- Published May 13, 1991
- By Chris Gregory, Anth Ginn and Dave Catlin
The English National Curriculum states “Pupils should estimate and measure quantities, and appreciate the approximate nature of measurement”. Practical measurement of length, weight, capacity, etc. is a common feature of early mathematics work. Unfortunately this often becomes the manipulation of standard units and the use of ready-made measuring devices. This assumes that children know what measurement is and have grasped the need for standard units. Such assumptions are unfounded. Understanding grows from practical experience of measurement over a considerable period of time and in many different contexts. “GO” looks at how using the Valiant Turtle and Roamer embodies the basic ideas of measurement
Chris Gregory is Senior Lecturer
in Mathematics Teaching at
The key ideas in measurement are:
- Measurement is a comparison of one thing with another
- Measurement is an approximate affair
- All measurements are inherently inexact
- Units are arbitrary. No particular magic resides in units like centimetres, kilograms or litres. These are adult conventions
- The approximate nature of measurement implies an ‘error’ – not a mistake but an unknown difference between what is intended and what is obtained
- Estimation before and after measuring is a vital part of learning and practising measurement skills
Mark Out the banks of an imaginary river and use a Roamer to measure its width to enable a bridge to be built. For this the pupils only need to know how to use the Forward command.Using the Roamer in, for example, the simple ‘river’ measuring activity, confronts children with all these key issues. In the river activity children have to decide what is being measured. Measure ment always has a practical context. This affects precisely what is measured. In this case the bridge needs to start and finish on ‘dry’ land so the measurement required is not ‘river edge’ to ‘river edge’. What units should be used? Children without experience of standard units will create units meaningful to themselves; Roamer units are very common conventions adopted by young pupils ?
Programming the robot to cross the river involves estimating distance and, if necessary, revising the estimate by ‘trial and error’. Most people asked to estimate the height of a room will think of it in multiples of their own body height. It takes time and many different practical activities for children to develop their own ‘yardsticks’ for estimating. The Roamer default unit of distance, one ‘body length’, offers a natural yardstick.
What is the width of the river? There are many answers to this problem. What is an acceptable answer is a matter of judgement involving practical issues. The issues of ‘error’, accuracy and tolerance are inherent to this judgement. Deciding on the acceptability of measurements A and C require careful considerations of practical aspects of the problem.
Most non-metric units reveal the importance of units in a personal way.