- Published Year: 2011
- Page count: 586
- File Size: 7 Mb
- Language: English
- Published by: American Mathematical Society
- Visited by: 7
- Rating/Review: 4.7
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ISBN:
0821852604
9780821852606
Keywords:
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Introduction to "Understanding Numbers in Elementary School Mathematics"
"Understanding Numbers in Elementary School Mathematics" is a comprehensive and thought-provoking book that dives deeply into the intricacies of the mathematical concepts taught in elementary schools. Written by renowned mathematics educator and author Hung-Hsi Wu, this book serves as a guide for educators, parents, and anyone interested in the foundations of mathematics to better grasp the principles and logic behind numerical systems and operations. Its goal is to reconnect readers with the mathematical precision and reasoning necessary to teach or understand elementary-level mathematics effectively while dispelling superficial or procedural misunderstandings often passed down through conventional teaching.
Detailed Summary of the Book
The book is built upon the premise that elementary mathematics is the foundation of all higher forms of mathematical thinking. Hung-Hsi Wu emphasizes the critical need to treat elementary mathematics as a rigorous and logical discipline at its core instead of reducing it to a set of disconnected rules memorized without understanding. The book systematically addresses the development of numbers from their most basic origin, starting with natural numbers, extending to the integers, and expanding into fractions and decimals.
Rather than adhering to quick, rule-based problem-solving methods, the book dives into the conceptual frameworks behind numbers, operations, and mathematical structures. For example, the treatment of fractions in this book is particularly noteworthy, as Wu explains fractions as numbers, integrating precision and logic to replace the typical ambiguity surrounding this topic. Additionally, topics like place value, the number line, and the fundamental properties of operations are approached with a level of depth that is both accessible and rigorous, enabling readers to form a deep appreciation of the subject matter.
Wu's pedagogical focus also extends to fostering mathematical reasoning. Every concept is presented with clarity, and misconceptions are carefully addressed, ensuring that teachers are better equipped to explain difficult topics. "Understanding Numbers in Elementary School Mathematics" thereby lays the groundwork for an educational approach rooted in logic, coherence, and clarity that benefits both teachers and students alike.
Key Takeaways
- Emphasizes the mathematical precision necessary to teach elementary mathematics effectively.
- Connects mathematics to real-world reasoning rather than presenting it as a series of disjointed rules.
- Redefines how foundational concepts such as fractions, decimals, and place value should be taught conceptually.
- Includes educational principles that help address and correct prevalent misconceptions about numbers.
- Equips educators with tools and strategies to teach mathematics with clarity and purpose.
Famous Quotes from the Book
"To teach mathematics, one must first understand mathematics—not merely as a collection of recipes for solving problems but as an intellectually coherent body of knowledge."
"Fractions are not a different kind of number but are numbers, just like integers, operating within the same numerical framework."
"Precision in teaching mathematics is not about making perfect calculations but about nurturing clarity in thought and understanding."
Why This Book Matters
The importance of "Understanding Numbers in Elementary School Mathematics" cannot be overstated. This book fills a vital gap in the world of education by addressing the deficiencies in the way mathematics is often taught to young learners. It provides educators with the intellectual tools to teach math properly, ensuring that students develop a deep and lasting understanding of its foundational principles.
Many current teaching strategies prioritize rote memorization, often at the expense of mathematical reasoning and logic. Wu's book challenges this approach by demonstrating how careful explanation, connected thinking, and an emphasis on the underlying logic can transform mathematics education. His work empowers teachers to impart knowledge in a way that instills confidence, curiosity, and competence in students.
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