Pyramid Approach to Teaching Recursive Use of Parentheses, Four Operations in Arithmetic

Pyramid Approach to Teaching Recursive Use of Parentheses

Parentheses are everywhere in mathematics and computer coding for grouping, orders of operation, defining functions, and clarity. It is not a problem at all for a machine to reach them. But how would you teach the use of parentheses in early mathematics, esp. with students who find their recursive use confusing? For example, 32 × (60-(3+(12÷4))). Abigail Fores (name used with consent and for credit), a teacher candidate in my class, came up with a pyramid approach, which takes the use of parentheses to a new dimension. We went back and forth a few times and designed a few models for experimentation. It remains open whether it helps elementary students grasp the ideas behind the layers and layers of parentheses. The numbers and parentheses can be colored with permanent markers or 3D printed with colored filaments.

Three levels may be adequate for an introduction. All four standard operations are covered. Each level has 4 choices. So there can be as many as 64 different problems. An extra fourth layer is added later, which can hold the first three layers. Again, the four operations are all included. With the extra layer, one can make 4 × 4 × 4 × 4=256 different problems! Just have fun.