The maths world is full of places to visit. One attraction well worth an extended pit stop is the maths mecca of Las Vagueness. It’s a place to play with mathematical ideas inside “concept casinos”. We’ve known them for years as classrooms.

You’ll find a lot of open-ended activities inside because they challenge learners to think from more than one angle. It’s a rich mathematising environment where risk-taking is the norm and wrong answers are welcomed because they contribute towards fuller understanding.

First-time visitors to Las Vagueness might be confused. They see maths as a black and white subject with straightforward answers. For example, consider the following statement: “5 and 7 are consecutive numbers”. Black and white thinkers will brush the idea aside. They will say that 5 and 6 are consecutive numbers, but not 5 and 7. Now enter the grey thinkers. They point out that 5 and 7 are consecutive: as odd numbers, and primes as well. In a sense, both are right but one is two-dimensional and the other is cubic. Grey thinkers look at concepts from all sides. Black and white thinkers fold their arms and leave things on the table.

Setting up this scenario is easy and a range of true-false gambits can be used. Some include: “The largest acute angle is 89 degrees”, “There are 64 squares on a chessboard”, “A rhombus has four lines of symmetry”, “A pentagon cannot tessellate”, “The next number after 0.6 is 0.7”, “The opposite numbers on a die add up to 7” and so on.

They all have a touch of ambiguity and they are open to interpretation, which in a concept casino habitat stimulates discussion, debate and learning conversations. When learners talk about these ideas they have to take a punt and stick their necks out. They might agree or disagree, but the real maths starts when they think out loud and justify their ideas supported with evidence. Some learners might see a parallelogram as a pushed over rectangle and conclude that it doesn’t have any lines of symmetry. But what about a square? A square is a parallelogram and has four lines of symmetry.

As a teacher, Las Vagueness is a great place to visit. You watch and listen. When children discuss their ideas they often get engrossed, which means you can pick up information as they chat. This is the time to judge the colour of their thinking. What children talk about sets the learning agenda, allowing you to use what they say to their advantage. It’s maths exploitation at its best

John Dabell is a teacher at Lawn Primary School in Derby

A number of speaking and listening objectives are met by debating true-false statements.

* Y3 Block B

Sustain conversation, explaining or giving reasons for their views or choices

* Y4 Block A

Respond appropriately to the contributions of others in the light of alternative viewpoints

* Y5 Block C

Understand the process of decision making

* Year 6 Block E

Understand and use a variety of ways to criticise constructively and respond to criticism