Language and mathematics: How children learn arithmetic through specifying their lexical concepts of natural numbers

When children are about 18 months old their speech output rapidly increases. It’s like an explosion where about 10 new words are learned every day. It seems as if children suddenly understand how they can use language to interact with their surroundings. At 21 months of age the 100-word milestone in productive vocabularies is reached (Pine, 2005). Words are still mostly content words, used to refer to concrete objects and to describe the relationship between objects with expressions such as “car there,” “mommy’s mug,” or “doggy sleep” being common. Around their second birthday they start to use words to describe the relationship of singular and plural. After being able to say and point out “car there” and doing so for all the cars seen at that moment, all of the sudden they say “car there, many car,” pointing out all the cars observed (Barner et al., 2007). With the usage of natural quantifiers infants engage verbally with the world of numerical relationships. Soon after this development, children are able to describe objects as being “two.” What seems like simply naming a group of things needs in fact the development of deep lexical concepts, which rely, on the one hand, on innate structures, and which, on the other hand, is learned from conversational interactions (Carey, 2009). Being able to name the number of things seen in their surroundings means that infants refer to lexical concepts which are concrete and abstract at the same time. The twoness of something is concrete because of being unique and distinct from being “three” or “one”; on the other hand, it is abstract because it names and highlights just one feature of the objects seen. At the same time the word “two” has a whole bundle of different significations. We are, for example, referring to two cars meaning the magnitude, to the second car meaning the numerical order, and to two gallons of water describing a continuous substance. So, while “two” always has the same numerical value, it differs in shape, color, form, and size (Wiese, 2007). To integrate all these and even more information into one lexical concept requires about six years to develop as we will elaborate in the chapter.