Make the most of children's enthusiasm for maths, even when it goes over the top, says Jenny Houssart
Does maths make you want to shout and scream? It certainly has that effect on some children. This is the story of unofficial talk in primary mathematics lessons, the occasions when children can't resist shouting out, when they make comments as asides during activities or even whisper surreptitiously in the ear of the person next to them.
Penny's story suggests one reason for shouting out. She had made several unasked-for comments during that lesson, as she often did. For example, when the teacher used the word "product", Penny remarked, "same as times". Penny often acted as a sort of unofficial translator in the classroom, explaining the teacher's actions or paraphrasing mathematical terms.
The teacher was being positive. He called out the names of various children and asked them to stand up. He then announced that all these children would be given a star, because they hadn't shouted out. "I haven't shouted out!" Penny shouted out indignantly. "You were shouting out," the teacher explained patiently. Penny grudgingly conceded that this was the case but added: "I was trying to help."
Penny was fairly confident in her understanding of what was going on. Neil, on the other hand, often found maths difficult and was slow to pick up new ideas. Neil's story tells of an exceptional incident when the penny suddenly dropped. This led to him sharing his success with everyone, with normal rules about classroom talk forgotten.
The teacher was holding up numbers and the children had to work out what had to be added to each number to make 20. She held up 14 and then prompted the children by saying: "What do you put with four to make 10?" "I get it!" Neil shouted suddenly, getting very excited. Looking at his number fan he said: "Mr Sixy, where are you?" In case anyone was in any doubt, this was followed by the comments: "I know, I know!" Another occasion on which some children are tempted to shout out is when they have noticed or discovered something. Such discoveries are often accompanied by comments such as "All you've gotta do" or "It's easy". These comments may sound like bragging, but they may also indicate that the child has seen a mathematical pattern or generalisation. Of course, many children do not shout out because they abide by the classroom rules. Hopefully they get an opportunity to share their discoveries within the rules.
Another way round the no-shouting rule is to whisper. The whisperers may be as desperate to say things as the shouters, but they seem less bothered about receiving a response. Noticing something is often a good reason for whispering. Whisperers also have a habit of wanting to add a thought. This often happens when children are counting or sequencing and someone continues in a whisper after a halt has been called. Sometimes they want to expand on what has been said, as in Sean's story. Whisperers also sometimes disagree with things under their breath. If someone makes a mistake on the board, they might well point it out. They have even been known to take issue with the teacher.
The teacher was introducing the idea of converting metres to centimetres. A previous session had involved converting centimetres to millimetres. When the teacher explained that one metre is a hundred centimetres, Sean said in a whisper: "A hundred centimetres is a thousand millimetres." A bit later the teacher started talking about a piece of string, which he said was just under a metre long. Sean said in a whisper: "999 millimetres perhaps."
Whisperers act like undercover mathematicians. They make discoveries, look out for inconsistencies and try to extend ideas. Shouters can be seen as acting mathematically too; they are sometimes desperate to share discoveries or are carried away by enthusiasm because they have suddenly made a leap in understanding. Unofficial talkers are worth listening for. They may be operating in a classroom near you.
ABC of talking types Do you recognise any of these classroom characters?
Alec likes to dispute answers and statements made by others. In extreme circumstances, he may even take issue with the teacher. Usually he knows enough about classroom rules to do this in a whisper. Sometimes Alec is just trying to be smart, sometimes he may be making a crucial mathematical point.
Betty acts as a sort of unofficial translator. If a complicated mathematical word is used, she will be ready with alternatives. She might also offer quick explanations if she thinks something has been missed out. Perhaps Betty's talents can be harnessed in helping to create a class mathematics dictionary or thesaurus. Perhaps she fancies a teaching career.
Colin speaks quietly after everyone else has stopped, a bit like the sound of a train disappearing in the distance. He loves counting and sequencing activities and often continues them further than asked. Sometimes he also has something to add to an answer or explanation. Colin might be encouraged by counting or sequencing activities in which the end point isn't specified. This could even lead to a discussion of infinity, though it could also lead to a very late playtime.
If Dora has noticed or discovered something she may not be able to resist telling everybody. This is a bit like Archimedes jumping out of the bath and shouting Eureka. Fortunately Dora is likely to keep her clothes on. Sometimes she may be more cautious and share her discoveries in a whisper. Her contribution may be crucial to the lesson - she may even encourage others to share their discoveries.