology ◽  
Baruch Spinoza ◽  
René Descartes ◽  
The Common ◽  
And Control

This introductory chapter explains the coverage of this book, which is about the relation between the concepts of rationalism, Platonism, and God. This book is intended as a contribution to the exploration and exposition of the common ground of the great early modern rationalist theories. It examines contemplation and control in Cartesian philosophy and analyses the priority of the perfect in the philosophical theology of the continental rationalists. It also provides commentaries on the relevant theories of philosophers Rene Descartes, Baruch Spinoza, and Gottfried Leibniz.

Introduction

2019 ◽  
pp. 1-42
Author(s):  
Adrian Briggs
Keyword(s):  
European Union ◽  
United Kingdom ◽  
International Law ◽  
Legal Framework ◽  
Private International Law ◽  
The European Union ◽  
The United Kingdom ◽  
The Common ◽  
Law And Legislation

This introductory chapter begins with a brief discussion of the effect of the unexecuted decision of the United Kingdom to leave the European Union. If the United Kingdom were to withdraw on the terms approved by Parliament, the resulting legal framework would, in principle, be that put in place by the European Union (Withdrawal) Act 2018. That is to say, on ‘Exit Day’, the European Communities Act 1972 will be repealed. This will, at a stroke, remove the legal basis upon which a substantial body of private international law takes effect in the legal order of the United Kingdom. The chapter then sets out the book’s focus, which is the conflict of laws, followed by discussions of the common law’s conception of private international law and legislation establishing private international law as European law.

Promoting Equity in Elementary School Mathematics

2022 ◽  
pp. 213-232
Author(s):  
Drew Polly ◽  
Madelyn Colonnese ◽  
Julie Bacak ◽  
Kaitlyn O. Holshouser ◽  
Wendy Lewis
Keyword(s):  
Elementary School ◽  
Learning Environments ◽  
Mathematics Teaching ◽  
Teacher Candidates ◽  
Teaching Practices ◽  
School Teacher ◽  
Elementary School Mathematics ◽  
Mathematics Tasks ◽  
Elementary School Learners ◽  
Mathematics Teaching Practices

This chapter describes the frameworks of mathematics tasks, equity-based mathematics teaching practices, technological pedagogical and content knowledge (TPACK), and how they relate to teaching for equity in virtual learning environments (VLE). The frameworks are used to describe vignettes from VLEs with elementary school learners and elementary school teacher candidates (future teachers). Implications of these vignettes include a need for an empirically based trajectory related to equity-based teaching practices as well as a need to consider which technologies in a VLE can be used to effectively promote equity-based mathematics teaching practices.

Implementation Example for the Structured Mathematics Teaching in Learning Environments During the Pandemic Period

2021 ◽  
pp. 301-326
Author(s):  
Eminer Nur Ünveren Bilgiç
Keyword(s):  
Distance Education ◽  
Learning Environments ◽  
Prospective Teachers ◽  
Mathematics Teaching ◽  
Learning Materials ◽  
Teaching Process ◽  
Course Content ◽  
Education Process

The purpose of the study is to provide exemplary work for academicians and field experts working in the field during the COVID-19 outbreak to effectively use technology in mathematics teaching environments in the distance education process and integrate it into teaching environments. Both the course content presented to prospective teachers and also the learning materials created by the prospective-teachers in line with the learning acquisitions of the course have become a part of the teaching process, and the teaching process has been structured by integrating both the course content and the prepared learning materials into the teaching process under the TPACK theory frame.

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