Truth of propositions
The idea of truth, including notions of 'true', 'not true' and 'sometimes true', underpins other ideas, such as:
- equality and equivalence
- deduction and proof
- chance and probability.
There are many opportunities for teachers of mathematics to ask questions:
- Is (this proposition) true?
- Is it just sometimes true, or is it always true?
- When is it true?
- How do you know?
- How could you demonstrate or show or prove that it is true?
A year 8 scenario about the tessellation of quadrilaterals is useful for illustrating a 'truth' activity.
Do quadrilaterals tessellate?
A teacher asked students to consider the statement "Any quadrilateral will tessellate" and whether this is true some of the time, all of the time or never true.