Adaptive learning

Adaptive Learning is a relatively new technology which enables the utilization of computers as interactive teaching devices. The focus of adaptive learning is to allow the computer to adapt the presentation of the material according to students' weaknesses as indicated by their responses to questions. The motiviation is to allow electronic education to incorporate the value of the interactivity afforded to a student by an actual human teacher or tutor. The technology encompasses aspects derived from various fields of study including computer science, education, and psychology.

Technology/Methedology

Adaptive learning systems have traditionally been divided into separate components or 'models'. While different model groups have been presented, most systems include models for the converyance of the information which is being taught (often called the 'instructional model'), a model for the student (most commonly called the 'student model'), and other components to deal with things such as interface. The student and instructional models interact with each other with the student model assessing the student's strengths and weaknesses, and the instructional model reacting to this information with appropriate teaching materials and methods.

Student Model

Student model algorithms have been a rich area for researches over the past twenty years. The simplest means of determining a student's skill level is the method employed in CAT (Computer Adaptive Testing). In CAT, the subject is presented with questions which are selected based on their level of difficulty in relation to the presumed skill level of the subject. As the test proceeds, the computer adjusts the subject's score based on their answers, continuously fine-tuning the score by selecting questions from a narrower range of difficulty.

An algorithm for a CAT-style assessment is simple to implement. A large pool of questions is amassed and rated by difficulty, either through expert analysis, experimentation, or a combination of the two. The computer then performs what is essentially a binary search, always giving the subject a question which is half way between what the computer has already determined to be the subject's maximum and minimum possible skill levels. These levels are then adjusted to the level of the difficulty of the question, reassigning the minimum if the subject answered correctly, and the maximum if the subject answered incorrectly. Obviously, a certain margin for error has to be built in to allow for scenarios where the subject's answer is not indicative of their skill level but simply coincidental. Asking multiple questions from one difficulty level greatly reduces the probability of a misleading answer, and allowing the range to grow beyond the assumed skill level should compensate for possible misevaluations.

Richer student model algorithms look to determine causality and provide a more extensive diagnosis of student's weaknesses by linking 'concepts' to questions and determining strengths and weaknesses in terms of concepts rather than simple 'levels' of ability. Because a number of concepts can influence a single question, questions have to be linked to all concepts in terms of relevance. For example, a matrix can list binary values (or even scores) for the intersection of every concept and every question. Then, conditional probability values have to be calculated to reflect the likelihood that a student who is weak in a particular concept will fail to correctly answer a particular question. After a student has taken a full test, the probabilities of weakness in all concepts conditional on inccorect answers in all questions can be calculated using Bayes' Law (these adaptive learning methods are often called bayesian algorithms).

A further extension of identifying weaknesses in terms of concepts is to program the student model to analyze the incorrect answers which the students submit. This is especially applicable for multiple choice questions. Consider the following question:

Simplify: 2x² + x³

a) Can't be simplified b) 3x⁵ c) ... d) ...

Clearly, a student who answers (b) is adding the exponents and failing to grasp the concept of like terms. In this case, the incorrect answer gives additional insight beyond the fact that it is incorrect.

Instructional Model

The instructional model generally looks to incorporate the best educational tools that technology has to offer (such as multimedia presentations) with expert teacher advice for how lessons should be presented. The level of sophistication of the instructional model depends greatly on the level of sophistication of the student model. In a CAT-style student model, the instructional model will simply have lessons ranked in some order which corresponds to the levels of difficulty which were used to rate the question pool. When the student's level has been satisfactorily determined, the instructional model can provide the appropriate lesson. The more advanced student models which provide assessments based on concepts need an instructional model which has its lessons organized by concept as well. The instructional model can be designed to analyze the collection of weaknesses and tailor a lesson plan accordingly.

When the incorrect answers are being evaluated by the student model, some systems look to provide feedback to the actual questions in the form of 'hints'. As the student makes mistakes, useful suggestions pop up such as "look carefully at the sign of the number". This can again fall in the domain of the instructional model, with generic concept-based hints being offered based on concept weaknesses, or the hints can be question-specific in which case there is really an overlap between the student and instructional models.