Profiles of algebraic competence

The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map algebraic symbols onto word problems was evaluated. Two weeks later, unassisted algebraic problem-solving tests were completed. Cluster analyses revealed four meaningful, relatively well-ordered, arithmetic/algebraic competence profiles reflecting partial knowledge states associated with the acquisition of algebraic understanding. The findings are discussed in terms of the conceptual changes associated with the acquisition of algebraic competence.