Indicator C.1.1. Know Relevant Mathematical Content
Well-prepared beginning teachers of mathematics have solid and flexible knowledge of core mathematical concepts and procedures they will teach, along with knowledge both beyond what they will teach and foundational to those core concepts and procedures.
Well-prepared beginning teachers of mathematics understand and solve problems in more than one way, explain the meanings of key concepts, and explain the mathematical rationales underlying key procedures. For example, a well-prepared beginner for Upper Elementary Grades recognizes that simplifying 3 ÷ ⅕ indicates the question “How many fifths are in 3?” Using a visual diagram as in Figure 2.1 and considering that one whole is comprised of five fifths leads one to realize that the answer will be 3 × 5 or 15.
This result can be generalized so that students recognize that dividing by any unit fraction is equivalent to multiplying by the denominator. Thus, this procedure can be built on a solid and flexible understanding of underlying mathematics. (See Chapters 4 through 7 for additional examples of the specific content for well-prepared beginners at each grade-band.)