Exercise: a question, or a problem which requires students to spend time and effort to complete. An exercise can be unfinished, finished with mistakes, finished without mistakes.

Instrument refers to assignment, test, quiz.

Item represents anything for which per-student grades are recorded (problems, questions, parts of questions.

Problem: A problem is a task for a student to perform that typically involves multiple steps

Step: A step is an observable part of the solution to a problem

Transaction: Students may make incorrect entries or ask for hints before getting a step correct. Each hint request, incorrect attempt, or correct attempt is a transaction; and a step can involve one or more transactions.

Knowledge components: A knowledge component is a piece of information that can be used to accomplish tasks, perhaps along with other knowledge components. Knowledge component is a generalization of everyday terms like concept, principle, fact, or skill, and cognitive science terms like schema, production rule, misconception, or facet. Each step in a problem require the student to know something, a relevant concept or skill, to perform that step correctly.

Opportunity: An opportunity is a chance for a student to demonstrate whether he or she has learned a given knowledge component. An opportunity exists each time a step is present with the associated knowledge component. The opportunity count increases by one each time the student encounters a step with the associated knowledge component. An opportunity is both a test of whether a student knows a knowledge component and a chance for the student to learn it. While students may make multiple attempts at a step or request hints from a tutor (these are transactions), the whole set of attempts are considered a single opportunity. As a student works through steps in problems (and multiple problems), they will have multiple opportunities to apply a knowledge component.

Learning curve: A learning curve is a line graph displaying opportunities across the x-axis, and a measure of student performance along the y-axis. As a learning curve visualizes student performance over time, it should reveal improvement in student performance as opportunity count (ie, practice with a given knowledge component) increases.

Error rate: The percentage of students that asked for a hint or were incorrect on their first attempt. Both incorrect actions (errors of commission) and hint requests (errors of omission—the student did not know how to perform the step on his or her own) are considered errors.

Assistance score: For a given opportunity, the number of incorrect attempts plus hint requests equals the assistance score.

Observation: An observation is available each time a student takes an opportunity to demonstrate a knowledge component.

Knowledge Component Mode (KC = skills): A list of mappings between each step and one or more knowledge components; also known as a Transfer Model or a Skill Model. Which KC you used? = Which skills you used?

LFA: Acronym for Learning Factors Analysis, a logistic regression method which uses a set of customized Item-Response models to predict how a student will perform for each knowledge component on each learning opportunity.

Learning object can be defined as a configurable software component, designed with a specific pedagogical objective, and able to manage some kind of learning activity on an e-Learning platform.

Symbolic object (analysis) is simply a cluster of elements in a population. Say, population of students can be partitioned into symbolic objects / groups based on the number of exercises they completed.