Algebraic thinking has a great impact on how successful a student is in algebra. Any discussion of unknowns, formulas, generalized patterns, placeholders, and relations in grades K and higher can provide students an opportunity to think algebraically (Usiskin, et al).

Algebraic thinking can be separated into two components: tools and ideas.

1. Mathematical Thinking Tools:

• Problem-Solving Skills
• Representation Skills: Visual, Symbolic, and Numeric
• Inductive and Deductive Reasoning Skills

2. The Study of Fundamental Algebraic Ideas

• Algebra as Generalized Arithmetic
• Algebra as a Language
• The Study of Functions and Mathematical Modeling

Shelly Kriegler, Professor of Mathematics at the University of California, Los Angeles, argues both tools and ideas are necessary for success in algebra:

"One can hardly imagine thinking logically (mathematical thinking tools) with nothing to think about (algebraic ideas). On the other hand, algebra skills that are not understood or connected in logical ways by the learner remain factoids of information that are unlikely to increase true mathematical competence."

Additional Resources:

• Algebra 1 Requirement for Graduation
• Algebraic Thinking Toolkit

References: Bass, H., Burrill, G., Usiskin, Z. (Eds). (2002). Studying Classroom Teaching As a Medium for Professional Development. Washington, D.C.: National Academies Press. Order this report from: National Academies Press

Kriegler, S. (2001). Just what is algebraic thinking? Algebraic Concepts in the Middle School, Mathematics Teaching in the Middle School. Reston, VA: National Council of Teachers of Mathematics. Order this report from: National Council of Teachers of Mathematics