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Mathematical ideas and techniques are used in a wide variety of work activities and in everyday life. In some instances their use is explicit and requires deliberate and considered selection and application. For example, installing a ducted heating system in a house requires the explicit application of mathematical ideas and techniques to specifications and costs so that comparisons can be drawn between alternative systems. Mathematical ideas and techniques also are applied explicitly in designing the system, planning the stages of installation and estimating quantities. But in other instances the extent to which mathematical ideas and techniques are involved may be obscure. In part, this arises because of the common perceptions that mathematical ideas and techniques are about basic number skins. Although basic number skins and operations are essential, mathematical ideas and techniques also involves the 'know how' of being able to choose efficient ways of doing things or judging when a particular outcome represents an appropriate answer or solution.
In the contemporary world the use of mathematical ideas and techniques is an important part of the functioning of organisations. It is integral to the process of making judgments and of ensuring the quality of a product or service. Many organisations, as they seek to establish themselves and to prosper in highly competitive world markets, rely on careful analysis of market trends, projections of growth and feedback from customers or clients. Analysing work flows and pinpointing areas for more efficient production techniques also draw upon the use of mathematical ideas and techniques. As work organisation changes, the need for Using Mathematical Ideas and Techniques exists not only for technical experts but is required by more people and shared between work units. Consequently, there is a demand for the use of mathematical ideas and techniques by a broader range of people.
Using Mathematical Ideas and Techniques focuses on the capacity to use mathematical ideas, such as number and space, and techniques, such as estimation and approximation, for practical purposes. One of the major ideas in this Key Competency involves the clarification of the purposes and objectives of the activity so that the most appropriate mathematical ideas and techniques may be selected. This can be illustrated by the way a shop assistant needs to be clear about the kind of account a customer requires before selecting, say, addition as the appropriate mathematical process. At a more complex level it may involve selecting the appropriate ideas and techniques to identify the factors to be taken into account in designing the shape, durability and cost of a container, including measuring and comparing lengths and calculating costs and quantities.
Another important idea in this Key Competency involves the application of mathematical procedures and techniques. For example, in making a garment, mathematical procedures and techniques underpin the laying and cutting of the fabric. At another level, mathematical procedures and techniques are needed to adapt a pattern to incorporate the design requirements of a client.
The Key Competency also involves making judgments about precision and accuracy. This can be demonstrated by the way in which a store hand will comply with the instructions to complete a stocktake. Also it encompasses the capacity to judge when an estimate is sufficient for the situation. For example, when estimating the materials required, a fencing contractor only needs to be accurate to the nearest two or three metres. But the estimate must be on the upper limit to allow for losses due to cutting and attaching and shaping.
A further important idea in this Key Competency is the interpretation and evaluation of outcomes and solutions. This means, for example, checking that the bill is reasonable for the order taken in a restaurant. It also involves evaluating the methods used in achieving a solution.
In summary, Using Mathematical Ideas and Techniques involves:
- clarification of the purposes and objectives of the activity;
- selection of mathematical ideas and techniques;
- application of mathematical procedures and techniques;
- judgment of level of precision and accuracy needed;
- interpretation and evaluation of solutions.
At Performance Level l, the primary focus of Using Mathematical Ideas and Techniques is the efficient and reliable use of mathematical techniques in everyday situations which are clearly defined. Performance Level 2 focuses on the sequencing and application of mathematical ideas and techniques in situations which require the selection of appropriate methods. At Performance Level 3, the primary focus is the selection, sequencing and application of mathematical ideas and techniques in situations where the best strategy requires the evaluation and adaptation of the method and the solution.
PERFORMANCE LEVEL 1
At this level a person:
- clarifies the nature of the outcomes sought; and
- selects the ideas and techniques for a task; and
- uses mathematical ideas and techniques reliably and efficiently; and
- meets accuracy requirements; and
- checks that the answer makes sense in the context.
PERFORMANCE LEVEL 2
At this level a person:
- clarifies the purposes of the activity and the nature of the outcomes sought; and
- identifies the mathematical ideas and techniques which are applicable; and
- selects, sequences and applies the mathematical ideas and techniques reliably and efficiently; and
- judges the level of accuracy required; and
- checks that the answer makes sense in the context.
PERFORMANCE LEVEL 3
At this level a person:
- defines the purposes and objectives of the activity; and
- recognises the assumptions which need to be made in order to apply an idea and technique; and
- adapts the idea and technique to fit the constraints of the situation; and
- makes decisions about the level of accuracy needed to resolve competing demands; and
- interprets and evaluates methods and solutions.
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