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ensure accuracy. Adding + It Up: Helping Children Learn
Mathematics teachers should know. Many of these ideas are
treated in more detail in textbooks intended for prospective
elementary school teachers. A major theme of the chapter is that
numbers are ideas—abstractions that apply to a broad range of
real and imagined situations. Operations on numbers, such as
addition and multiplication, are also abstractions. Yet in order
to communicate about numbers and operations, people need
representations—something physical, spoken, or written. And in
order to carry out any of these operations, they need
algorithms: step-by-step procedures for computation. The chapter
closes with a discussion of the relationship between number and
other important mathematical domains such as algebra, geometry,
and probability. At first, school arithmetic i