Children's Awareness of Structural Relationships Embedded in Addition and Subtraction Word Problems

Butlin, John Stanley (2010). Children's Awareness of Structural Relationships Embedded in Addition and Subtraction Word Problems. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000d691

Abstract

A common practice in primary schools is the use of tasks that involve children solving word problems. A great deal of research has focused on improving children's performance in these tasks by various forms of instruction. This study aims to reveal transitions in children's thinking about; and awareness of structural relationships embedded in word problems by involving children in tasks focused on word problems, but getting them to sort, and match problems,and to construct their own similar problems. The intention was to investigate the nature of the activity that learners engage in when working on these tasks with a view to informing discussion about the role of word problems in the mathematics curriculum.

A small group of Year 4 children worked on solving, sorting, matching and constructing tasks approximately once every four weeks over a several month period. Data was collected in the form of written recordings made by the children, transcripts of dialogue and field notes. The approach taken to the study was broadly in the spirit of grounded theory and drew heavily on the Discipline of Noticing (Mason, 2002). Using aspects of this framework,accounts-of the data were constructed and these were carefully analysed with the intention of providing accounts-for the phenomena that were observed.Two main themes emerged from the analysis. The first I describe as persistent behaviour. This is the tendency for children to display similar behaviour and attend to similar foci across tasks and over time, despite this behaviour, on occasion, being inappropriate. The second theme, in contrast, was unstable behaviour. This is the tendency for children to display variation in behaviour when responding to tasks that might be expected to produce similar responses.Attempts are made to account-for these phenomena and implications for teaching and learning are discussed. It is concluded that the potential of word problems as a pedagogical tool might be better exploited if learners experienced long term immersion in sorting, matching and constructing tasks in addition to the more common focus on solving.