Instructional Practices

Multiplication and Division

To learn more about the development of multiplication and division understanding in elementary and middle school, please view the following short videos:

Array Model in Secondary

Secondary math courses build upon and support the elementary focus of teaching for deep understanding before teaching procedurally. Many of the basic models introduced in elementary are re-visited and expanded upon in middle school and in high school allowing students to make connections with prior learning.

k-12-math-array

Learning Math Conceptually

Why are students taught conceptually before moving to the procedure?

  • To understand the meaning, the use and connections between addition, multiplication, subtraction, and division;

  • To understand the "why" and "how" of operations and not just memorizing steps (what most of us learned in school);

  • To select from a repertoire of computational strategies (including mental computation) for each operation;

  • To be proficient mathematicians;

  • To promote students' capacity to think flexibly of numbers as sums and differences of other numbers with all mental and written calculations.

When do we teach procedurally?

  • The procedure, also known as an algorithm, is sometimes a more efficient strategy for students when in written form.

  • As students make connections and show understanding of the operation conceptually, they begin using an algorithm.

  • Differentiated instruction in small group provides the flexibility for teachers to assess children's readiness to move to the procedure.

Research of Best Instructional Practices