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Summary of Reference

Irwin, Kathryn & Ell, Fiona

Visualising and the move from informal to formal linear measurement

Bibliographic data:
 In B. Barton, K. Irwin, M. Pfannkuch, & M. Thomas (Eds.)(2002). Mathematics Education in the South Pacific: Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, (pp.358-365). Sydney: MERGA

This paper discusses 8 and 9-year-olds understanding of informal and formal measurement. It argues that children’s skill in visualisation should be fostered as the basis of this understanding.

Data were gathered from interviews with 43 students from four schools. The students were asked to perform five tasks. Their teachers were also interviewed. The first two tasks investigated student’s use of informal measurement; the third and fourth tasks investigated formal measurement; and the fifth task the interrelationship between formal and informal measurement. The formal measurement tasks were adapted from those reported in Nunes’ and colleagues’ work as well as one from the TIMMSR study. In particular the interviewers sought information on children’s use of visualisation, how they went about measuring, their use of units and fractional units, and their measuring experiences. They had a particular interest in the “unwritten rules for units and iteration”.

The first two tasks involving ribbons and tiles showed good accuracy in visualisation of length by 9-year-olds in particular. Most students used a tool such as their fingers or a pencil. In the second more difficult visual estimate task few overestimated while more students underestimated. A high percentage of both 8- and 9-year-olds measured accurately. The authors note that “even reasonably accurate answers demonstrated some misconceptions”. These related to “failing to respect the unspoken rules of iteration”. They explain these unspoken rules as “the need for each unit to be right next to the previous one”; “the need to count only completed iterated units, and give the remaining portion a fractional name”; “the need to count all iterations”; and “the need to count each unit or partial unit only once”.

The third task about formal measurement involved finishing a drawing of a ruler. The analysis reveals that less than half of either 8- or 9-year-olds “showed understanding that the first unit was the same size as other units”. Again the students who were unsuccessful “ignored the unwritten rules of measurement that all units must be the same size, ‘1’ marks the end of the first unit”. The fourth task of measurement with a broken ruler showed that students’ visualising was not always successful. In the fifth task measuring a picture of a folded string placed next to a ruler very few students measured accurately. The implications that the authors draw from these results are that students’ first preference was for visualising, followed by a preference for using their fingers to measure. They conclude by suggesting that students’ skills in visualising be fostered as a way of moving from informal to formal measure.