Many stories have made children long to be detectives or athletes, and helped build the image of those with sporting and musical talents. It is harder to find books portraying positive images of mathematicians, or suggesting that talents for accurate addition or fast multiplication are special. Fortunate-ly, they do exist - and some specifically celebrate children's ability to calculate mentally. As well as painting a favourable picture of young mathematicians, they can encourage children to carry out mental calculations while creating useful mathematical possibilities.
Perhaps the youngest mathematical star in children's literature is "Calculating Connie" in Dick King-Smith's eponymous story. This amusing tale appeals to children towards the end of the infant years, though it offers mathematical starting points ranging from counting fingers and deciding which number follows two, to mental calculation of VAT.
Connie is a toddler with remarkable ability, adding numbers in her head when she is only two - though harder problems have her screwing up her face and sticking out her tongue. But her talents develop as the story progresses. She can recognise odd or even numbers, total shopping bills and calculate using percentages. She becomes contemptuous of pocket calculators and, unfortunately, of her parents! Ultimately, Connie receives a bump on the head and loses her powers.
Marty Malone is an older mathematician, star of Betsy Duffey's The Maths Wiz. Marty's love of maths has him calling his pet guinea pigs Plus and Minus. Predictably, they multiply and Marty happily charts the number of pets in the house, though his mother takes a dim view.
The story explores Marty's attempts to come to terms with his new school, especially PE lessons. He is aided by his maths teacher's creative approach to problem-solving, and the promise of a maths club picnic. Marty is also cheered by a note passed to him in a maths lesson, consisting of just a number. This heralds the start of a new friendship which, as the teacher suspected, is the real solution to Marty's problems. Roald Dahl's Matilda is a famous prodigy, recently heroised in a popular film. Sadly her abilities are not appreciated by her parents. Her mother thinks looks are more important for girls, while her father denies that complicated calculations can be done mentally. Yet he sees a use for maths.
As a crooked used car salesman, he takes a keen interest in increasing his profits by decreasing the stated mileage of cars!
Then Matilda goes to school. The chapter dealing with her first lesson with Miss Honey says a lot about multiplication, with the enlightened Honey inviting Matilda to explain her mental methods. Miss Trunchbull's maths lessons, on the other hand, are a wonderful caricature of all the negative possibilities of tables tests. As children emerge with stretched ears and sore heads, she delivers firm opinions about multiplication. They include a rather direct method of teaching the commutative property and a firm denial that multiplication can be performed as repeated addition.
Most children are neither Martys nor Matildas, but they can all be encouraged to calculate mentally, and to improve and take pride in their mathematical performance. These stories can help, while making a welcome change from strings of beautiful, brave or daring heroes and heroines so busy taking the world by storm that they miss out on mathematical adventure.
Calculating Connie Younger children might like to correct Connie's incorrect counting (chapter three) or say how old people of various ages will be on their next birthday.
Encourage children to identify pairs of numbers they can add mentally, as Connie does in chapter two. This chapter also lends itself to mental addition of prices.
Can children identify the correct words used for large numbers in chapter three, and say what they mean and how they are written?
Can older children calculate percentages of amounts of money (chapters two and three)? Do they know a method for mentally calculating VAT at 17.5 per cent?
"Calculating Connie" is one of two stories in Connie and Rollo, by Dick King-Smith, published by Young Corgi Books.
The Maths Wiz Suppose the guinea pigs have babies in multiples of three or five and find the total. Or stick to multiples of four but assume all the guinea pigs continue to reproduce.
Encourage children to improve their speed of calculation, or ask them to find particular calculations for which they have quick methods - and explain what those methods are.
Ask children to suggest possible calculations for Marty's T-shirt. We are told it bears a long calculation with the answer 3,742. You may wish to invent a T-shirt with a shorter answer.
Investigate how answers change as something is added to the original question, or if the question is changed in some other way.
The Maths Wiz by Betsy Duffey is published by Puffin Books. The guinea pigs feature in the first chapter. The other ideas above relate to the chapters describing the maths lesson and its aftermath (entitled "Triple Uh-Oh", "A Note to Marty" and "3,742").
Matilda Which tables do the children know? Which do they find easy to learn and why?
Suggest problems capable of solution by either addition or multiplication. Which operation do children prefer? Do they understand the links, or that the order of the numbers to be multiplied is irrelevant?
What methods do children use for multiplying larger numbers by two? Can they multiply two 2-digit numbers mentally and explain their methods?
Collect advertised prices of used cars. Can the children read the prices and put them in order? Can they calculate profits, given buying and selling prices?
Matilda by Roald Dahl is published by Puffin Books. The calculations related to used cars are based on the chapter "Arithmetic". The other ideas arise from the maths lessons described in "Miss Honey", "The Weekly Test" and "The Third Miracle".