Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)

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…

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Changes in the elementary and junior high school mathematics curriculum that have occurred in the last 20 years and that may occur in the future are discussed. (MK)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)