Finding and using patterns in linear generalising problems

Abstract

Linear generalising problems are questions which require students to observe and use a linear pattern of the form f(n)=an+b with b≠0. This study reports responses of students aged between 9 and 13 to these questions, documenting the mathematical models that they select, the strategies used in implementing them and the explanations they give. Substantial inconsistency of choice of model is observed; students who began a question correctly frequently adopted a simpler but incorrect model for more difficult parts of the question. Students who had undertaken a course in problem solving implicitly used a linear model more frequently and consistently and their explanations more often related the s..