Conceptual Understanding of Spatial Measurement1

Although there has been considerable research into students ’ learning of length, area, and volume measurement, there is very little research into their relationship. This paper describes a developmental study of how 96 students in Grades 1-4, randomly selected from six public schools across the Sydney metropolitan area, related measurement in these three domains. Two methods of measuring volume (by filling and by packing) were included. The results indicate a clear increase in students ’ understanding of unit structure of length, area and volume across Grades 1 to 4 with volume (packing) being the most difficult. Volume (filling) was closely aligned to length. These results support the wisdom of highlighting the similarities and differences in the unit structures of length, area, and volume measurement in a teaching context. Apart from general surveys such as NAEP and TIMSS, we know of no measurement studies which have simultaneously investigated students ’ understanding of length, area, and volume or the relationship between them. Several studies have compared two attributes, however. Some studies have addressed the confusion between perimeter and area (e.g., Lehrer, Jenkins & Osana, 1998); Outhred and Mitchelmore (2000) highlighted th