ABSTRACT
This chapter discusses division mistakes in math instruction and explains the misunderstandings behind them. After she introduced division and the long division symbol, Jane presented to her children a problem for demonstration: 8 ÷ 4. At the beginning stage of learning division, children are only exposed to problems such as the one just mentioned, where the dividend is larger than the divisor. In a mathematical expression for division, which operand gets divided by which operand does not depend on their magnitudes. Saying "the larger number goes inside" can cause serious misunderstanding on children's part. The common saying "Division is repeated subtraction" is applicable to the subtractive interpretation but not to the distributive interpretation—and the modeling for one interpretation is different from that for the other. Jane presented to her children the procedure for long division of a 2-digit number by a 1-digit number.
