Children's understanding of area concepts: development, curriculum and educational achievement

As one part of a series of studies undertaken to investigate the contribution of developmental attributes of learners to school learning, a representative sample of forty-two students (age from 5 years and 3 months to 13 years and 1 month) was randomly selected from a total student population of 142 students at a small private primary school in northern Australia. Those children's understandings of area concepts taught during the primary school years were assessed by their performance in two testing situations. The first consisted of a written classroom test of ability to solve area problems with items drawn directly from school texts, school examinations and other relevant curriculum documents. The second, which focused more directly on each child's cognitive development, was an individual interview for each child in which four "area" tasks such as the Meadows and Farmhouse Experiment taken from Chapter 11 of The Child's Conception of Geometry (Piaget, Inhelder and Szeminska, 1960, pp. 261-301) were administered. Analysis using the Rasch Partial Credit Model provided a finely detailed quantitative description of the developmental and learning progressions revealed in the data. It is evident that the school mathematics curriculum does not satisfactorily match the learner's developmental sequence at some key points. Moreover, the children's ability to conserve area on the Piagetian tasks, rather than other learner characteristics, such as age and school grade seems to be a precursor for complete success on the mathematical test of area. The discussion focuses on the assessment of developmental (and other) characteristics of school-aged learners and suggests how curriculum and school organization might better capitalize on such information in the design and sequencing of learning experiences for school children. Some features unique to the Rasch family of measurement models are held to have special significance in elucidating the development/attainment nexus.