The Pattern and Structure Mathematics Awareness Project ( PASMAP) has investigated the development of patterning and early algebraic reasoning over a series of related studies with 4 to 8 year olds. We assert that an awareness of mathematical pattern and structure enables real mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, salient underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students' representation, abstraction and generalisation of mathematical ideas.
A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in the evaluation throughout the 2009 school year and at follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented a regular program. PASMAP focused on unitising and multiplicative structure, simple and complex repetitions, growing patterns and functions, spatial structuring, congruence, similarity and transformation, the structure of measurement units and data representation. Emphasis was also laid on visual memory and simple generalisation.
Students were pre- and post- tested with I Can Do Maths (ICDM) (Doig & de Lemos, 2000) in February and December 2009, and September 2010; from pre-test data two 'focus' groups of five students in each class were selected and these 190 students were interviewed using a 20-item Pattern and Structure Assessment.
Broadly, the study shows that both groups of students made substantial gains on ICDM and PASA across all assessments but highly significant differences were found for PASMAP students' (0.002), outperforming the regular group on PASA scores. Qualitative analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability were able to develop improved structural responses over a relatively short period of time.
The PASMAP can enable a deeper and broader approach to assessment and serve to inform a much more challenging framework of mathematical ideas commensurate with young children's potential. A follow up study, Transforming Children's Mathematical and Scientific Reasoning is in progress.