Humans learn as much from failure as success - make enough mistakes, and you'll eventually learn the right way. But what is true in the university of life is not necessarily true in the classroom.

Consider the primary school student who just can't grasp simple three-figure subtraction - repeated errors lead the child no closer to a correct method of calculation.

Professor Webb, of Deakin University's School of Computing and Mathematics, says where natural intelligence fails, artificial intelligence may help.

Professor Webb has studied the application of artificial intelligence (AI) to education, and came up with a technique for creating simple representations of information that teachers wanted to convey to students.

"If you know what body of knowledge students have already absorbed, then you can focus on what they haven't learned, and you can also assess how well they are comprehending the information.

"There's a wealth of things they may understand, or misunderstand, but precisely what have they misunderstood, and why?"

Professor Webb developed his first AI model to evaluate primary students' subtraction skills. Students were given a test sheet containing a number of three-figure subtraction problems, and by analysing their answers, he was able to construct a model predict the answers each student was likely to give when tested on a similar set of subtraction tasks.

"There are at least three major different ways of doing subtraction, and they all work perfectly. The type of error each student makes can be influenced subtly be the general approach to subtraction that they adopt."

Professor Webb said that the model had led him into machine learning - although the technique he was using was radically different to any being used by specialists in the field.

He has since re-implemented his technique, using a program called C.45, widely used by AI researchers.

"C.45 normally makes categorical predictions - such as that the student will get the right answer, or the wrong answer. With my approach, it produces a large array of categorical predictions, then resolves them to produce a number - it predicts what the wrong answer will be, digit by digit, depending upon the subtraction technique the student is using."

"When a student gets a particular answer wrong, there is about a 33 % chance they will also get it wrong in the next test. They get the same wrong answer about a third of the time, a different wrong answer a third of the time, and the right answer a third of the time. This makes it very difficult to predict students' subtraction behaviour.

"We build up a picture that enables us to characterise the types of problems the student is likely to get wrong, and what they are doing wrong for those problems.

"The teacher then knows the student has misapprehended a certain procedure, and can focus on teaching the student the correct procedure."

Professor Webb says that although the AI system was originally developed to help teach arithmetic, it can be applied wherever specific processes can be identified within a learning procedure, to predict the types of errors students will make.

It has been applied to tasks ranging from teaching word classes in English grammar - nouns, pronouns, and verbs - to teaching musical scales.

Professor Webb believes his modeling systems could even help engineers to design better electronic appliances. If devices like video recorders were redesigned on the basis of the errors made by baffled consumers, they would become more intuitive to use, and more user-friendly.