Challenges in the ‘teens’
When children learn to say the counting words, it is quite common for them to experience some problems with the ‘teens’. The teen number words often sound very similar to other number words. For example, ‘thirteen’ sounds similar to ‘thirty’, ‘fourteen’ to ‘forty’, ‘fifteen’ to ‘fifty’ and so on. Although it can be surprising to hear the response ‘ninety-one’ when you ask a child what number comes after ‘nineteen’, this is a logical answer if the child treats the number words ‘nineteen’ and ‘ninety’ as being the same.
This problem of understanding the naming of numbers between ten and twenty also includes the two number words eleven and twelve that occur before the ‘teens’. The old English or Germanic origins of eleven and twelve suggest that they originally meant “one left over” and “two left over”, respectively. However, the etymology of the pre-teen number words eleven and twelve does little to support a child’s search for consistent structure in the counting word sequences. As well as reversals in the ‘teens’ where the smaller value is named before the larger value (e.g. the four comes before the ten in fourteen) students need to interpret two different modifications of “ten”; ‘teen’ and ‘ty’, neither of which clearly says “ten”. Since the ten and ones structure of the ‘teens’ is not transparent in English, more learning time must be devoted to developing an understanding that the numbers from 11 to 19 express one group of ten and a particular number of ones.
Knowledge of a student’s use of the sequence of number words is a powerful indicator of the efficiency of addition and subtraction methods. Wright (1989) distinguished between the development of the forward sequence of number words and the backward sequence of number words, describing five levels in each as well as an emergent level. The levels are summarised in the following tables.