Discoveries of Charles Babbage in the 1800s are described. Origins of the difference engine, his calculating machine, the principles of computation applied to tables, and the design and construction of his engine are included. (MNS)

Discusses the mistakes of Kirschner, the German philosopher and mathematician, in calculating factorials of large numbers by hand in the 1600s. Uses computer technology to calculate those numbers now. (ASK)

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

Discusses ways that calculators and computer microworlds, such as LOGO and Shape Makers, can be used as tools for exploration, problem solving, and empowerment in school mathematics. Includes suggestions for classroom activities. (Contains 12 references.) (MKR)