How do students' solutions to a problem-solving task change after attempting to understand an algebra-focused sample solution?

Abstract \ud \ud This study, in the context of mathematical problem solving, aims to \ud explore the ways in which a piece of sample work affects pupils’ solutions \ud to problem-solving tasks. Mathematical problem solving is a rich, evolving \ud field and the use of sample work is a relatively recent development within \ud it. Many people believe sample student work to be useful (Evans and \ud Swan, 2013; Evans, Mullins and Waring, 2014) but there is not a wealth of \ud empirical evidence surrounding it. In this study four problem-solving tasks \ud were used with the same class; each had potential to be solved \ud algebraically. For each task an algebraically themed piece of sample work \ud was carefully designed by the researcher. Pupils’ work on the tasks before \ud and after attempting to understand the sample work provides the main \ud data source. Follow up interviews were carried out with four students, \ud chosen based on work they had produced. The prominent theme emerging \ud was that the influence the sample work had on pupils’ solutions depended \ud on how readily pupils understood the sample solution. This is argued to \ud pertain to Vygotsky’s zone of proximal development. The implications of \ud this and other findings in relation to design and use of sample work are \ud discussed