ABSTRACT
This chapter discusses many common mistakes in math instruction and explains the misunderstandings behind them. While 0 is indeed immediately before 1 in terms of the relative positions for whole numbers, having children count starting at 0 is problematic. Natural numbers came into being in the most natural manner. The number 0, in contrast, came into the picture very late. Its concept as used in modern times originated in the 7th century, and this number was introduced into decimal system as late as in the 13th century. Counting numbers, as the term indicates, are numbers used for counting, and they start at 1. Tally marks are essentially a one-to-one correspondence between the number of marks and that of actual objects or people. When counting real objects, people may do it by different quantities at a time, such as by 1s, by 2s, and by 5s. The numeration system used by most peoples over the world today is the Hindu-Arabic system.
