The Development of Mathematical Language in a Young Child: A Pilot Study

Mathematics is a language, for the communication of ideas. During their preschool years, children develop a mathematical language base which they build on through further exposure to mathematical ideas. Teachers need to be aware of the early development of mathematical language and understand what language children are bringing to the preschool education environment. Thomas, Tagg, and Ward (2003) note that young children are often more capable at mathematics than had been expected in the past. Educators are becoming increasingly aware of the significance of this mathematical base and its ongoing influence on the student's development in mathematics. Cements, Sarama, and Dibase (2003) state, "robust mathematical learning by all children is a necessary base for later learning and it is necessary to keep children from falling permanently behind in mathematics" (p. 105). The importance of a vocabulary register within a subject area for the growth of a child's understanding in that subject is well acknowledged, and Meaney (2006, p. 39) states "without fluency in this register, many students struggle to learn and/or communicate what they know to others". In what order and at what rate does this language and understanding of basic mathematical terms develop? Children acquire oral language from a young age. Initial attempts to vocalise may just be to produce and imitate sound. Then children develop the ability to put meaning to the sounds they hear and produce words. By three years of age, they have, according to Lust (2006, p. 271), a "vocabulary of some 1,000 words". This leads to the question: How many of these words relate to mathematical language, and in what order does the young child's use of mathematical vocabulary develop? The first question, though, is what does mathematical language consist of for young children? The New Zealand Beginning School Mathematics (BSM) Programme (Department of Education, 1985a, 1985b, 1985c) has three modules that are based around: comparisons and relationships; shape, movement, and position; and classification, order, and pattern. This programme recognised the importance of developing mathematical language, the desirable vocabulary being listed at the start of modules. The order of acquisition of terms is influenced by whether the terms are adjectives, nouns, or verbs. Clark (2006) found that assigning names to properties was much more complex than naming objects. "Color is a property, and terms for properties appear to be more difficult to grasp than do those for objects, actions and relations" (Clark, 2006, p. 339). Children learning a new word fix that word to previously learnt knowledge, and this reference is more abstract for certain areas of mathematical language. Number and colour are words assigning properties, whereas geometric words relate to objects and actions. It would therefore be expected that the language for position and shapes would become part of a child's vocabulary before words relating to number and colour. Although a child may use colour words from about two years and six months, they rarely assign the correct meanings to these words: By 2 years 6 months to 3 years of age, they can produce a variety of color words in response to What color is that? but the colors they offer are rarely correct because they have yet to fix the reference of terms such as red, green, blue and yellow. Fixing reference is just the first step in assigning some meaning to an unfamiliar term. The next is filling in details of the meaning. (Clark, 2006, p. 340) The property words for colour and number may be more difficult to understand than object or position names, as the colour and number words can be assigned to a range of objects. There can be a red tree, red dress, red car (all with a variety of textures and hues), or there can be three balls, three people, three biscuits. …