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Early Algebra

Author : Carolyn Kieran

Publisher : Springer

Page : 48 pages

File Size : 34,92 MB

Release : 2016-07-11

Category : Education

ISBN : 3319322583

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Book Description

This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.



The Real ACT (CD) 3rd Edition

Author : ACT, Inc.

Publisher : Peterson's

Page : 936 pages

File Size : 12,17 MB

Release : 2011-09-06

Category : Study Aids

ISBN : 9780768934403

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Book Description

The Real ACT Prep Guide with CD is the only book with insider test-taking tips and strategy, practice, and insight from the makers of the ACT. This is the only guide that includes 5 previously administered, full-length ACT tests written by the actual test maker (including 2 NEW practice tests). Also included is ACT content and procedures you'll follow when actually taking the test, along with in-depth review of the optional Writing Test and how it is scored; examples of all the question types; and suggestions on how you might approach the questions. The supplemental CD features a complete electronic copy of Peterson's Cool Colleges 101 and additional online college planning resources from Peterson's. The only guide that includes 5 previously administered, full-length ACT tests written by the actual test maker (including 2 NEW practice tests) ACT content and procedures you'll follow when actually taking the test Valuable information about tuition payment plans All the question types you can expect to find on the ACT Suggestions on how you might approach the questions and Peterson's tried-and-true test-taking strategies and tips



Research on Teaching and Learning Probability

Author : Carmen Batanero

Publisher : Springer

Page : 40 pages

File Size : 25,17 MB

Release : 2016-07-12

Category : Education

ISBN : 3319316257

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Book Description

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.







Mathematical Modelling and Applications

Author : Gloria Ann Stillman

Publisher : Springer

Page : 620 pages

File Size : 25,69 MB

Release : 2017-11-05

Category : Education

ISBN : 3319629689

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Book Description

This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.



Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Author : Carolyn Kieran

Publisher : Springer

Page : 443 pages

File Size : 34,22 MB

Release : 2017-12-04

Category : Education

ISBN : 3319683519

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Book Description

This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.



The Intentional Teacher

Author : Ann S. Epstein

Publisher : Conran Octopus

Page : 284 pages

File Size : 17,37 MB

Release : 2014

Category : Education

ISBN : 9781938113062

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Book Description

Young children and teachers both have active roles in the learning processHow do preschoolers learn and develop? What are the best ways to support learning in the early years? This revised edition of The Intentional Teacher guides teachers to balance both child-guided and adult-guided learning experiences that build on children's interests and focus on what they need to learn to be successful in school and in life.This edition offers new chapters on science, social studies, and approaches to learning. Also included is updated, expanded information on social and emotional development, physical development and health, language and literacy, mathenatics, and the creative arts. In each chapter are many practical teaching strategies that are illustrated with classroom-based anecdotes.The Intentional Teacher encourages readers to- Reflect on their principles and practices- Broaden their thinking about appropriate early curriculum content and instructional methods- Discover specific ideas and teaching strategies for interacting with children in key subject areasIntentional teaching does not happen by chance. This book will help teachers apply their knowledge of children and of content to make thoughtful, intentional use of both child-guided and adult-guided experiences.



Qualitative Choice Analysis

Author : Kenneth Train

Publisher : MIT Press

Page : 282 pages

File Size : 20,26 MB

Release : 1986

Category : Business & Economics

ISBN : 9780262200554

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Book Description

This book addresses two significant research areas in an interdependent fashion. It is first of all a comprehensive but concise text that covers the recently developed and widely applicable methods of qualitative choice analysis, illustrating the general theory through simulation models of automobile demand and use. It is also a detailed study of automobile demand and use, presenting forecasts based on these powerful new techniques. The book develops the general principles that underlie qualitative choice models that are now being applied in numerous fields in addition to transportation, such as housing, labor, energy, communications, and criminology. The general form, derivation, and estimation of qualitative choice models are explained, and the major models - logit, probit, and GEV - are discussed in detail. And continuous/discrete models are introduced. In these, qualitative choice methods and standard regression techniques are combined to analyze situations that neither alone can accurately forecast. Summarizing previous research on auto demand, the book shows how qualitative choice methods can be used by applying them to specific auto-related decisions as the aggregate of individuals' choices. The simulation model that is constructed is a significant improvement over older models, and should prove more useful to agencies and organizations requiring accurate forecasting of auto demand and use for planning and policy development. The book concludes with an actual case study based on a model designed for the investigations of the California Energy Commission. Kenneth Train is Visiting Associate Professor in Economics at the University of California, Berkeley, and Director of Economic Research at Cambridge Systematics, Inc., also in Berkeley. Qualitative Choice Analysisis included in The MIT Press Transportation Studies Series, edited by Marvin L. Manheim.



Teaching Tech Together

Author : Greg Wilson

Publisher : CRC Press

Page : 229 pages

File Size : 31,88 MB

Release : 2019-10-08

Category : Computers

ISBN : 1000728153

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Book Description

Hundreds of grassroots groups have sprung up around the world to teach programming, web design, robotics, and other skills outside traditional classrooms. These groups exist so that people don't have to learn these things on their own, but ironically, their founders and instructors are often teaching themselves how to teach. There's a better way. This book presents evidence-based practices that will help you create and deliver lessons that work and build a teaching community around them. Topics include the differences between different kinds of learners, diagnosing and correcting misunderstandings, teaching as a performance art, what motivates and demotivates adult learners, how to be a good ally, fostering a healthy community, getting the word out, and building alliances with like-minded groups. The book includes over a hundred exercises that can be done individually or in groups, over 350 references, and a glossary to help you navigate educational jargon.