Towards Deep Understanding of Elementary School Mathematics: A Brief Companion for Teacher Educators and Others – Ebook TR

The book is intended to serve as a brief companion for mathematical educators of elementary teacher candidates who learn mathematics within a college of education both at the undergraduate and graduate levels. Being informed by mathematics teaching and learning standards of the United States, Australia, Canada, Chile, England, Japan, Korea, Singapore, and South Africa, the book can be used internationally.

The teaching methods emphasize the power of visualization, the use of physical materials, and support of computer technology including spreadsheet, Wolfram Alpha, and the Geometer's Sketchpad.

The basic ideas include the development of the concepts of number, base-ten system, problem solving and posing, the emergence of fractions in the context of simple real-life activities requiring the extension of whole number arithmetic, decimals, percent, ratio, geoboard geometry, elements of combinatorics, probability and data analysis.

The book includes historical aspects of elementary school mathematics. For example, readers would be interested to know that two-sided counters stem from the binary system with its genesis in the 1st millennium BC China of which Leibnitz (17th century) was one of the first notable proponents. The genesis of the base-ten arithmetic is in the Egyptian mathematics of the 4th millennium BC, enriched with the positional notation with the advent of Hindu-Arabic numerals in the 12th century Europe.

Contents:

• Preface
• Teaching PreK — K Mathematics
• Teaching Operations in Grades 1–4
• Conceptual Shortcuts
• Decomposition of Integers Into Like Addends
• Activities with Addition and Multiplication Tables
• Using Technology in Posing and Solving Problems
• Fractions
• From Fractions to Decimals to Percent
• Ratio as a Tool of Comparison of Two Quantities
• Geometry
• Elements of Combinatorics: Counting Through a System
• Elements of Probability Theory and Data Management
• Developing Technology Used in the Book
• Appendix — Activity Sets: 300 Problems and Questions
• Bibliography
• Index

Readership: Prospective teachers of elementary mathematics, teacher educators, graduate students in mathematics education doctoral programs.

Key Features:

• Provides mathematical educators of prospective elementary school teachers with the basic ideas of elementary mathematics and with the modern-day methods of teaching conducive to deep understanding of the subject matter
• Many historical connections and cultural origins of elementary mathematics are highlighted throughout the book including the names of Pythagoras, Confucius, Plato, Aristotle, Fibonacci, Pascal, Leibnitz, Euler, Gauss and other great thinkers of the past
• Reflects the author's more than two decades of work of preparing teacher candidates, both at the undergraduate and graduate levels, to teach mathematics in the elementary classrooms of the United States and Canada