One of the issues raised by parents is how to look at change in children's understanding of mathematics. In short, as a parent, how do I know if my child is really learning anything worthwhile about mathematics? Although there is no simple answer to this question, we can offer some guidelines for tracking change. In this newsletter, we will focus on spatial reasoning: reasoning about shape, measurement, depiction and navigation. Although children experience space all the time by virtue of living in the world, we intend to help children develop a mathematical language to describe their experiences.
Taking a Long View
Most programs of assessment try to measure change in short periods of time 
a few minutes, a lesson, a few days. CGI takes a different view  changes in
children's understanding of mathematics occur gradually over a long period of
time  years not days. Generally, we expect children's spatial reasoning to
develop in two ways:
(l) First, over time, children's reasoning about space becomes more representational  they are able to represent space by symbolizing, and talking. What was first known perceptually drawing, becomes known again mathematically. Children's representational skills grow.
(2) Second, over time, as children's reasoning about space becomes more representational, children begin to integrate representations  drawings are integrated with language, diagrams are labeled with numbers, and so on.
SHAPE
We look for growth in children's reasoning about the structure of space. This
includes ideas like dimension (2D, 3D), transformation (motions in a plane),
and visualization (how to take a space "apart" and put it back together
mentally). We look for the development of language to describe and think about
shapes, including describing relationships among different shapes and their
properties (ideas like sides, faces, angles, and systems of classification).
Early in the school year, children generally do not have very elaborate ways
of talking about or representing spatial structure. Your child's portfolio
provides snapshots of his or her development in this area.
MEASURE We look forgrowth in children's reasoning about measure of length, area, and volume. This includes ideas like appropriate units of measure, the importance of measuring with like (identical) units, and ways to iterate units to obtain a measure. Your child's portfolio should show the development of his or her thinking about length, area, and volume. 

DEPICTION Look for growth in children's abilities to draw maps or scale models, use nets to describe 3D space, and to make and interpret diagrams. 

NAVIGATION Look for growth in children's reasoning about large scale space. This includes ideas like position and direction, using a compass, making maps, using Logo, writing directions, and describing routes. 