Teachers of young children have a unique opportunity to begin building a community of learners where children exchange mathematical ideas with one another and with the teacher. Young children are natural risk takers. Their focus is on making sense of their world rather than getting the correct answer. We can take advantage of this willingness to risk as we focus our teaching around the process of doing mathematics and making sense of mathematics. By accepting multiple forms of communication from young students, we allow them to show their understanding in ways that are meaningful to them. While one child may need to draw pictures of his thinking, another student may be able to begin to connect her drawings to written language, whereas a third student may be ready to begin using symbols to communicate the same idea. This gives all students an opportunity to be successful in mathematics and enables the teacher to meet each child's individual needs.
Only at is after students have experience using various ways to communicate ideas can they begin to connect their invented symbols to the standard notation of mathematics, and to connect their everyday language to mathematical language and symbols in a meaningful way. The classroom teacher's job is to recognize the appropriate times for helping students make these connections.
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