Learning Over Time

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.