Global nodes in a topic cluster

A learner’s overall characteristics are represented by global nodes, the beliefs not specific to any topic. We are particularly interested in the following two characteristics:

1. Acquisition-rate – Implies how fast a particular student learns a new topic. When a new topic is introduced, the learner’s performance is measured on an initial set of questions, to determine this characteristic. The purpose of measuring acquisition rate is two fold -> one, to aid in planning the pace at which new topics should be introduced, and two, to help in question-generation where more than one sub-skills can be involved.
2. Student’s challenge level – There is quite a difference in terms of how much negative outcome a learner can tolerate. The purpose of measuring this characteristic is to model the level of failure/challenge that is appreciable to the learner, which would then be used to keep the game at a playable level.

Let’s consider the structure of a topic(sub-topic)-cluster we get considering the two global nodes, and observe the relationships between the local and global nodes.

Figure 1: Global nodes added to a topic cluster

In Figure 1, G1 and G2 refer to the newly introduced global nodes. L1, L2, L3 and L4 are the local nodes of the topic-cluster.

The G1-L1 edge does not represent an exact causal relationship, and it would be inappropriate to update belief for G1 on L1’s posterior belief based on conditional probability. Rather, acquisition rate(G1) would be measured as a rate of change in L1.

The L4 node corresponds to the learner’s choice of topic from options, where the interface would be similar to Image 3 in the Tuxmath post. The idea as of now is to present the learner with recommended choices for topics(lessons) to practice (like one hard, medium and easy). The nature of node L4 would be quaternary, i.e. a learner can choose either of the three recommended choices(H,M,E) or choose a completely different(D) topic. The learner’s choice will determine how much challenge he is willing to take (G2). And the relationship G2-L4 is causal in the way that more challenge level of a learner corresponds to an increasing chance of L4 node being hard(H).

Even though one may argue that global nodes complicate the model, they allow better inferencing about learner’s knowledge in a particular topic/sub-topic, taking into account both topic-related characteristics and learner’s characteristics.