While interacting in a well-developed math center, children have the opportunity to learn about the mathematical standards as defined by the National Council of Teachers of Mathematics (NCTM). These are numbers and operations, geometry, measurement, algebra, and data analysis. Although the early childhood teacher needs to provide experiences relating to each of these standards, the primary emphasis for pre-K through second-grade children is numbers and operations, geometry, and the measurement standards.

In addition, children in the early childhood years need to develop math process skills including problem solving, reasoning, communicating, connecting, and representing (NCTM, 2000). These process skills transcend mathematics, involving lifelong skills that children need to be successful in all areas of their lives. For example, in early childhood classrooms we can find many examples where children need to use problem-solving skills (planning a fair way to share a toy with a friend, determining a way to keep a tower of blocks from falling, or keeping a pool of water from sinking into the sand). We will explore each of these math processes in more depth.

### Problem Solving

Common steps for problem solving involve understanding the problem, making a plan for solving the problem, implementing the plan, and reflecting to see if the solution works or the answer makes sense (Copley, 2000). Problem solving not only entails learning and practicing these steps but also acquiring dispositions to problem solve. “An effective problem solver perseveres, focuses his attention, tests hypotheses, takes reasonable risks, remains flexible, tries alternatives, and exhibits self regulation” (Copley, 2000, p. 31).

### Reasoning

When children reason they “draw logical conclusions, apply logical classification skills, explain their thinking, justify their problem solutions and processes, apply patterns and relationships to arrive at solutions, and make sense out of mathematics and science” (Charlesworth, 2005, p. 142).

### Communicating

Children share their mathematical ideas in a variety of ways. They may communicate verbally or nonverbally (charts, tallies, and drawings). Even very young children display their mathematical knowledge (holding up two fingers when asked their age).

### Connecting

“The most important connection for early childhood mathematics development is between the intuitive, informal mathematics that students have learned through their own experience and the mathematics they are learning in school” (NCTM, 2000, p. 132). As discussed earlier, children naturally use math to solve problems they encounter in their natural world. Unfortunately, as children begin school and use formal mathematics, they often begin to view math as a set of rules and procedures rather than as a way of solving everyday problems. Teachers can help children to avoid this by using familiar manipulative materials to teach math, making children’s natural mathematics visible by using math vocabulary to describe their activities, and using examples from children’s experiences when introducing a math concept.

### Representing

Representing assists children in organizing, recording, and sharing information and ideas (NCTM, 2000). Children might use fingers, make tallies, create diagrams, produce graphs, make maps, or draw pictures to represent their knowledge (Copley, 2000).

When developing the math center, it is important to consider the appropriate math standards. Equally important is helping children use the math process skills as they use the materials. For example, Carmen was enjoying sorting rocks into groups by color. Juanita pointed out that Carmen was classifying the rocks (tied mathematical language to an informal math activity). She asked Carmen how she was grouping the rocks (stressed mathematical communication). When Carmen had completed the classification, Juanita asked her if she could think of other ways that she might classify the rocks (encouraged problem solving).