Algebra: 4 Big Ideas Go to Articles
For many, algebra is a confusing jumble of symbols and equations. Until recently, this abstract area of mathematics was first introduced to students in high school, where it was often approached as a set of procedural rules for solving equations (Kilpatrick & Izsák, 2008). Developing algebraic thinking in the early school years provides a solid foundation for later algebra symbol work (Warren, 2008). Teaching children the big ideas (key concepts) of early algebra (Warren, 2008; explained below) through real-world problems helps them understand its rules and applications.
1 Equivalence and Equations
“Equals” means equivalent sets rather than a place to write an answer. Simple real-world problems with unknowns can be represented as equations. Equations remain true (balanced) if the same change occurs to each side. Unknowns can be found using the balance strategy.
2 Patterns and Functions
Operations almost always change an original number to a new number. Simple real-world problems with variables can be represented as “change situations”. “Backtracking” or reversing a change can be used to find unknowns.
3 Properties
Arithmetic properties apply. The commutative law and associative law apply to addition and multiplication but not to subtraction and division. Addition and subtraction are inverse operations, and multiplication and division are inverse operations. Adding or subtracting zero, and multiplying or dividing by 1, leaves the original number unchanged. In certain circumstances, multiplication and division distribute over addition and subtraction.
4 Representations
Different representations (e.g. graphs, tables of values, equations, drawings, everyday language) help with identifying trends and finding and interpreting solutions to real-world problems.
References
Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In Greenes, C.E. & Rubenstein, R. (Eds.), Algebra and algebraic thinking in school mathematics: Seventieth yearbook (pp. 3–18). Reston, VA: The National Council of Teachers of Mathematics.
Warren, E. (2008). Algebra for all. Brisbane, Australia: ORIGO Education.
