Why is Factoring So Important? Factoring Series Part I

By Beth Richardson, RME High School Math Coordinator

“Of all pre-college curriculum, the highest level of mathematics one studies in secondary school has the strongest continuing influence on bachelor’s degree completion. Finishing a course beyond Algebra 2 more than doubles the odds that a student who enters postsecondary education will complete a bachelor’s degree (Adelman, 1999).”

Picture taken from
http://www.aplusalgebra.com/algebra-tiles.htm

The United States is boosting the rigor of its mathematics curriculum. The state of Texas requires students to receive 4 math credits, 3 of which must be Algebra 1, Geometry, and Algebra 2 in order to graduate. Another highly recognized initiative is the Common Core State Standards (CCS) adopted by most states. The traditional pathway of the nation-wide CCS requires high school students to take Algebra 1, Geometry, Algebra 2, and, in most cases, one other math course.

Based on the above information, completing Algebra 2 is a target for our students. Therefore, we need to provide our students with the math skills and knowledge that will lead them towards success. As a former Algebra 2 teacher, I strongly believe a crucial concept for success in Algebra 2 is factoring. Students are required to use factoring as a problem solving strategy and a method of simplification with multiple parent functions and equations (ex: quadratic, rational, and all 4 conic sections) throughout the curriculum.

Many students struggle with factoring. At its core, is an application of the distributive property in which students should begin developing in elementary school through arithmetic. In Algebra 2, factoring of polynomials with variables is a complex, abstract idea. Few students are provided experiences to connect the application of the distributive property with their prior learning. We need to make this clear to them. It is important to take time and explain the underlying mathematical properties at play.

Concrete and visual models are great tools to use when new material is introduced. They help give students a real-world context to connect abstract algebraic properties. Below are some samples of models that are used with the distributive property when students are first learning the concept and when students apply the concept to factor in algebra.

A typical model used to demonstrate
the distributive property in 4th grade.

A typical model used to teach factoring
(opposite of distribution) in Algebra.

Summing it All Up
So, how do we help students’ transition between the different uses of the distributive property (including factoring) while understanding that the property always remains the same? In the next parts of this factoring series, we will explore specific strategies that can be used in elementary, middle, and high school to help cement factoring and the underlying distributive property.

Teachers of all grade levels, we’d like to know strategies you use (types of diagrams, models, vocabulary) that you’ve found help your students be successful with the distributive property and/or factoring. Your comments will help shape our next blogs in this series.

Texas Education Code: Chapter 74: Curriculum Requirements 
Common core state standards for mathematics: Designing high school mathematics courses based on the common core state standards. Appendix A
Common Core Standards Writing Team. (2011). Progressions for the common core state standards in mathematics (draft). Retrieved from http://www.isbe.net/common_core/pdf/math_progression052911.pdf
Adelman, C. (1999). Answers in the Tool Box: Academic Intensity, Attendance Pattern, and Bachelor’s Degree Attainment  http://www2.ed.gov/pubs/Toolbox/Part1.html