Teaching mathematics

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# 5 Summary of Week 5

In Week 5 you have looked at functional thinking and how this is introduced using the idea of the function machine which works by operating on an input to produce an output. This led to a consideration of number sequences where the input is the position in the sequence and the output is the number (or term) at that position. Finally the idea of covariance was introduced where there are two quantities which vary together according to a relationship. The two quantities can be plotted on a graph and the shape of the graph is determined by the function itself. Although the concept of the function is a sophisticated one, the approaches you met in week five show that it is possible to carefully introduce it to learners in the middle years.

You should now be able to:

• introduce learners to the concept of functions using concrete and pictorial representations (such as the function machine) and to develop this towards more abstract representations of functions
• use other representations, with which the learners are familiar, to build on their understanding of functions
• explain to learners how two unknowns can vary together according to the rule (or function) connecting them.

Next week you will learn about the teaching and learning of geometry, including how shapes are defined according to their properties and problem solving in geometry.

You can now go to Week 6 [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

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