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Understanding Numbers in Elementary School Mathematics
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[This book] delivers the mathematical knowledge that elementary-grades teachers need. ---- American Educator
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I found this book after my son encountered some difficulties with his third grade math work. In attempting to bring him up to speed with the class work I first looked to his textbook, and then also Internet resources such as Kahn Academy and YouTube. I became a little frustrated with my lack of a complete understanding of the subject, which is somewhat tricky for an adult to teach since there are so many dependencies on concepts that have not yet been introduced (e.g. you can't subtract a larger number from a smaller one before you know about negative numbers).
Some Google searching turned up this book and although it is quite expensive, I ordered a copy figuring that my kids have a few years to go in elementary school so the cost can be amortized. Also, compared to the cost of a private tutor for my son, the price is very reasonable.
The first thing to say is that you need a mathematical background in order to get value from this book. I found it easy to read and understand, but I'm an engineer who had to study math well into my 20's. If you struggled with High School Math, this probably isn't the book for you.
I found the book to be tremendously useful in pinning down the somewhat non-rigorous, shifting sands of the textbook and class material. It's also just a plain interesting read for anyone with an interest in mathematics. For example you learned long division at school, but how, exactly, does it work?
So for anyone who is mathematically fluent, but a little hazy about the details of fractions, multi-digit multiplication, and why learning 11 and 12-times tables is a stupid idea, this is the book for you!
It is rigorous, interesting, challenging and thought provoking. It should also be the basis for the instruction of ALL mathematics teachers, not just elementary school teachers as the title might suggest. His presentation on multiplication and the use of the number line for fractions changed my life and my practices in the classroom
This is truly a must read and do the exercises book for anyone seeking fundamental understanding of numbers and the origins of the algorithms we take for granted like invert and multiply, multiply the numerators and the denominators....
This is indeed a remarkable book for those who choose to take the time and the effort to learn (and teach) Elementary Mathematics.
After more than 10 years experimenting with teaching school teachers Professor Wu, a research mathematician himself from UC Berkeley, has taken a comprehensive and systematic approach to the bread and butter of Elementary Mathematics (K-6): Whole numbers, Fractions and Rational Numbers. It covers from the importance of Place Value in our numeral system to the Basic Laws of Operations for the understanding of the Standard Algorithms. It grants the reader with a thorough analysis and demystification of Fractions, a different view of Rational Numbers, and much more.
The number line is skillfully used throughout the book as a visual tool although, at times, a non-geometric approach would complement some of the concepts and examples. Always accompanied by useful and challenging self-assessment teaching exercises.
I have used and re-used the content of this book in preparing to teach Professional Development courses or while revising textbooks for publishers. Each time I've learned something new. Ever so subtle, ever so revealing of the complex simplicity of Arithmetic.
Wu's book is no less important for the mathematics educator. Knowing and understanding the mathematics content is an indispensable guide for the educator to find its way to the student. Without it, he'll be drifting at the mercy of ever changing pedagogical theories.
I not only recommend this book, as I hope it will be become a reference for present and future generations of teachers, educators, textbooks publishers and all eager to learn school mathematics as it should be taught. Our teachers deserve the best and our children deserve no less.
I only wish this book and Wu's trainings were available before I got into the classroom. Since learning of him and from him I have yet to find anything comparable in the existing professional development pool.
If you want to do your students a favor, may they be pre-service teachers, in-service teachers, or K-8 students, read this book!