Knowledge Space Theory: Estimating Knowledge Structure

In mathematical psychology, a knowledge space is a combinatorial structure describing the possible states of knowledge of a human learner.

Let's look at a simple analogy -

Imagine the town you live in as a complete domain of knowledge, if you know every part of the town, you have a knowledge state which covers the complete domain of knowledge. But, if you only know the street where you live in; then, you have a knowledge state which only covers a part of the complete domain - highlighted in yellow now.

By identifying the user's knowledge states, we can understand his/her knowledge boundaries. In the illustration above, you can imagine the boundary to be the yellow circle. Within educational settings, this is helpful because we can then find out what the user knows and does not know.

To estimate the user's knowledge state, we use a probabilistic approach by relating (1) the observed data to (2) all the possible knowledge states.

In this application, we want to demonstrate this process by allowing you to (1) build a knowledge structure on elementary probability theory, and (2) complete a quiz to estimate your probable knowledge states.

Don't forget to press the 'Done' button when you are finished

Please note that the empty set (marked by 0) and the full item set Q are always contained.

In the "quiz" tab, you can experience an adaptive assessment of your knowledge in out small probability domain.

We start with an equal probability distribution over the knowledge structure you have developed. After each of your answers, the probabilities are update according to the Bayesian Updating formula.

On the left side, you see the question and answer possibilities, on the right side a Hasse diagram of your knowledge structure indicating the current probability distribution.

Select the probabilities for careless errors and lucky guesses which influence the strength of the probability update.