ment as well as opportunities and experiences, including instruction. The teaching-learning paths can provide the basis for curriculum and can be used by teachers to assess where each child is along the path.

Although it is true that young children are more competent in mathematics than many early childhood teachers, parents, and the general public believe, there are limits to what they can do in mathematics. The committee kept this in mind throughout the study process, and thus the teaching-learning paths presented in this report are both foundational and achievable.

The first content area is number, including whole number, operations, and relations. Working with number (e.g., learning to count) is the primary goal of many early childhood programs; however, when given the opportunity, children are capable of demonstrating competence in more sophisticated mathematics activities related to whole number, operations, and relations. For example, cardinality—knowing how many are in a set—is a key part of children’s number learning. Relations and operations are extensions of understanding number. The relations core consists of such skills as constructing the relations more than, less than, and equal to. The operations core includes addition and subtraction.

The second major content area is geometry, spatial thinking, and measurement. Children’s foundational mathematics involves geometry or learning about space and shapes in two and three dimensions (e.g., learning to recognize shapes in many different orientations, sizes, and shapes). A fundamental understanding of shape begins with experiences in which children are shown varied examples and nonexamples and understand attributes of shapes that are mathematically relevant as well as those (e.g., orientation, size) that are not. As children progress along the teaching-learning path, they need opportunities to discuss and describe shapes, and, on the basis of these experiences, they gain abilities to combine shapes into pictures and eventually learn to take apart and put together shapes to create new shapes. Young children also need instructional activities involving spatial orientation and spatial visualization. For example, they can use mental representations of their environment and, on the basis of the representation, model relationships between objects in their environment. Importantly, children’s knowledge of measurement helps them connect number and geometry because measurement involves covering space and quantifying this coverage. Later, children can compare lengths by measuring objects with manipulable units, such as centimeter cubes.

Number is particularly important to later success in school mathematics, as number and related concepts make up the majority of mathematics content covered in later grades. However, it is important to point out that concepts related to number (and relations and operations) can also be explored through geometry and measurement. In addition, geometry



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