moments. At other times it is useful to say ‘can you tell me about this?’ This helps
to get an accurate connection between their thinking and their graphics. It is better
to ask the child as soon as possible after they have finished their representation. At
other times children change the meaning of their marks completely. Sometimes they
forget some of the details if there is too long a time between representing and
explaining what they have done. Some children choose not to say anything about
their mathematics on paper and this should be respected. This usually happens with
younger children and less confident older children. When they do feel confident
and choose to speak then it is an important growth point. It shows they are begin-
ning to explain their thinking and this reinforces their own ideas. Building up this
relationship with the child leads to extended dialogues. Children appreciate this
one-to-one attention in an atmosphere that is non-threatening.
What the child did
Looking at children’s actions tells us their intentions through certain kinds of graph-
ics, usually in schemas, dynamic and action representations. We have found chil-
dren who use any of these three are at a highly experimental stage and when they
visit new concepts they revisit these features.The mathematics
In what mathematics is the child engaged? This could be any aspect of number or
calculations, measurement, space and shape, problem-solving or data handling.
Parents’ and carers’ comments
Parents play a vital part in this assessment. They will be interested in their own chil-
dren’s representations and may be able to add comments about what they do at
home. Samples of children’s home maths add to the profile and gives us a more
holistic view of the child’s understanding.Assessment
We recommend a positive model of assessment..Every child’s mathematical marks
are treated as ‘intelligent responses’ (Pound, 1999). Good-quality assessment takes
time to work out and quality assessment of children’s learning goes beyond the
superficial: it probes further.
All of the above help to build up a picture to make a real and useful assessment of
children’s mathematical thinking through their own representations.The next step
The next question is how might we develop and support the children’s own mathe-
matics. By working through the above points closely, we have now gathered useful
information to support and develop the child’s understanding. At this stage we need
to consider carefully what the child needs, to continue their development so we can
plan accordingly. Figure 10.2 is a model to show the cycle of assessment, planning
and teaching.
Figure 10.2 illustrates the way in which observations can be used to inform teach-
ing that supports deep levels of learning (Worthington and Murchison, 1997).198 Children’s Mathematics8657part 2.qxd 04/07/2006 17:35 Page 198