Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)

Explores the five multiplication techniques found in the 12th century Lilavati by Bhaskara, which appear again in the 1494 Summa by Pacioli. Includes a student worksheet. (KHR)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Sixty-four adults were tested on simple addition and multiplication problems presented in Arabic digit or English number-word format. Overall, response times and error rates were much higher with the word format, but more important, presentation format interacted with arithmetic operation and problem size. (DR)

This study argues that maximizing early childhood educators' abilities to create social opportunities for co-construction of knowledge rests on two understudied assumptions, one theoretical and one empirical. Theoretically this study rejects the notion of language as an impartial conveyor of knowledge in favor of one in which math and language…

The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…

This textbook is designed to teach the principles of Arithmetical Science as far as they are involved in the elementary processes, and to secure a reasonable degree of accuracy and rapidity in expressing numbers and computing results. This work presents at first the idea of numbers connected with visual representations of objects; afterward, when…

Presented is a paradigm for teaching basic and semibasic arithmetic facts to children with arithmetic difficulties, in which the student progresses from the use of concrete materials such as blocks, to the use of diagrams such as tally marks, to a reasoning process, to responding in an automatic manner. (DLS)

Described is a multiplication unit for intermediate aged emotionally disturbed boys which used citizen band radio terms and a drawing of a road to record individual progress. (CL)

Some proposals on how children may learn the basic multiplication facts through practical activities based on the rectangle. (MM)

A "flipping" clown figure can be used on a number line to help students conceptualize operations using negative numbers. (SJL)

Discusses a teaching method for multiplication using manipulative materials. Provides examples of the teaching method and activities using individual chalk boards. Two references are listed. (YP)

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

Discusses the generalization of the meaning of multiplication for whole numbers. Presents an example for multiplication of fractions. Provides several diagrams to help improve understanding. (YP)