Analyzes the nature and growth of students' algebraic knowledge and thinking from an epistemological perspective supported by historical observations. Focuses on two crucial transitions: from the purely operational algebra to the structural algebra of a fixed value of an unknown and then to the functional algebra of a variable. (Contains 58…

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

This study considers two problems related to cognitive development: "Is development hierarchical?" and "If so, what are the mechanisms involved in the process of development?" Analysis of the results of an experiment lead to differentiation of stages of development, and problem-solving strategies at each level are discussed.…