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.
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