Each ALEKS subject, such as Beginning Algebra, has a knowledge structure associated with it. The knowledge structure for Beginning Algebra, for example, is covered by about 300 ALEKS items (or problem types). A knowledge state is a subset of items which may correspond to the knowledge of an actual student (i.e., there may be a student who has mastered exactly those items, and no others). A knowledge structure is the family of all the knowledge states that we may encounter for a given subject.

An ALEKS structure affects virtually every aspect of ALEKS's functioning. In the ALEKS assessment mode it enables ALEKS to make inferences from student answers, keeping the ALEKS assessments brief, but uncannily accurate.

The structure is also crucial in the ALEKS Learning Mode. Using the structure of Beginning Algebra, for example, the system knows precisely which items are in the inner fringe and outer fringe of each of the knowledge states in ALEKS for Beginning Algebra. The items in the outer fringe of a student's knowledge state are those items that the student is the most ready to learn next. (From a technical standpoint an item is in the outer fringe of a state if adding that item to the state results in a feasible knowledge state.) These items are presented to the student in MyPie when the student moves the mouse pointer over the ALEKS pie chart. Similarly, an item in the inner fringe of a student's state is an item either recently learned or one whose mastery by the student might be shaky. (Technically, an item is in the inner fringe of a state if removing that item from the state results in another feasible knowledge state.) They are presented to the student when the student is having difficulty in the ALEKS Learning Mode and during ALEKS review.

An additional benefit of the proliferation of connections among items in ALEKS is its extreme flexibility from the students' viewpoint: for any particular topic, there is a vast number of possible approaches, or learning paths, which may lead students to mastery of that topic. This flexibility does not imply, however, that any order is possible. Each learning path leading to a particular topic must contain, at a minimum, the items which are "below" such topic in the ALEKS structure. That is, we may say that the more "advanced," or "highest," topics in an ALEKS structure are those for which the ALEKS system will require the student to learn the largest number of other items before those items will be presented to the student.