Modeling with Mathematics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Modeling with Mathematics PDF full book. Access full book title Modeling with Mathematics by Nancy Butler Wolf. Download full books in PDF and EPUB format.
Author: Nancy Butler Wolf
Publisher: Heinemann Educational Books
ISBN: 9780325062594
Category : Education
Languages : en
Pages : 0
Get Book Here
Book Description
"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley, Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think "This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level." -David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America We all use math to analyze everyday situations we encounter. Whether we realize it or not, we're modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics, Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including: collecting data and formulating a mathematical model interpreting results and comparing them to reality learning to communicate their solutions in meaningful ways. This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark. Through detailed examples and hands-on activities, Nancy shows how to guide your students to become active participants in mathematical explorations who are able to answer the question, "What did I just figure out?" Her approach values all students as important contributors and shows how instruction focused on mathematical modeling engages every learner regardless of their prior history of success or failure in math.
Author: Nancy Butler Wolf
Publisher: Heinemann Educational Books
ISBN: 9780325062594
Category : Education
Languages : en
Pages : 0
Get Book Here
Book Description
"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley, Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think "This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level." -David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America We all use math to analyze everyday situations we encounter. Whether we realize it or not, we're modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics, Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including: collecting data and formulating a mathematical model interpreting results and comparing them to reality learning to communicate their solutions in meaningful ways. This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark. Through detailed examples and hands-on activities, Nancy shows how to guide your students to become active participants in mathematical explorations who are able to answer the question, "What did I just figure out?" Her approach values all students as important contributors and shows how instruction focused on mathematical modeling engages every learner regardless of their prior history of success or failure in math.
Author: Edward Beltrami
Publisher: Academic Press
ISBN: 1483267865
Category : Technology & Engineering
Languages : en
Pages : 294
Get Book Here
Book Description
Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.
Author: Christian R. Hirsch
Publisher:
ISBN: 9780873539739
Category : Mathematical models
Languages : en
Pages : 0
Get Book Here
Book Description
Mathematical modeling plays an increasingly important role both in real-life applications and within mathematics education itself. This 2016 volume of Annual Perspectives in Mathematics Education (APME) focuses on this key topic from a wide variety of perspectives and distinguishes it from modeling mathematics.
Author: Richard Lesh
Publisher: Springer Science & Business Media
ISBN: 9400762712
Category : Education
Languages : en
Pages : 635
Get Book Here
Book Description
Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.
Author: Sarah P. Otto
Publisher: Princeton University Press
ISBN: 1400840910
Category : Science
Languages : en
Pages : 745
Get Book Here
Book Description
Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
Author: Walter J. Meyer
Publisher: Courier Corporation
ISBN: 0486137244
Category : Mathematics
Languages : en
Pages : 450
Get Book Here
Book Description
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition.
Author: Michael Friedman
Publisher: Birkhäuser
ISBN: 9783030978327
Category : Mathematics
Languages : en
Pages : 443
Get Book Here
Book Description
This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.
Author: Alan Garfinkel
Publisher: Springer
ISBN: 3319597310
Category : Mathematics
Languages : en
Pages : 456
Get Book Here
Book Description
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
Author: K.P Gravemeijer
Publisher: Springer Science & Business Media
ISBN: 9401731942
Category : Education
Languages : en
Pages : 304
Get Book Here
Book Description
This book explores the option of building on symbolizing, modeling and tool use as personally meaningful activities of students. It discusses the dimension of setting: varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction; and the dimension of the theoretical framework of the researcher: varying from constructivism, to activity theory, cognitive psychology and instructional-design theory.
Author: Elizabeth G. Arnold
Publisher: National Council of Teachers of English
ISBN: 9781680540468
Category : Mathematical models
Languages : en
Pages : 0
Get Book Here
Book Description
This book explores what it means to teach modeling. In part I, the authors discuss mathematical modeling broadly and allow you to explore the student practices and perspectives involved, how modeling can empower students, and classroom communities that support modeling. In part II, the authors launch you on your journey of becoming a teacher of modeling by illustrating features of modeling that are evident in the classrooms of teacher who engage their students in modeling and by sharing specific strategies for making modeling a part of your own classroom practices. In part III, they examine the complementary perspectives of mathematical and statistical models, the role of modeling in the secondary mathematics curriculum, and the role of technology in supporting modeling. Finally, they share wisdom from other teachers who have engaged in this journey and invite you to join in the modeling community.
