How young children make their world mathematical (with the help of language)
Many researchers have investigated how human language develops, with psycholinguists, sociolinguists and educational linguists searching for evidence of how natural language intersects with learning in different domains, specifically in the learning of mathematics.
Children are instructed in the symbolic and abstract world of maths as they engage with their world experientially. They learn by example, from people who engage with mathematics themselves in a systematic way. An example of such engagement is the imitative saying of words in the count list (one, two three…), preparing them for maths learning and serving as a place-holder for later conceptual understanding. Children pick up on a (rather long) ‘meme’ – the list of sequenced words that they hear and repeat. They learn the ‘count meme’ and say it, but their language is not numerically meaningful at first, although it is a source of great enjoyment – especially if they note how their parents react because the two year-old is not only learning to speak, but also to ‘count’!
Well, this is not yet real counting. Most children learn to count (for real) only when they can see the one-to-one correspondence between objects that they count out. It takes a long time to cement this knowledge. It also takes a long time to get the sequence right and to establish an understanding of which number comes ‘before’ or ‘after’ another number. Children develop a personal mental line of numbers, but its neurological representation is not the same for each child. It is not as if there is a straight ‘numberline’ representation in each person’s mind. I still have the same representation that I had as a grade one child. My mental image is more like a wobbly line graph than a horizontal line.
In this type of cognitive development, as in the learning of the count list, the language used by a child features strongly. Later on, it can become one of the obstacles in solving word problems.
Why language of learning matters
While learning to make their world mathematical, children rely on the language in which they encounter facts, procedures and concepts of maths – communicated in a specific language. But, the structures of languages differ. Spoken languages sound very, very different. When I go into a grade R class where everyone speaks Sesotho, and then go to a class next to it where everyone speaks isiZulu, I hear different intonations, accents, sounds, pauses and also tempo.
The big picture of language as a powerful tool in early education is very much like digging and filling the foundations of a house one wishes to build. So, if children come to school they learn new words and sentences in their home language (or not). They also learn to identify written symbols (1, 2, 3…) which, at the same time, have a linguistic name too. On top of that they have to learn the procedures of how to use all of this data, and then try to build a concept. They do all of this at quite a speed – in one language, with some South African code-switching to English here and there when the instruction is not in English (or Afrikaans).
Most children in our country move on to grade 4 and they learn via a dense school curriculum and, on top of that, they encounter all of this in English – a very challenging language to learn to read and write and to get to know the logic of its grammar and syntax.
Considering all of this, I would say that one way to prepare young children to learn mathematics and science, is to insert English as a language of reading in the areas of Science, Technology, Engineering and Mathematics (STEM), as soon as possible. In the SARChI Chair that I hold on the University of Johannesburg Soweto campus, this is our main project. We are investigating ways to bring the English terminology and syntax into English readers (books for learning to read) and we are developing reading tests that use the content knowledge of STEM in the SA curriculum.
One of the assets of a multilingual country is that we can translate back and forth and look for meaning by accessing other languages. Ensuring that each child can read and communicate in their home language is the first component of the building of their house of knowledge. But, we cannot fully utilise this asset when English is not firmly established by the middle grades of primary school.
Author: Professor Elizabeth Henning
SARChI Chair: Integrated Studies of Learning Language, Mathematics and Science in the Primary School
University of Johannesburg
| To this day when I imagine numbers in a sequence, not using symbols, the mental picture is this line graph. The horizontal numberline is a good heuristic too, but not always, because it is nearly always represented as a straight line. It is one version. Switching from one language of instruction to another language of instruction during teaching and learning. SARChI Chair in Integrated Studies of Learning Language, Mathematics and Science in the Primary School.|