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| Teaching and learning Measurement | Measuring equipment used in schools | Activities | The language of measurement | The measurement topics covered on this CD-ROM extend well into secondary school level. However both primary and secondary teachers need a firm grasp of these topics. Many secondary level concepts arise, if only in an informal sense, in primary school. Teaching
and Learning Measurement Here is a framework for teaching and learning measurement from the early years.
PLACIFIER is a useful reminder of the nature of activities for measurement teaching. It is not meant to be sequential. Not all aspects would be included in every lesson nor in the teaching of every concept. Some aspects only apply to the early years. At times you will cycle back and forth through various aspects. 'Language' and 'Real Applications' have a role at each stage of development. Elaboration of the Framework Children develop an awareness of the concepts of quantities (attributes), including under what conditions an attribute is conserved, through structured exploration. Structured exploration to develop an awareness of an attribute needs good choice of contrasts and similarities. Developing awareness of volume, for example, will require objects with the same volume, but differing on other attributes (e.g. height, shape, mass) and objects differing in volume but with the same height or length or mass or general shape. Discussion during activities is crucial to introduce and then use the necessary vocabulary. Attribute awareness is reinforced by comparing objects on one or more attributes, eg. length and/or mass, and the simultaneous development of associated language. Both direct and indirect comparison activities should be undertaken. Most of the principles of measurement can be developed using non-standard units, including the fundamental principle that the number of units that matches the given property can be used, with the unit, as a valid description (measure) of that property. Another important principle that can be developed through nonstandard units is that if the unit is smaller, the number of units measuring a given object is greater. Experience with comparison and nonstandard units can precede formal or standard (ie common) units. Once proficiency in measuring using the metric system is established, appropriate interrelationships between attributes can be investigated and used for calculations. For example, length is used to find the area of a rectangle. The goal of all measurement is competent application of measurement concepts and principles in real-life situations. Measurement derives its sense from practicality so an emphasis on pen and pencil activities is inappropriate. Applications begin in the early primary years - they are not left until later. Real-life measurement situations often involve estimation. The selection of appropriate measuring tools and units is an important aspect of estimation in practice. Progress in developing measurement skills is dependent on the development of prerequisite number and computation skills.
(The
PLACIFIER mnemonic was derived from one used by Lola Hill of Deakin
University.)
Measuring equipment used in schools There are numerous pieces of equipment which can be used in measurement activities in the primary school. We have listed some ideas below. Early primary years
Middle and upper primary years
Secondary years Similar equipment as in upper primary and more precise equipment is used. Scientific instruments now often have a digital display.
Generally, activities can be sequenced from those where concrete materials are used in a direct way (early primary) to activities where a mixture of concrete materials and pictorial or other representations are used with indirect comparison using units of measure, both nonstandard and standard (middle primary). Activities finally move towards the abstract (later primary and secondary), e.g. given the dimensions of a cube, find the volume. It needs to be noted that even at later primary and secondary levels, students will still be working with concrete materials at times.
An emphasis in all activities at all levels would be on language, from the earliest levels, with 'bigger than', 'smaller than', to later levels with the more complex language of comparison, e.g. 'this is three times as long as.' Examples of activities at the different levels, early (early primary), middle (middle primary) and late (late primary and secondary) could be: Length
Area
Perimeter
Volume
and Capacity
Mass
Time
Angles
Temperature
The language of measurement When measuring we compare objects. Some examples of the comparative language we use are listed below:
We also use words and phrases to indicate location and proximity:
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