Understanding Numbers in Elementary School Mathematics by Hung-Hsi Wu (PDF)

Description

This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7. Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.

User’s Reviews

Editorial Reviews: Review [This book] delivers the mathematical knowledge that elementary-grades teachers need. —- American Educator

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Although this book’s intended audience is those teaching elementary mathematics (and presumably their teachers), I figured it would be worthwhile reviewing from the perspective of a parent of elementary school children: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!

⭐As an advocate for mathematics education, a mathematics instructor, engineer, scientist and edupreneur, and having attended seminars presented by Dr. Wu I will categorically state that Dr. Wu’s book should be recognized as a milestone in elementary school mathematics.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 classroomThis 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….

⭐Great review – provides indepth mathematical development of basic operations with numbers to better even a practicing teacher’s understanding of the “why’s” behind the mathematics we all take for granted.

⭐All math teachers need to read this book. Especially elementary teachers.

⭐I bought this book in part based on the 5 star reviews. I’m guessing the reviewers are not pre-service or in-service teachers. The MAA review matched up pretty well with my impressions: http://www.maa.org/publications/maa-reviews/understanding-numbers-in-elementary-school-mathematics

⭐This book and author has made an amazing impact on my teaching. Wu is able to provide context for mathematical topics that have long been overlooked. I no longer teach the procedures for how to calculate something i.e. division of fractions problem, but I am able to explain the concept in a way that makes sense mathematically. The logical sequence in this text is something I attempt to mirror as well. No skipping around!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!

⭐Great

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