Design of a System for Automated Generation of Problem Fields

Abstract

We describe the design of a computer system for problem field generation in mathematics. The concept of problem field refers to a sequence of related problems. The relationship between the problems assures that their successive solution promotes deep learning of the topic (sequence problems). We define four relations between the field’s problems: difficulty and rule, question or property preservation. The problem’s difficulty is given by problem-type, algebraic complexity and difficulties of the problem’s question and rule used for solution. A problem field based on difficulty will modify one of the above elements in order to get new problems from existing ones. In rule- and property-preserving generation the field’s problems differ in their type or difficulty level. In question preserving generation the problems maintain the initial problem’s unknown. Once the details of the change are established the new problem will be generated using templates, rules and examples.