Making a Computer-Based Tutorial Environment for Mathematics “Intelligent” : The Design, Implementation and Evaluation of a Tutorial System that Learns

Over recent years, many computer-based tutorial systems have been developed, including some covering various mathematical topics. However, many such systems have either been limited to multiple choice or short answer questions, without detailed feedback tailored to the student’s responses.

In the last few years, we have started to develop a computer based tutorial system [1] for intermediate mathematical topics such as calculus and linear algebra, linked to a symbolic manipulation package, which gives automatic feedback specific to the student’s answers, including comments relevant to addressing “common mistakes” which the student may have made. A similar system to ours has also been developed and used at Brunel University [4].

At present, the “common mistakes” and how they are dealt with have to be identified and encoded manually by “experts, namely experienced teachers of mathematics. It is proposed for this project to make such tutorial systems more “intelligent” by noting students’ responses to individual questions and exercises, in a manner which has been previously done for students learning computer programming [2], then using statistical pattern recognition and machine learning techniques to identify automatically what are “common mistakes” for each type of question. This should facilitate improving the tutorial system to make it respond appropriately to a wider range of student errors, including the possibility of errors which even an experienced teacher may not have anticipated.

As a potential further extension to the system, we propose using a rule-based agent, with either tutor-specified or automatically learned rules, to implement an `Adaptive Course Sequencing System', as described in [3], which will allow students to grant the tutoring system a level of autonomy in guiding them through exercises of varying levels of difficulty and on different topics, to assist the students in becoming sufficient competent in one topic before moving to another, and suggesting appropriate sequences of exercises and topics in an to optimise each student’s learning experience.