Box 6–16 Expanded Algorithm for Multidigit Division with Fewer Steps
permits the use of products likely to be known. It can be made as brief as the current standard algorithm for those who can manage the abbreviation. This accessible division algorithm has been proposed as an alternative for some time and since at least the 1950s has been used in some textbooks.78
The example of the accessible method given in Box 6–15 shows a solution that might be produced by a student very early in learning division. Box 6–15 also gives a model that supports accessible methods. The student builds up copies of the divisor until the dividend is reached and then reads off the quotient. A later version of the procedure by the same student is given in Box 6–16. At this point the student no longer needs the drawing to give meaning to the steps. This version can readily be related to the more common method in Box 6–14.
Research indicates that U.S. children can understand and explain procedures for calculating with multidigit numbers rather than just executing them mechanically. This conclusion, which is especially well established for addition and subtraction,79 means that mathematical proficiency with multidigit arithmetic is achievable by students even at early grades. In fact, a higher level of performance can be achieved at earlier grades than is currently expected.80