Intelligent-Tutors

The Indian National Curriculum Framework has a part of the objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted at Indian metros reported concern for students’ mathematics learning. Regular classroom teaching, except in some private coaching, does not include teaching of problem solving in mathematics and involves mere practicing exercises and drill of known exercises. Schoenfeld gave a framework for describing mathematical thinking containing four components: resources, heuristics, controls and beliefs. Since childhood we develop ontology of the notions we learn. This ontology gets expanded when we keep learning more. Ontologies used for teaching need to incorporate elements of mathematical thinking popularized by problem solving experts. So, teaching by using such ontology of problems, problem solving methods, and tasks would be beneficial to students. In this paper we argue about how and why ontologies can be used for teaching problem solving in mathematics at high school level. As a proof of concept we give examples and describe an ontology named MONTO that can be used for teaching problem solving in mathematics. Also, we discuss and compare the MONTO ontology with some other ontologies available in the literature that are used for teaching. We developed and evaluated the MONTO ontology for Surface Area and Volume (3D Solids) problems taught as part of the national curriculum in India and the results obtained were satisfactory.