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Many different methods of multidigit computation have been used historically and are now used around the world, but the context in which multidigit computation now occurs has changed. The worldwide availability of electronic calculators has decreased the need for complex computations. The emphasis now can be on understanding methods as well as performing them. This paper outlines a research program conducted over thirty years to find and test multidigit computation methods that are mathematically desirable and that many kinds of students and teachers can understand and explain. A nurturing Math Talk classroom environment, in which students made and explained math drawings supported sense-making by students and teachers. Powerful and simple math drawings were also developed and assessed. The methods and math drawings identified by this research for multidigit adding, subtracting, multiplying, and dividing are described. Examples are given of student explanations with the drawings. The criteria for deciding which methods are mathematically desirable are given, and the methods are judged by these criteria. Some methods that are common in various countries but that are difficult and may stimulate errors are described so that they might be replaced by the best methods identified by this research. How these methods fit the math standards of two different countries, the United States and China, is described. Sense-making about and using the identified best methods can reduce errors and engender understanding.

The Best Multidigit Computation Methods: A Cross-cultural Cognitive, Empirical, and Mathematical Analysis