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This book speaks about physics discoveries that intertwine
mathematical reasoning, modeling, and scientific inquiry. It offers
ways of bringing together the structural domain of mathematics and
the content of physics in one coherent inquiry. Teaching and
learning physics is challenging because students lack the skills to
merge these learning paradigms. The purpose of this book is not
only to improve access to the understanding of natural phenomena
but also to inspire new ways of delivering and understanding the
complex concepts of physics. To sustain physics education in
college classrooms, authentic training that would help develop high
school students' skills of transcending function modeling
techniques to reason scientifically is needed and this book aspires
to offer such training The book draws on current research in
developing students' mathematical reasoning. It identifies areas
for advancements and proposes a conceptual framework that is tested
in several case studies designed using that framework. Modeling
Newton's laws using limited case analysis, Modeling projectile
motion using parametric equations and Enabling covariational
reasoning in Einstein formula for the photoelectric effect
represent some of these case studies. A wealth of conclusions that
accompany these case studies, drawn from the realities of classroom
teaching, is to help physics teachers and researchers adopt these
ideas in practice.
This book speaks about physics discoveries that intertwine
mathematical reasoning, modeling, and scientific inquiry. It offers
ways of bringing together the structural domain of mathematics and
the content of physics in one coherent inquiry. Teaching and
learning physics is challenging because students lack the skills to
merge these learning paradigms. The purpose of this book is not
only to improve access to the understanding of natural phenomena
but also to inspire new ways of delivering and understanding the
complex concepts of physics. To sustain physics education in
college classrooms, authentic training that would help develop high
school students' skills of transcending function modeling
techniques to reason scientifically is needed and this book aspires
to offer such training The book draws on current research in
developing students' mathematical reasoning. It identifies areas
for advancements and proposes a conceptual framework that is tested
in several case studies designed using that framework. Modeling
Newton's laws using limited case analysis, Modeling projectile
motion using parametric equations and Enabling covariational
reasoning in Einstein formula for the photoelectric effect
represent some of these case studies. A wealth of conclusions that
accompany these case studies, drawn from the realities of classroom
teaching, is to help physics teachers and researchers adopt these
ideas in practice.
This valuable resource provides an overview of recent research and
strategies in developing and applying modelling to promote
practice-based research in STEM education. In doing so, it bridges
barriers across academic disciplines by suggesting activities that
promote integration of qualitative science concepts with the tools
of mathematics and engineering. The volume's three parts offer a
comprehensive review, by 1) Presenting a conceptual background of
how scientific inquiry can be induced in mathematics classes
considering recommendations of prior research, 2) Collecting case
studies that were designed using scientific inquiry process
designed for math classes, and 3) Exploring future possibilities
and directions for the research included within. Among the topics
discussed: * STEM education: A platform for multidisciplinary
learning. * Teaching and learning representations in STEM. *
Formulating conceptual framework for multidisciplinary STEM
modeling. * Exploring function continuity in context. * Exploring
function transformations using a dynamic system. Scientific Inquiry
in Mathematics - Theory and Practice delivers hands-on and concrete
strategies for effective STEM teaching in practice to educators
within the fields of mathematics, science, and technology. It will
be of interest to practicing and future mathematics teachers at all
levels, as well as teacher educators, mathematics education
researchers, and undergraduate and graduate mathematics students
interested in research based methods for integrating inquiry-based
learning into STEM classrooms.
This valuable resource provides an overview of recent research and
strategies in developing and applying modelling to promote
practice-based research in STEM education. In doing so, it bridges
barriers across academic disciplines by suggesting activities that
promote integration of qualitative science concepts with the tools
of mathematics and engineering. The volume's three parts offer a
comprehensive review, by 1) Presenting a conceptual background of
how scientific inquiry can be induced in mathematics classes
considering recommendations of prior research, 2) Collecting case
studies that were designed using scientific inquiry process
designed for math classes, and 3) Exploring future possibilities
and directions for the research included within. Among the topics
discussed: * STEM education: A platform for multidisciplinary
learning. * Teaching and learning representations in STEM. *
Formulating conceptual framework for multidisciplinary STEM
modeling. * Exploring function continuity in context. * Exploring
function transformations using a dynamic system. Scientific Inquiry
in Mathematics - Theory and Practice delivers hands-on and concrete
strategies for effective STEM teaching in practice to educators
within the fields of mathematics, science, and technology. It will
be of interest to practicing and future mathematics teachers at all
levels, as well as teacher educators, mathematics education
researchers, and undergraduate and graduate mathematics students
interested in research based methods for integrating inquiry-based
learning into STEM classrooms.
This book deals with recent developments in classification and data analysis and presents new topics which are of central interest to modern statistics. In particular, these include: classification models and clustering methods, multivariate data analysis, symbolic data, neural networks and learning devices, phylogeny and bioinformatics, new software systems for classification and data analysis, as well as applications in social, economic, biological, medical and other sciences. The book presents a long list of useful methods for classification, clustering and data analysis. By combining theoretical aspects with practical problems it is designed for researchers as well as for applied statisticians and will support the fast transfer of new methodological advances to a wide range of applications.
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