The National Council of Teachers of Mathematics (NCTM) poses constructivist ideas in its "Principles and Standards for School Mathematics" (2000). NCTM supports mathematics instruction that takes a developmental perspective; starts and builds on what children know; and leads children to construct relational understanding, problem-solving abilities, and the ability to reason logically. In this context, learning is change, and development of mental associations and these associations are influenced by the quality and quantity of experience (Van de Walle 2007). Understanding grows as webs of interrelated ideas become more complex, and this happens in classrooms that contain rich experience, time for integration and reflective thought, and opportunities to take action and use what is known. The authors' aim in writing this article is to merge information about the learning cycle with NCTM's constructivist view to help teachers of mathematics understand their students' brain cycle as they develop mathematical concepts and competencies. The authors believe that this is an important focus because other professionals who work with children--such as pediatricians, psychologists, and speech pathologists--all receive information about the brain, its development, and its structures and processes, but educators often do not. It seems logical that teachers, whose main role is helping children learn, should have the same information (Wolfe 2001). (Contains 4 figures.)