Solving Equations is All about Balance: Using Virtual Manipulatives in the Middle School Classroom

Background

The Common Core State Standards for Mathematics (CCSSM) include grade-specific content standards and over-arching mathematical practice standards. An important theme of the algebra strand of the CCSSM is that middle school students are expected to reason about and solve one-variable equations (CCSSO, 2011). For example, a sixth grade-specific standard (6.EE.7) states students should solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px= q for cases in which p, q, and x are all nonnegative rational numbers. A similar example at the eighth grade level (8.EE.7) states students should solve linear equations in one variable. Additionally, according to the sixth-grade standard 6.NS.5, students should understand that positive and negative numbers are used together to describe quantities having opposite directions and values.

Students often face challenges in mathematics content, especially when trying to make sense of abstract concepts such as solving one-variable equations. Specifically, researchers have identified three common challenges that students often face when attempting to solve equations:

• 1.

  Lack of understanding of the equal sign (Knuth, Stephens, McNeil, & Alibali, 2006).

• 2.

  Lack of symbolic understanding within an equation (Kilpatrick & Izsak, 2008; Poon & Leung, 2010).

• 3.

  Reliance on procedural knowledge without conceptual understanding (Capraro & Joffrion, 2006; Siegler, 2003; Star, 2005).

Students can increase their understanding of solving equations in one-variable by interacting with representations found in virtual manipulatives (Durmus & Karakirik, 2006; Sarama & Clements, 2009).