Why, Why Should I Justify?

Algebraic thinking in the middle grades involves constructing generalizations, moving beyond the focus of specific calculations in elementary school. This creates exciting opportunities to examine the validity of general arguments. Creating rich mathematical tasks and asking questions related to justification encourages students to examine what constitutes a valid justification for a general statement. Such reasoning bridges the mathematical activity that occurs at the elementary level and the reasoning that is necessary at the high school level. This manuscript discusses various justifications underlying middle-grade students' algebraic generalizations. (Contains 5 figures.)