#### Development Team:

#### Jessica Loke

#### Martin Losert

#### David de Segovia

#### Wai Wong

#### Chris Yndgaard

#### Extended by:

#### Cord Hockemeyer

**Knowledge Space Theory:
**

Estimating Knowledge Structure

Estimating Knowledge Structure

In mathematical psychology, a

*is a combinatorial structure describing the possible***knowledge space***of a human learner.***states of knowledge**-
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

*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.*

**knowledge state**By identifying the user's

**, 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.**

*knowledge states*To estimate the user's

**, we use a probabilistic approach by relating (1) the observed data to (2) all the possible**

*knowledge state***.**

*knowledge states*In this application, we want to demonstrate this process by allowing you to (1) build a

**, and (2) complete a quiz to estimate your probable**

*knowledge structure on elementary probability theory***.**

*knowledge states*#####

In this application, you have two options:

Then, you can simulate being a new student by answering a quiz.

After each of your answers, we will update the probabilities of your possible knowledge states.

#####
These are all the possible response patterns.

As a default structure, we have checked the patterns which belong the knowledge structure observed from a previous
classroom sample. Both the empty set and the Q (full) set states have already been included.

You can use the one available, or create your own.

#### 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.