Generating automated problem sets for rapid content delivery and adaptive learning modules

Abstract

Problem solving plays a critical role in the education of young engineers. Word problem sets are a vehicle that educators use to teach and assess that skill. While textbooks, problem repositories, and online learning systems provide a host of interesting problems there will always be a need to generate new problems to increase variety, to prevent students from cheating, and to facilitate robust student learning environments. While current online learning systems provide educators with problems that allow for individual numerical values to be randomized, they do not allow for randomized problem structures that challenge comprehension. This paper develops a method to create new problem sets through the development of software tools that apply a series of automated generation algorithms. Several common undergraduate engineering word problems are distilled into archetypes (generalized problem descriptions that will facilitate automated authoring). One archetypical problem in each of the following disciplines is chosen: in particle dynamics (two-dimensional projectile motion), in thermodynamics (ideal-gases in piston-cylinder devices), and in circuits (equivalent resistance). For each archetype, algorithms codify problem parameters and generate a compatible list of inputs and outputs, problem diagrams, word problem text, and solution sets. Problem text is created using natural language programming (with varying levels of human intervention) and problem solution sets are constructed using a computer algebra system. The problem sets are then presented to undergraduate mechanical engineering students as traditional course content such as homework, quizzes, and tests, and as part of adaptive learning modules or games in learning management systems. The relative difficulty of each automatically created problem is estimated with a heuristic and compared against student performance.