each other. No two pieces of children’s thinking on paper are the same because no
two children’s minds are the same: we all have different experiences to form our
thinking. Think of snowflakes – each has a different pattern, and all are exquisitely
beautiful. It is the same with children’s own mathematics on paper: as the children
get older they slowly refine their skills to include more efficient strategies and inte-
grate the standard forms of symbols on paper with understanding.
The first sample (Figure 10.3) is provided together with an example of an assess-
ment form with all the relevant sections we have discussed previously (Figure 10.4).Figure 10.3 Amelie’s dice gameWhole-class assessment
A very open question is useful for whole-class assessment purposes. An open question
is much more personal and infinite compared to an ‘open-ended’ question which
seems in some respects to indeed have an end. Take the question ‘how many ways can
you make 20?’ This may show us how many ways a child can make 20 but it does not
show us what else a child knows. The question itself is a very useful investigation-type
question and can show us many aspects of a child’s thinking, but we limit knowing
what the child wants to tell us she knows about mathematics. Open questions are
useful to use when you actually do not know what the children know. This might
happen at the beginning of a new school year or when you start a new mathematics
topic. The following assessment on a child’s mathematical marks came from a class
who had been asked by the teacher in the second week of school ‘What do you know
about numbers?’ She wanted to know what they knew about numbers before she
planned her teaching sessions and her learning environment. The teacher encouraged
children to choose what they needed. In this example Jason had chosen to use a com-
bination of materials (see Figure 10.5). As well as writing materials, he had chosen cir-
cular stickers to represent a quantity and cut out paper numerals for the number 37.200 Children’s Mathematics8657part 2.qxd 04/07/2006 17:36 Page 200