Effective programs preparing teachers of mathematics at the early childhood level require at least one mathematics content course (or equivalent professional-learning experiences) focused on key mathematical ideas and processes that are important in early mathematics, including problem solving, number, operations, spatial thinking, shapes, measurement, and early algebraic thinking. [Elaboration of P.2]
Early childhood educators are responsible for establishing the mathematical foundation for children from birth to age 8 years. This is an especially critical period for laying the groundwork of mathematics ideas and understandings as well as forming early positive attitudes toward mathematics and statistics. Well-prepared beginners need to study the mathematics content relevant to children’s learning of mathematics in preschool and the primary grades as well as the mathematics that extends through the elementary grades. Understanding this range and progression of major mathematical domains enables well-prepared beginners to support programmatic coherence between preschool and the primary grades and from the primary grades into upper elementary school. For well-prepared beginners to utilize the learning trajectories, they must understand the underlying mathematics—a core element of learning trajectories (too often neglected). The trajectories highlight mathematical content and proficiencies important for early childhood educators, including the importance of both composing and decomposing number, composition and decomposition of shapes, spatial thinking, subitizing, angle size, length, area, and volume as well as early multiplication and division ideas and early fractions.
For these reasons, effective programs for preparing teachers of mathematics at the early childhood level and others who support young children’s learning of mathematics provide opportunities that enable candidates to learn mathematics content and practices throughout the range of the preschool and elementary school. Tables 4.2, 4.3, and 4.4, highlight the important mathematical concepts for well-prepared beginners to know and understand deeply. These concepts, identified in The Mathematical Education of Teachers II (CBMS, 2012), focus on counting and cardinality, operations and algebraic thinking, number and operations in base ten, measurement and data, and geometry. Further, programs immerse candidates in such mathematical practices as reasoning, sense making, and problem solving while they learn content. Candidates learn to explain their thinking, recognize structures, and generalize. Program personnel guide candidates in making mathematical connections among approaches to solving problems, among mathematical topics (e.g., measurement of area and multiplication), and between mathematics and other disciplines. Programs employ teaching strategies consistent with those that are effective with young children. Such programs develop positive dispositions toward mathematics, including persistence and a desire to engage in posing and solving problems.
Studying mathematics content is necessary but not sufficient. High-quality early childhood teacher preparation programs weave together the learning of mathematics content, the study of specific mathematics pedagogies and effective mathematics instruction, and, at the core, developmental knowledge of children’s mathematical thinking and reasoning.