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Children Learn Mathematics: A Learning-Teaching Trajectory with Intermediate Attainment Targets for Calculation with Whole Numbers in Primary School

Marja van den Heuvel-Panhuizen, editor
Publisher: 
Sense Publishers
Publication Date: 
2008
Number of Pages: 
260
Format: 
Paperback
Price: 
39.00
ISBN: 
978-90-8790-396-1
Category: 
General
[Reviewed by
Janet Wansick
, on
10/27/2009
]

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 learning-teaching trajectories, or what the book defines as the learning process that children follow. These trajectories are not seen as a linear, step-by-step 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 in-depth 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 7th and 8th 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 Heuvel-Panhuizen

INTRODUCTION 

M. van den Heuvel-Panhuizen

LEARNING-TEACHING TRAJECTORIES WITH INTERMEDIATE ATTAINMENT TARGETS 

 Part I – Lower Grades Primary School

K. Buys

PRE-SCHOOL 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 Heuvel-Panhuizen 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 Heuvel-Panhuizen

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 

Dummy View - NOT TO BE DELETED