Development and pilot test of the rate and accumulation concept inventory

Many of the rate of change and accumulation processes that we commonly encounter reflect the behaviors of complex systems. Solving complex system problems within engineering requires the ability to interpret the meaning of a function that is modeling a dynamic situation. This ability is essential for engineers. Thus, knowing how students think and learn about rate and accumulation processes in complex systems can help educators better prepare students for their engineering careers. Engineering students often have various robust misconceptions that can persist throughout their education and may hinder their ability to learn new material. Concept inventories can identify some of these misconceptions. Existing discipline-specific inventories include assessments of conceptual frameworks related to rate and accumulation processes. However, these inventories measure context-specific understandings of rate and accumulation processes and do not delve into the mathematical and scientific conceptual frameworks that may underlie contextual misconceptions. This paper builds on previous evidence that many engineering students possess robust misconceptions about rate and accumulation processes. These findings led to the development of the Rate and Accumulation Concept Inventory (RACI), which is intended to assess students' conceptual understanding of rate and accumulation processes. Three categories of conceptual understanding are included in the RACI: (1) first order calculus, (2) mass flow, in particular water flow, and (3) heat transfer. Pilot testing of the RACI took place in a sophomore civil and environmental engineering course. Results from pilot testing indicated the presence of persistent misconceptions among the students in all three categories of understanding. Student performance on the RACI went from 56% to 59% after instruction. Internal consistency reliability was assessed using Cronbach's Alpha; values were 0.77 for the entire instrument and ranged from 0.64 to 0.76 for the three concept categories of the RACI.