Maths Without Limits
Opening Young Minds to Endless Possibilities

Many teachers will introduce a new idea in a Maths lesson by presenting a problem and then getting the class to suggest possible answers. These will be discussed and the teacher will lead the class to the correct answer.

The problem with this approach is that only a few of the pupils are involved. Others listen to the debate without really engaging with it, simply waiting to find out at the end of the discussion ‘how you do it’.

What is needed is an approach where, instead of telling pupils whether their answers are right or wrong, the teacher challenges the pupils to engage with each others’ suggestions and develop their own understanding of the rightness or wrongness of each idea put forward.

Benefits

The key benefits of this process, compared with the typical question and answer approach are as follows:

 Traditional Question and Answer Teacher-led Dialogue Only a proportion of pupils are fully involved. Less confident pupils opt out of the thinking because they have not understood. All pupils are challenged to participate in the thinking process. The teacher is aware of the fact that some pupils are finding the discussion stimulating and some are finding it difficult or appear disinterested. The teacher is fully aware of the level of understanding and thinking blocks of individual pupils. The thinking goes at the pace of those who are participating in the discussion. The thinking goes at a pace which allows all pupils to remain on board in the learning process. Learning is superficial, dealing only with the problem presented. Learning is deep and engages with a whole raft of related concepts and ideas.

How it Works

There are two main ingredients in this process

1   The “Why” Question

• The teacher puts a question to the class.

• When a pupil gives an answer to the question the teacher does not declare whether the answer is right or wrong.

• Instead, the teacher asks the question “Wny? Why do you think that?” and gets the pupil to make their thinking explicit.

• The teacher then follows up the explanation by asking another pupil by name, “N____, What do you think?” and again asks “Why?”

• The teacher gets the buy in of a less confident pupil, (who was perhaps already beginning to tune out and lose interest) by again asking “N____, what do you think?” and again asking “Why?”, supporting this pupil in verbalising whatever understanding they might have.

• The teacher gets the input of other pupils as necessary.

• The teacher gets the general agreement of the whole class or group on whether the new idea should be kept or discarded.

2   Playing the Daft Laddie or Daft Lassie

• In the course of the discussion the teacher makes a suggestion /puts forward an idea which is clearly wrong and asserts “that’s right isn’t it?”

• If the class is unresponsive or acquiescent (being unused to the teacher ever saying anything that is wrong!) then the teacher spells it out more carefully, making the nonsense of the idea more obvious.

• Pupils challenge the teacher with a chorus of “No”s.

• The teacher responds in pantomime style with a questioning “Nooo??”

• Pupils then eagerly explain why the teacher is wrong and what they think the correct idea is.

• The teacher can then act further as daft laddie or lassie to elicit further ideas, or come out of role to clarify the current agreed thinking with further use of “Why?” as explained above.

Note on Effective Use

As with all teaching tools, the teacher-led dialogue process outlined above should be used in combination with other teaching methods. If used to excess in every lesson, it would make learning very tedious and laborious. Each teacher will want to develop their own style, assessing for themselves and for the group of pupils they are working with, when the process should be used, and the best combination of the two ingredients. However, if used well and in appropriate measure, teacher-led dialogue can have a radical effect, creating a real engagement in the learning process among less enthusiastic and less confident pupils and taking all pupils, able and less able alike, on a journey of discovery together.