Building meaning through problem solving practices: the case of four-year olds

• We present a classroom research concerning the problem solving process.
• We compare four-year old children's response to a given mathematical problem before and after teaching intervention.
• Teaching intervention helped the children develop skills and positive attitudes.
• Significant differentiation was noted in children's graphical representations, strategies and attitudes.
• Four-year old children can gradually apply the mathematical problem solving process successfully.

This paper deals with the attempt to study four-year old children's potential to engage in the mathematical problem solving process and their ability to construct mathematical meaning through their engagement with the process. We studied: (a) whether teaching could contribute to the development of the essential cognitive skills for solving a mathematical problem of detecting all possible additive combinations giving a specific sum and (b) whether children's familiarization with graphical representation practices of solutions could give meaning to the mathematical problem solving process, in a way that children would benefit from it in their involvement and effectiveness concerning the process. Findings showed that four-year old children's consistent involvement with the mathematical problem solving process enabled them to develop, apply and demonstrate skills and mathematical conceptual understanding in order to solve the given mathematical problems. The role of the teacher, in organizing the classroom learning environment as well as carrying out the teaching intervention, was essential to the development of the children's skills, abilities and mathematical conceptual understanding.