Development of children's understanding of length, area and volume measurement principles

Abstract

This study investigated the concurrent development of children’s understanding of length, area, and volume measurement in Grades 1-4. From a 45-minute interview, an attempt was made to derive three parallel scores assessing understanding of each of five measurement principles: the need for congruent units, the importance of using an appropriate unit, the need to use the same unit when comparing objects, the relationship between the unit and the measure, and the structure of the unit iteration. Valid comparisons could only be made across three of these five principles. On the others, student scores increased with grade, with length preceding area and area preceding volume in most cases. The results have several implications for teachers. Measurement has long been regarded as an important component of numeracy (Cockcroft, 1982). It constitutes a separate strand in the official syllabuses of all Australian states and territories, and receives a similar emphasis in the US and the UK. The focus is on the measurement of the spatial attributes of length, area, and volume, and most concepts are expected to be mastered in primary school. School syllabuses frequently make statements about children’s measurement learning that are at least partly based on research. For example, the recently revised New South Wales mathematics syllabus outlines a developmental sequence for the early grades that includes the following statement of the basic principles of measurement: Students develop the key understandings of the measurement process using repeated informal units. These include: 1. the need for repeated units that do not change 2. the appropriateness of a selected unit 3. the need for the same unit to be used to compare two or more objects 4. the relationship between the size of the unit and the number required to measure, and 5. the structure of the repeated units. (Board of Studies NSW, 2002, p. 91) Most of the research on which such statements are based has investigated length, area, and volume measurement concepts separately. This paper describes an attempt to validate the development assumed in syllabus documents and in particular to relate children’s development of the three attributes.