Curriculum sequencing is one of the key components in an intelligent tutoring system [19,27,30]. In our approach, the topics are represented in a dependency graph, with links representing the relationship between topics, which include prerequisite, co-requisite, related, and remedial. Remedial topics such as special topics are not required to be learned by all the students. Each topic is divided into subtopics corresponding to smaller grained units that allow the intelligent tutor to reason at a finer level. When a subtopic is displayed to the student, the actual content is dynamically generated based on the student model.

Curriculum sequencing can be seen as a two-step process: finding relevant
topics and selecting the best one. A student is ready to learn a topic only
if he has performed sufficiently well on its prerequisites. How well a topic
is learned is judged by the student's performance on and his access patterns
to the course materials. The access patterns include how much time he has
spent studying a topic, whether he used corresponding multimedia materials
such as audio and video, and if the topics were reviewed multiple times.
Specifically, the performance on a topic is determined based on the following
three factors:

- Quiz performance. Quizzes give a tutor the most direct information
about the student's knowledge. Quizzes can be dynamically constructed based on
the student model. Questions are provided to cover the topics most
recently completed, as well as topics that should be reviewed. Each question
has a level of difficulty, which is also used in
updating the student model. Correctly answering a harder question demonstrates
a higher ability than correctly answering an easier question. The quiz scores
are calculated using the following formula:

(2)

- Study performance. The main interaction that students have with the
learning environment is through viewing or listening to the course materials
in multimedia forms. The study score is used to judge how much comprehension
the student has gained through these activities. A topic is usually presented
in multiple pages and each page is assigned a weight corresponding to its
importance. Then, the study score in the range from 0 to 1 is calculated based
on the pages visited and the amount of time spent on each page. An optimal
time for each page is used as the baseline.
If the student spends this optimal amount,
then the score for the page is 1. As he moves away from this point, his score
decreases. The study score of a student on a topic is the weighted sum of the
scores on the pages calculated as follows:

where is the number of pages, is the weight on the th pages with , and is the score on the th page. If page is studied more than once, the total time on the page is used for .

- Reviewed topics. The review score on a topic records how much the
student has returned to review the topic again. It is based on how many times
the topic is reviewed and how much of the materials is viewed each time. If a
student is reviewing frequently, then he has not learned the material. The
review score is in the range from 0 to 1 and starts at 1 for each topic.
Each time the student reviews the topic, the review score is updated by
multiplying the value calculated using the above equation
().

These three scores, quiz performance, study performance, and reviewed topics,
are then combined into a single value, *learned score*, indicating how
well the topic is learned. The quiz score is the most important among the
three. When a student has a reasonably high quiz score, such as over 0.8, then
the other scores do not matter much and the final value is the quiz score.
However, if his quiz score is less than 0.8, the other factors become
important, and the final value is a weighted sum of the three scores with
weights such as 0.7, 0.2, and 0.1, respectively.

The *ready score* of a topic indicates whether the student is ready to
learn the topic or not. It is calculated based on the topic's learned score
and its pretopics' learned scores. If a given topic's learned score is too
low, it should be presented again, perhaps being taught differently than it
was the first time. In order to start a new topic, a student should show
sufficient scores in its pretopics. One formula of the ready score is the
weighted-sum of the topic's learned score and its pretopics' learned scores
with predetermined weights.

In IDEAL, the student has the option of letting the teaching agent choose the next topic or choosing it himself. In both cases, the student must achieve sufficiently high ready score for the topic. If the teaching agent is asked to choose the next topic, it will choose one with the highest ready score. If the student decides to choose the next topic, he is presented the topic dependency graph annotated with suggestions on which topics to repeat and/or which new topics to study.

Once a topic is chosen, how to teach, such as how to dynamically construct page contents, can be made based on the three individual topic scores. For example, a student who has poor quiz scores on a topic and who has not studied the topic for very long should be treated differently from a student with the same quiz score but who spent much more time studying. The second student should be presented with more background materials to improve his comprehension. Furthermore, each time a student reviews a topic, it should be taught in a different way than it was the last time.