After a review of conceptual development, it is appropriate to examine how misconceptions occur and why certain types of conceptual errors are so common in school mathematics. Without such considerations, teachers cannot help their students replace their misconceptions with new concepts.
Indeed, conceptualization often means a correction of prior misconception. Therefore, as they follow the essential steps of Concept-Rich Instruction, teachers often encounter the challenge—at times remarkable challenge—of altering students' misconceptions. To be effective, teachers must anticipate, understand, and know how misconceptions are replaced by the formal concepts. This chapter focuses on typical students' misconceptions in mathematics, how they develop, and how they change through effective instruction.