Table Of ContentAdvances in Mathematics Education
Yeping Li
Edward A. Silver
Shiqi Li
Editors
Transforming
Mathematics
Instruction
Multiple Approaches and Practices
T ransforming Mathematics Instruction
A dvances in Mathematics Education
Series Editors:
Gabriele Kaiser, University of Hamburg, Hamburg, Germany
Bharath Sriraman, The University of Montana, Missoula, MT, USA
International Editorial Board:
Ubiratan D’Ambrosio (São Paulo, Brazil)
Jinfa Cai (Newark, NJ, USA)
Helen Forgasz (Melbourne, Victoria, Australia)
Jeremy Kilpatrick (Athens, GA, USA)
Christine Knipping (Bremen, Germany)
Oh Nam Kwon (Seoul, Korea)
For further volumes:
http://www.springer.com/series/8392
Y eping L i • E dward A. S ilver • S hiqi L i
E ditors
T ransforming Mathematics
Instruction
M ultiple Approaches and Practices
E ditors
Y eping L i E dward A. S ilver
D epartment of Teaching, Learning S chool of Education
and Culture U niversity of Michigan
Texas A&M University A nn Arbor, M I, U SA
C ollege Station, TX, U SA
S hiqi L i
D epartment of Mathematics
E ast China Normal University
P utuo, C hina
ISSN 1869-4918 ISSN 1869-4926 (electronic)
I SBN 978-3-319-04992-2 ISBN 978-3-319-04993-9 (eBook)
D OI 10.1007/978-3-319-04993-9
S pringer Cham Heidelberg New York Dordrecht London
L ibrary of Congress Control Number: 2014938206
© Springer International Publishing Switzerland 2 014
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S eries P reface
This volume of the series Advances in Mathematics Education edited by Yeping Li,
Edward Silver, and Shiqi Li on “Transforming Mathematics Instruction” provides
the reader with an overview on different approaches for transforming mathematics
instruction. Departing from the evidence from large-scale assessments pointing out
to strong weaknesses of many educational systems from all over the world, especially
the strong learning gap between East Asian and Western learners, the current book
seeks to survey and synthesize current research developments on innovative
approaches for the change of mathematics classroom culture. There is a wealth of
studies on the quality of education in general and the quality of mathematics education
in particular, partly summarized by current meta-studies. However, most of these
studies focus on Western countries. The current book overcomes this weakness by
including not only studies and approaches from Western countries but also approaches
from East Asian countries as well, refl ecting their own way of innovative mathematics
teaching. With this impressive overview on transforming mathematics instruction
from Eastern and Western countries, this book will provide an insightful summary
on possible ways to improve mathematics education while considering various
cultural infl uences which the reader will hopefully fi nd interesting.
U niversity of Hamburg, H amburg, G ermany G abriele K aiser
U niversity of Montana, M issoula, M T, U SA B harath S riraman
Series editors
v
P reface and Ack nowledgements
C lassroom instruction is commonly seen as one of the key factors contributing to
students’ learning of mathematics, but much remains to be understood about teach-
ers’ instructional practices that lead to the development and enactment of effective
classroom instruction, and approaches and practices developed and used to trans-
form classroom instruction in different education systems.
T his book surveys and examines several different approaches and practices that
contribute to the changes in mathematics instruction, including: (1) innovative approaches
that bring direct changes in classroom instructional practices, (2) curriculum reforms
that introduce changes in content and requirements in classroom instruction, and
(3) approaches in mathematics teacher education that aim to improve teachers’
expertise and practices. It also surveys relevant theory and methodology development in
studying and assessing mathematics instruction.
T ransforming Mathematics Instruction is organized to help readers learn not
only from reading individual chapters, but also from reading across chapters and
sections to explore broader themes, including:
– I dentifying what is important in mathematics for teaching and learning emphasized
in different approaches
– E xploring how students’ learning are considered and facilitated through different
approaches and practices
– L earning and understanding the nature of various approaches that are valued in
different systems and cultural contexts
– Probing culturally valued approaches in identifying and evaluating effective
instructional practices
The book brings new research and insights into multiple approaches and practices
for transforming mathematics instruction to the international community of mathe-
matics education, with 25 chapters and four section prefaces contributed by 56
scholars from 10 different education systems. This rich collection is indispensable
reading for mathematics educators, researchers, teacher educators, curriculum
developers, and graduate students interested in learning about different instructional
vii
viii Preface and Acknowledgements
practices, approaches for instructional transformation, and research in different
education systems.
I t will help readers to refl ect on approaches and practices that are useful for
instructional changes in their own education systems, and also inspire them to
identify and further explore new areas of research and program development in
improving mathematics teaching and learning.
We want to take this opportunity to thank and acknowledge all of those who have
been involved in the process of preparing this book. This has been a wonderful col-
laboration. The work on this book has not only brought together long time friends
and colleagues, but also created new professional connections and new friends. We
want to thank all those who were so ready and willing to contribute to the topic
that is proven to be very important to the international mathematics education
community.
T exas A&M University, USA Yeping Li
U niversity of Michigan, USA Edward A. Silver
E ast China Normal University, China Shiqi Li
C ontents
T ransforming Mathematics Instruction: What Do We Know
and What Can We Learn from Multiple
Approaches and Practices? ................................................................................... 1
Y eping L i, E dward A . S ilver, a nd Shiqi L i
P art I Transforming Mathematics Instruction with
a Focus on Changes in Instructional Practice
P reface to Part I .............................................................................................. 1 5
D avid C larke
M odelling in Mathematics Classroom Instruction: An Innovative
Approach for Transforming Mathematics Education ................................. 2 1
K atrin V orhölter, G abriele K aiser, a nd Rita B orromeo Ferri
G uided Reinvention: What Is It and How Do Teachers
Learn This Teaching Approach? .................................................................... 3 7
M ichelle S tephan, D iana U nderwood-Gregg, a nd Erna Y ackel
C hallenging Mathematics with Multiple Solution
Tasks and Mathematical Investigations in Geometry .................................. 5 9
R oza L eikin
T ransforming Professional Practice in Numeracy Teaching ....................... 8 1
M errilyn G oos, V ince G eiger, a nd Shelley D ole
E xploratory Activity in the Mathematics Classroom .................................. 1 03
J oão P edro d a Ponte, N eusa B ranco, a nd Marisa Q uaresma
T he Affordances of Using Visibly Random Groups
in a Mathematics Classroom .......................................................................... 1 27
P eter L iljedahl
ix
