Developing Algebraic Reasoning

Algebraic reasoning involves representing, generalizing, and formalizing patterns and regularity in all aspects of mathematics.… The focus is on patterns, functions, and the ability to analyze situations with the help of symbols.… [Algebraic reasoning] is at the heart of mathematics as a science of pattern and order.… As algebraic reasoning develops, so must the language and symbolism that have been developed to support and communicate that thinking, specifically equations, variables, and functions.
Van de Walle 2001, p. 384

Algebraic reasoning introduced in the early grades develops into the ability to reason proficiently using equations, variables and functions. Developing algebraic reasoning requires that teachers design mathematical tasks that include opportunities for:

• using problem-solving strategies
• exploring multiple approaches and multiple solutions
• displaying relationships visually, symbolically, numerically and verbally
• translating among different representations
• interpreting information within representations
• inductive and deductive reasoning
• generalizing patterns
• providing justifications (i.e., proof).
  

Assessment and Algebraic Reasoning

It is appropriate to gather data that indicate the degree to which students make generalizations based on their mathematical experiences and use appropriate language and symbolism to represent these generalizations. Since pattern and regularity can be found in nearly all areas of mathematics, algebraic reasoning should be developed and assessed throughout the curriculum. Students who ask questions like "Will that work for any numbers?" or who observe similarities from one area of mathematics to another are using algebraic reasoning. 
Van de Walle 2001, p. 400