Interpreting children’s drawings as indicators of mathematical structural development

The set of papers comprising this symposium report selected aspects of separate research projects. To address the theme of this symposium - Young children’s transition to mathematical drawing – each researcher has critically reflected on children’s drawings to highlight the diversity in the characteristics of those drawings, and the ways in which they represent (or do not represent) mathematical concepts or processes. In doing so we seek to problematize the expectation that most children will ‘naturally’ develop drawing skills during pre-school and the first few years of school, that are effective for representing and communicating mathematical meaning. Although ‘drawing’ is only specified a few times as a necessary form of representation in Australian Curriculum (Foundation to Year 2), the expectation is emphasised more strongly through the student work samples provided as illustrations of performance standards. For example, of the twelve ‘Satisfactory’ work samples provided for Year 1 in the Australian Curriculum website (ACARA, 2014), seven of the tasks required drawn responses. The drawings include pictorial representations of quantities, operations and problem solutions, as well as more formal diagrams (number line, graph and a map indicating routes, directions and informal distances). In an assessment situation, what is actually being assessed, the child’s mathematical understanding or their drawing skills? Our concern is that a substantial number of children struggle to develop the required drawing skills, and that many teachers are not aware of the need to explicitly support the development of mathematical drawing. The purpose of this symposium is to draw on some existing research to argue the case for further research that can inform early-years classroom pedagogy designed to obviate the potential learning barrier experienced by many children because of their under-developed drawing skills.