Functions with Integers

Linear equations (y = mx + b) are a cornerstone to algebraic thinking, requiring people to solve for unknowns (x, y) and interpret slopes (m) and intercepts (b). However, students often struggle with these concepts (Hattikudur et al., 2012), particularly with understanding slope direction (positive vs. negative). Negative numbers pose additional cognitive challenges due to their abstract nature, as they do not readily map onto real-world objects (Prather & Alibali, 2008). This abstractness may further complicate students' ability to work with linear equations. The current study investigated the ability of U.S. college students to generate and identify linear equations, focusing on slope direction and task difficulty.