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Open questions in maths teaching - supported by a motivating maths display

Thursday, 31 December 2015
Learning journeys and working walls will be going up in classrooms this week but also remember your staffroom - a motivating and informative display can support teachers too. What could it include? This display, from a school I visited in 2012, includes some open ended questions that are a key part of good maths teaching. 

So what could you add to a maths display for your staffroom?  


• Include your school's current maths focus and add simple ways to put it into practise. 
In this display the school focus was building a problem-solving approach to maths planning. The teachers were using a contextual problem as a starting point and then giving that problem 'legs' by making connections with lots of maths areas. It includes ‘Talk, use trial and error, convince yourself, explain’, ‘Think creatively in your maths lessons’ and ‘Maths is all around us’.


• Also include a few key questions to use in a maths lesson. It is interesting that no matter what approach a school takes for teaching maths the same key questions arise, these are the basics of good quality maths teaching. The following questions are regularly seen as part of a mastery approach, but they are methods that have been used in effective maths lessons over many years. It is good, however, to be reminded of them again and to make sure they are part of our teaching repertoire. 


'What do you notice?'

A phrase frequently heard in a Shanghai/Singapore style lesson is 'What do you notice?' As this 4-year old poster shows, that's not new, but it is still very effective.

'What do you notice?' is an open ended question that allows children to think about the maths without having to find a single correct answer. Look at this list of numbers:

0  2    4     6     8     10     12    14    16    18    20

Children may suggest that they can all be divided by 2, they are every other number (on a number line), the last digits repeat 2-12, 4-14, 6-16 and finally they may give you the answer you were possibly looking for - that they are all even numbers. In providing the things that they notice children will be learning some of the features of even numbers and so deepen their understanding. 


'What patterns can you see?'

Again another great open ended question. Using the same set of even numbers children can describe a pattern and then predict the next number.  The good thing with asking for the patterns they can see is that this can then lead on to making rules and generalisations - so important in mathematics. 

'Is that always, sometimes or never true?'

Having a statement and then asking children to say whether it is always, sometimes or never true is a great way to really think through properties of numbers and shapes. Multiples of 5 are even numbers. Is that always, sometimes or never true? This can lead onto 'How could you prove it?' and 'What else do you notice?' They may discover that when 5 is multiplied by even numbers the answer ends in 0 (and is even) and if multiplied by an odd number the answer ends in 5 (and is odd).

Here are a few more questions that allow pupils to talk, explain and show their understanding:

‘What have you discovered?’

‘How did you find that out?’

‘Why do you think that?’

‘Have we found all the possibilities?’

‘Can you explain your reasoning?’ 


Each of these puts the emphasis on valuing the pupils' responses within a climate of discovery and active learning. Most importantly it allows you as a teacher to determine the understanding of individuals and assess whether to move on a little and challenge further or whether to consolidate or go back a few steps to clarify and help them make sense of the maths.

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This display was used to support building a problem-solving approach to maths planning using a contextual problem as a starting point. When planning in this way, teaching maths around a theme, the key is to keep an eye on the objectives and expected outcomes but make the most of any other maths that fits the theme. This gives opportunities for reinforcement and enrichment. 
Related articles:

Linking a working wall to a learning journey
How are they different and how can they be brought together?

How one teacher linked a working wall to a learning journey
A teacher followed the ideas above and this is the result

Learning journey - make is a personal poster

Children can show their own progress in the form of a poster presentation
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