In the scholarly article Relational Understanding & Instrumental Understanding, the author, Richard Skemp, explores the difference between two types of understanding: relational and instrumental. As they relate to math, relational understanding is that by which an individual grasps the reasoning behind a rule or method, while instrumental understanding consists only of the memorization and application of rules by which a person might complete a mathematical problem. In this article, Skemp advocates a student’s need for relational understanding in order for the student to generalize their knowledge and develop problem solving skills.
While many teachers would ideologically applaud the argument for relational understanding and teaching, finding methods by which to facilitate this type of understanding can be challenging. A key to growing a student’s desire for relational understanding is fostering opportunities for a student to discover mathematical principles.
Technology offers a variety of tools teachers can utilize in order to encourage such discovery. For example, when teaching students about Slope-Intercept Form, one can incorporate video demonstrations, like this video, and digital manipulatives, such as this. The video offers explanation more closely aligned with instrumental understanding, but the digital manipulative can be paired with guided questions in order to enable students to experiment and see for themselves how changing the slope m effects the steepness of a given line. In this way, the Slope-Intercept Activity incorporating both video and manipulative elements gives students the opportunity to gain full appreciation for how and why the Slope Intercept Form works.