Approaching Algebra through Sequence Problems: Exploring children's strategies

We describe the first phase of a project concerned with the foundations of algebra. Data consists of the responses of 11 year-olds to selected questions from national tests. We focus on one question, which concerns a sequence of shapes and classify successful methods and incorrect solutions. The most common method of successful solution involves some form of table of numbers. Other methods include drawing and use of a relationship. Examination of incorrect answers suggests four common errors. The idea of a ‘best method’ proves problematic, as both the apparently sophisticated and reliable methods sometimes produced incorrect solutions