P(init)
← You (0.32)
0
1
Mastery (0.95) →

Putting it all together

It's time to put your knowledge to the test!

How do the settings below relate to the BKT parameters? Answer the questions to the right. The sliders will unlock before the test begins.

0
P(init): 0.25
1
Letter Similarity: 0.5

When similarity is low (closer to 0), you'll see letters that look less similar.

0

1

Letter Familiarity: 0.5

When familiarity is low (closer to 0), you're likely to see letters you haven't learned before.

0

1

Time to Sign: 0.5

When time is low (closer to 0), words will be signed more quickly.

0

1

Great Work!

Press try again to repeat the simulation with different parameters. Otherwise, select continue.

Try Again Continue

What is the word being signed above?

Click to fill in the blanks! Each parameter should only be used once.

Which parameter is most directly impacted by letter similarity?

Which parameter is most directly impacted by letter familiarity?

Which parameter is most directly impacted by time to sign?

Answers: letter similarity — P(slip) letter familiarity — P(guess) time to sign — P(transit)

You got it! Time for a thought question: why was P(init) not an answer option for the 3 questions you just answered?

Hint: How is P(init) inherently different from the other three parameters? What is its role in BKT? Think mastery bar.

Tell me!

Remember that we ultimately use P(init) to estimate skill mastery. The other parameters —P(guess), P(slip), and P(transit)— are used to update P(init)'s value, but they themselves remain constant throughout the learning exercises.

Optional: Learn about the math behind BKT by expanding the section below. Press continue when you're ready to move on.

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See the math +

Every time the student answers a question, BKT calculates P(learned), the probability that the student has learned the skill they are working on, using the values of our 4 main parameters. The formula for P(learned) depends on whether their response was correct.

First, we compute the conditional probability that the student learned the skill previously (at time n-1), based on whether they answered the current question (at time n) correctly or incorrectly.

Then, we use the result of our first calculation to compute the conditional probability that the student has learned the skill now (at time n).

For the next question, we use P(learned) as the new value of P(init). And as you now know, once P(init) ≥ 0.95, we say that the student has achieved mastery.