English is not the best language for numbers

In German apart from the irregular numbers “elf” (11) and “zwoelf” (12) the two digit numbers (those between 10 and 100) have names that start with the quantity of units followed by the quantity of tens. Hence 21 is “ein und zwanzig” or one and twenty and 56 is “sechs und fuenfzig” or six and fifty. This makes it easier for the German school child to do mathematics in their head than it is for an English speaking pupil. When performing addition we are taught to add the units first, then carry any tens created across before adding up the tens. Because of the way that German orders the digits with the units coming first, it is easy for the German child to add the units first before moving onto adding the tens. In doing mental maths, the English speaking child faces a different type of problem. In order to focus on the quantity of units, the English speaker has first to ignore the number of tens, and the problem they face is not with the addition, but with remembering what the original numbers were. In the example above, adding twenty one and fifty six, the child (or adult for that matter) has to ignore the “twenty” and focus on the “one”, and then ignore the “fifty” and focus on the “six”. Now these two numbers can be added, six plus one gives us seven. Now to focus on the tens. But what were they? Having discarded the first half of the two digit numbers from memory in order to focus on the units, the difficulty the pupil has is in recalling what the original quantities of tens were. So whereas German pupils are buoyed up by their ability to do two figure sums in their heads, English speaking pupils are discouraged by their failure to do so. But this has nothing to do with their mathematical ability, it is a result of the language that they use. At Puppet Maths we teach mental arithmetic differently. We teach children to visualise numbers as quantities of physical articles, which allows them to add them in any order they like. We encourage them to count up. So in the example above we would encourage the pupils to imagine 21 pence and 56 pence as coins. Then they could add them up adding the fifty and the twenty to get seventy pence, and then the one and the six to get seven pence. This visualisation, and the performance of the addition in the order in which the digits are used in the name of the numbers overcome the memory problem, and allows children to succeed in this aspect of mental arithmetic.