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In this day of comparing the mathematics achievement of students on an international scale, this book provides a glimpse of elementary mathematics as organized by the Dutch Ministry of Education. Divided into lower grades primary and higher grades primary, the book describes a specific curriculum addressed in elementary school in the Netherlands: “The examples of student behavior and outlines of teaching activities are intended to give a helicopter view of the learning experience that children encounter in primary school.” This book is designed to give a description of learningteaching trajectories, or what the book defines as the learning process that children follow. These trajectories are not seen as a linear, stepbystep regimen, because that would “not correspond with the natural course of (the) learning process.”
This book illustrates some important points about mathematics education of young students. Many of these points coincide with statements made from the Mathematics Association of America and the National Council of Teachers of Mathematics. For example, “Apart from developing a critical mind and learning to trust their own thinking power, the students will also need to be helped to discover joy in mathematics.” The ideas presented stress that students need to be confronted with other students’ thinking because alternative solutions can push the student’s own thinking into “new and fruitful directions,” much like the discussions taking place in the United States about students being able to communicate and reason mathematically.
The book is divided into two parts: Lower Grades Primary School and Higher Grades Primary School. Then the sections are further divided by content. In the Lower Grades section, the focus is on calculations and developing students’ number sense. In the Higher Grades, the focus turns to mental mathematics, estimation, as well as the number and number relations that are important to further a students’ number sense development. Within each of these topics there are examples of student work, student discussions, and a discussion of a variety of teaching strategies. In some sections, the author also provides a comparison of “categories” or models of teaching the same concept.
The language of this book is somewhat challenging for the educator outside of the Netherlands because the terminology seems very different. However, once the reader moves past some of the terms and gets to the heart of the book it is very interesting. This book provides several specific examples of mathematics problems and explanations of student and teacher reasoning with those problems. I found the examples and explanations to be very informative about the education of elementary (primary) students.
I think most educators will see that the content in the Netherlands is not that different from the content being taught to students in the United States. This text reinforces the importance of indepth understanding of mathematics. I would recommend this text to Mathematics Educators. It provides a very good look into elementary education in the Netherlands, while at the same time reinforcing effective mathematics education that could be taught anywhere.
Janet D. Wansick (jwansick@ecok.edu ) is an assistant professor of mathematics at East Central University in Ada, OK. She began her teaching career in the middle school classroom teaching 7^{th} and 8^{th} grade mathematics before moving to the high school and eventually to the college level. She works with numerous classroom teachers at all levels and conducts mathematics partnership workshops. Her research areas of interest include mathematics education, curriculum and pedagogy, and mathematical assessment.
FOREWORD 

M. van den HeuvelPanhuizen 
INTRODUCTION 
M. van den HeuvelPanhuizen 
LEARNINGTEACHING TRAJECTORIES WITH INTERMEDIATE ATTAINMENT TARGETS 
Part I – Lower Grades Primary School
K. Buys 
PRESCHOOL YEARS – EMERGENT NUMERACY 
A. Treffers 
KINDERGARTEN 1 AND 2 – GROWING NUMBER SENSE 
A. Treffers 
GRADE 1 (AND 2) – CALCULATION UP TO 20 
A. Treffers and K. Buys 
GRADE 2 (AND 3) – CALCULATION UP TO 100 
A. Noteboom, J. Bokhove and J. Nelissen 
GLOSSARY PART I 
Part II – Higher Grades Primary School
M. van den HeuvelPanhuizen and K.Buys 
BIG LINES 
A. Treffers 
NUMBERS AND NUMBER RELATIONSHIPS 
K. Buys 
MENTAL ARITHMETIC 
A. Treffers, A. Nooteboom and E. de Goeij 
COLUMN CALCULATION AND ALGORITHMS 
M. van den HeuvelPanhuizen 
ESTIMATION 
E. de Moor and J. van den Brink 
CALCULATOR 
J. Nelissen and A. Treffers 
TEACHING FRAMEWORK 
J. Bokhove and A. Noteboom 
GLOSSARY PART II 
Appendix
CORE GOALS MATHEMATICS END PRIMARY SCHOOL 

NOTES 