The relationship between research and practice has long been an
area of interest for researchers, policy makers, and practitioners
alike. One obvious arena where mathematics education research can
contribute to practice is the design and implementation of school
mathematics curricula. This observation holds whether we are
talking about curriculum as a set of broad, measurable competencies
(i.e., standards) or as a comprehensive set of resources for
teaching and learning mathematics. Impacting practice in this way
requires fine-grained research that is focused on individual
student learning trajectories and intimate analyses of classroom
pedagogical practices as well as large-scale research that explores
how student populations typically engage with the big ideas of
mathematics over time. Both types of research provide an empirical
basis for identifying what aspects of mathematics are important and
how they develop over time. This book has its origins in
independent but parallel work in Australia and the United States
over the last 10 to 15 years. It was prompted by a research seminar
at the 2017 PME Conference in Singapore that brought the
contributors to this volume together to consider the development
and use of evidence-based learning progressions/trajectories in
mathematics education, their basis in theory, their focus and
scale, and the methods used to identify and validate them. In this
volume they elaborate on their work to consider what is meant by
learning progressions/trajectories and explore a range of issues
associated with their development, implementation, evaluation, and
on-going review. Implications for curriculum design and future
research in this field are also considered. Contributors are:
Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary
Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret
Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates,
Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne
Siemon, Max Stephens, Ron Tzur, and Jane Watson.
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