Proportionality, Steepness, and Slope in the Middle Grades

The learning of slope is important in school algebra, and understanding the concept of slope requires knowledge of proportional reasoning and steepness. This mixed-methods study examines middle school participants'' abilities to solve steepness problems in three different contexts and of varying difficulty levels, the connections between proportionality and steepness that middle school participants exhibit, and the strategies which middle school participants use to solve steepness problems. It was concluded that participants'' abilities to solve steepness problems are related to their abilities to reason proportionally. The findings of this research contribute to literature on early algebraic reasoning that explores ways in which algebraic topics such as slope can be made accessible to students prior to their formal studies of algebra.