The arithmetic connection

From test and interview data obtained during an investigation into Grade 10 students' conceptions of algebraic generalisation and justification, we have extracted evidence of the extent to which these students have coordinated the worlds of arithmetic and algebra, and can move freely between them. The data show more dissociation than we expected, even among students who were successful at standard algebraic tasks. Conceiving algebra as generalised arithmetic may obscure the many genuine obstacles that the learner has to overcome in moving from fluent performance in arithmetic to fluent performance in algebra while achieving and maintaining a smooth coordination of both modes of action.