Bayesian Knowledge Tracing or BKT is an algorithm that tries to predict how likely it is that a student has mastered a skillbased on answering problems correctly or incorrectly (no partial credit).
How it Works
Achieve3000 Math uses BKT to adjust mastery as students work on problems.
BKT considers whether a student’s performance is based on 4 factors:
 Prior knowledge of the concept
 Demonstrating knowledge of the concept
 Guess (gets it right but does not know the concept)
 Slip (knows the concept but makes a mistake)
If a student uses the stepbystep feature, will it give them the same amount of mastery as if they figured it out without it, or will it be slightly lower?
Student's understanding is evaluated through their mastery. Students can get a problem wrong and still have their mastery level increase if they went through the stepbystep problems and answered those correctly. The reason is that the student is understanding the skill and increasing their mastery, in accordance with how BKT works.

Mastery of a problem set increases when a student:

Answers a problem correctly

Answers a step correctly
Mastery of a problem set decreases when a student:

Answers a problem incorrectly

Skips to the steps

Answers a step incorrectly
Mastery of a problem set does not change when a student:

Restarts a problem (can do this twice per problem)

Clicks “Show answer” in a step

These are the formulas behind Bayesian Knowledge Tracing that Achieve3000 Math uses to determine a student's mastery level.
Curious to know more about Bayesian Knowledge Tracing and the history behind it, then you can visit the Wikipedia page for it by clicking here!