Print Version Only Chapter 1 Algebraic Thinking – Informal Math Modeling

You might wonder why future elementary teachers should master algebra, a topic usually studied (by that name, anyway) in 8th grade and beyond. But the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics-Algebra at

The National Council of Teachers of Mathematics (Open in new window) has algebra standards beginning in kindergarten as shown below.

In prekindergarten through grade 2 all students should…

• use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations;
• model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols;

 In grades 3–5 all students should…

• represent the idea of a variable as an unknown quantity using a letter or a symbol
• express mathematical relationships using equations;
• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions

In the Massachusetts Mathematics Curriculum Framework…

Grade 3 – 3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic.

8. Solve two-step word problems using the four operations for problems posed with whole numbers and having whole number answers. Represent these problems using equations with a letter standing for the unknown quantity.

Elementary school students already have some background in abstraction and generalization, the fundamental ideas in algebra. They are all capable of learning to formalize these ideas. Your job as an elementary school teacher will be to provide your students with even more experiences in abstraction and generalization in a mathematical context, so that these ideas will be more natural when they get to a class with the name “Algebra.”