“This paper describes a lesson taught to Judy’s Y2 class in a rural Hertfordshire primary school. It shows how meaningful mathematics can be made accessible to young children and, importantly, how fundamental issues of variant and invariant properties might be developed. An important component of this understanding is the position to term relationship – the relationship (or rule) between the position, n, of a number in a sequence and the number itself. In short, it is our view that young children, when given appropriate opportunities, can operate at levels substantially higher than the curriculum would indicate was likely.”
The teacher in this case made an animal, a dog, using linking cubes. The general shape was expanded upon to make two larger animals in a ‘family’ of three dogs.
“We discussed the dogs we had made. My questions and prompts were intended to alert them to an awareness of those elements of the dogs that remained constant (invariant) and those that changed. In respect of those elements that changed the intention was to encourage their understanding as to the systematic, and therefore predictable, nature of that change.”
The key to the children’s understanding seems to be labelling each of the parts of the dog, head, legs, shoulders, body and bottom. Once they could apply these labels to each of the three dogs, they could see how the animal was made up. They then used this knowledge to predict the make up of the fourth dog.
After this, they applied their knowledge to their own animals – working out the 4th and 10th members of the family. Some did this in tables, some did this in sentences, but they all could do it regardless of their mathematical abilities. Some were making generalised statements linking the term in the sequence to the body parts. All good stuff and remarkable when you consider that these children are in Year 2…
Reference:

Andrews, P., Sayers, J. (2003) ‘Algebraic Infants’ Mathematics Teaching, Vol. 182, pp. 1822
[…] 2: use ideas from algebraic infants. Modelling how a family of dogs can be constructed. Legs, shoulders, bum, body, head – with only […]