Children can be encouraged to reason, to conjecture about the way things are, and to check those conjectures. The emphasis is on children thinking for themselves, rather than repeating what the teacher wants. Children will want to communicate, listen, and clarify their own thinking in the process of communicating with others. Teachers questioning techniques including those intended to help children understand concepts, hypothesize, and generate interesting questions can help children appreciate the mathematics that surrounds them. Children can prepare to represent data in charts and graphs by sorting and organizing objects into groups to find out which group has more or less.
Mathematics also helps children understand, organize, and analyze their science experiences.
They can experience the connections between math and music when exploring rhythm and patterns, and between math and art when working with symmetry and design. However, in our eagerness to help children meet the standards, we must take care not to use instructional methods that give the appearance of high math achievement but that, in fact, interfere with real growth in understanding. Children are much more capable and confident when they are allowed to make sense of things instead of trying to follow someone else s thinking. Teachers, parents, and administrators will want to keep in mind that meeting the standards is a long process. Before children can meet this standard with understanding, they must be able to recognize a variety of triangle shapes and distinguish these from a variety of hexagon shapes.