Thinking Skills: Critical Thinking and Problem Solving

112 Unit 3 Problem solving: basic skills

Approximately what proportion of the two

tiles will be needed to cover the whole floor?

A three white to one black

B two white to one black

C equal quantities of both

D two black to one white

E three black to one white

Spatial reasoning involves the use of skills that

are common in the normal lives of people

working in skilled craft areas. Imagine, for

example, the skill used by joiners in cutting roof

joists for an L-shaped building. This is also

necessary for many professionals: the surgeon

needs to be able to visualise the inside of the

body in three dimensions and, of course,

architects use these skills every day of their lives.

Spatial reasoning questions can involve

either two- or three-dimensional tasks, or

relating solid objects to flat drawings.

Thinking in three dimensions is not

something that comes easily to all people, but

undoubtedly practice can improve this ability.

In the simplest sense, a problem-solving

question involving spatial reasoning can

require visualising how an object will look

upside down or in reflection. More

complicated questions might involve relating

a three-dimensional drawing of a building to a

view from a particular direction or the

visualisation of how movement will affect the

view of an object. This chapter is shorter in

terms of description than most of the others

but there are more examples at the end; this is

an area where practice is more important than

theory.

The next example involves a problem-

solving task in two dimensions.

3.9 Spatial reasoning

Commentary

This seems a relatively simple problem, but the

answer is not immediately obvious. This is an

example of a tessellation problem. There are

various ways to go about solving it – one way is

to continue drawing the pattern until you have

enough tiles that you can estimate how many

of each are needed. Another, more rigorous,

method is to identify a unit cell that consists of

a number of each tile, which may be repeated

as a block to cover the whole area. Such a unit

cell for this problem is shown in the drawing.

If you now think carefully, you can imagine

that this block of three tiles could be repeated

The drawing shows part of the tiling pattern

used for a large floor area in a village hall.

This is made up of two tiles, one circular

(shown in black) and one irregular six-sided

tile (shown in white).

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