Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

Presents several alternatives to customary algorithms for whole number arithmetic. Includes a brief history of each algorithm and discusses why each might be useful for particular kinds of children. (KHR)

Encourages teachers to allow opportunities for students to present alternative algorithms, whether the students invent them or learn them, then lead a discussion about the meaning of the operations with the goal of students understanding why the algorithm works. Teachers with students of similar racial and ethnic backgrounds should encourage the…

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Describes an informal research activity in which third grade students invent their own algorithms for multidigit multiplication and division. Discusses teaching implications and action research ideas. (ASK)

Discusses using what students already know about taking away objects when teaching subtraction and gives six lessons to develop language for discussing and recording subtraction situations that give meaning to the subtraction algorithm. (MKR)