Discovering Linear Equations in Explicit Tables

When teaching algebra concepts to middle school students, I often hear questions that echo my own past confusion as a young student learning to write linear equations using data tables that show only input and output values. Students, expected to synthesize the relationship between these values in symbolic representation, grow frustrated when they do not recognize that implicit relationship quickly. “All students, regardless of prior knowledge and experiences, can explore pattern tasks” (Smith 2007). The structure of a four-column explicit table allows students of all abilities (from low achieving to honor students) to understand the relationship between the values found in linear equation tables. After implementing four-column tables, I found that students required less instructional interference from me, they developed self-efficacy, understood and retained the material, and attained higher year-end test scores.