NCTM states three central mathematical themes in grades 3-5: "multiplicative reasoning, equivalence, and computational fluency" (NCTM, 2000, p. 144). Each theme contains many connections to highlight and build on. By emphasizing connections within and among mathematical topics, a teacher can reduce a seemingly infinite list of topics and goals to a manageable set of key ideas. Students benefit because it is much easier to learn and remember a new idea if it can be related to something they already understand.

Mathematical knowledge is of little use unless it can be activated and accurately applied to diverse situations. When solving problems, and when learning new concepts, students should develop the habit of looking for connections to past learning and past problem-solving experiences. Students become aware of the variety of situations in which an idea can be useful as they are encouraged to recognize and discuss connections within mathematical topics and among types of problem situations.

  Defining the Connections Standard