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Learning Over Time - Learning Trajectories in Mathematics Education (Hardcover)
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Learning Over Time - Learning Trajectories in Mathematics Education (Hardcover)
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The driving forces behind mathematics learning trajectories is the
need to understand how children actually learn and make sense of
mathematics-how they progress from prior knowledge, through
intermediate understandings, to the mathematics target
understandings-and how to use these insights to improve instruction
and student learning. In this book, readers will come to understand
what learning trajectories are, the research and methodology that
are necessary for developing them, and gain insight into potential
applications of learning trajectories. A synthesis and research
outcome in their own right, learning trajectories provide detailed
description of instructionally-grounded development of mathematical
concepts and reasoning from the perspective of student learning,
and, overall, building on decades of accumulated experience in
mathematics education research. However, their greater importance
may lie in their potential as frameworks that contribute an
unprecedented coherence across classroom instruction, professional
development, standards, and assessment, by focusing squarely on
conceptual understanding and reasoning instead of assessment-driven
procedural knowledge. This potential was sufficiently compelling as
an organizing framework to have been cited as a basis for the
Common Core mathematics standards, the new mathematics learning
expectations that are now consistent across most of the United
States. (Among the conference attendees were the writers of the
Common Core State Standards for Mathematics, at the beginning of
the Standards drafting process.) This book is an outgrowth of a
conference on learning trajectories, hosted in 2009 at North
Carolina State University, which examined research on learning
trajectories. An overarching message of the chapters in this volume
is that learning trajectories, by focusing on how children's
mathematical reasoning develops, are coming into their own as a
rigorous underpinning for both instruction and accountability. Some
of the learning scientists featured in this volume have played
major roles learning trajectories' evolution--from small-scale
day-to-day conjectures by individual teachers, to systematic
research endeavors that teachers and scientists alike can use to
interpret standards, plan instruction, and formatively assess
student work. The work in this volume will be of interest to
mathematics educators, teachers, and professional development
specialists.
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