The author discusses some unique and non-routine ways of developing the multiplication facts. (CT)

A random sample of 214 fourth grade students randomly assigned to two treatments completed 15 programmed lessons on multiplication of whole numbers. The treatments differed in the physical referent used in the programmed lessons. One group used an array as the physical referent (Repeated-Addition). The other used a coordinate system and ordered…

A discussion of the various algorithms used for multiplication. Repeated addition, arrays, the distributive law, Egyptian and Russian Peasant Multiplication, Gelosia, Napier's Rods and Genaille's Rods are all described, and examples of multiplying using each method are explained. (DT)

Early experience with grouping objects is valuable for later understanding of and work with place value, division, and multiplication. Examples are drawn from the Developing Mathematical Processes Curriculum Project at the Wisconsin Research and Development Center for Cognitive Learning. (RS)

In the winter of 1965, an experimental course in Elementary Number Theory was presented to a 6th grade class in the Hosmer School, Watertown, Massachusetts. Prior to the introduction of the present material, students had been exposed in class to such topics from the University of Illinois Arithmetic Project as lattices, number lines, frame…