Blending layers of CUMULATE's user model

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This work is focused on mutual influence of heterogeneous user activity types (reading texts, viewing examples, and solving problems) on user's knowledge of some educational domain. Ordinarily CUMULATE's considers them separately by classifying them to modeling tiers or levels, each corresponding to a level of Bloom's taxonomy of intellectual behavior. Great part of this work is devoted on cross-tier user modeling. Namely, how user activity can (positively) influence on another/other layer(s).

Study 1

In this study we have inspected the influence of the comprehension layer of CUMULATE's user model (viewing examples) on the application layer (solving problems). Our approach was to create "blends" of problem-solving tier of the user model and weighted (from 0 to 1, with .1 step) example viewing tier Our hypotheses were that:

• Using example browsing activity when modeling problem solving improves model accuracy
• Different users benefit from different “blends” of user model levels

In addition we wanted to se if

• There is a single optimal blend for all users, and. or
• Classes of users benefitting from different model blends can be determined

Data

We were using previously collected student usage logs collected from 4 Database Management courses offered during Fall 2007 and Spring 2008 semesters at the University of Pittsburgh and Dublin City University. Each course had roughly the same structure, an identical set of 48 problems served by SQLKnoT system, and an identical set of 64 examples served by WebEx system. Basic usage statistics are given in the table below.

School	Semester	Level	No. of users	Avg. problem attempts	Avg. example views	Avg. distinct problems	Avg. distinct examples
U. of Pitt	Fall 2007	U*	27	156.40	189.00	29.96	32.07
U. of Pitt	Fall 2007	G	20	61.70	104.70	29.95	29.10
U. of Pitt	Spring 2008	U	15	26.94	46.65	16.35	10.29
DCU	Spring 2008	U	52	81.68	257.25	22.82	38.63

• U – undergraduate, G – graduate

Procedures

Out of 114 users who took the class 56 were chosen. The criteria was that the user had to cover at least 33% of problems (15/48) and at least 33% of examples (15/64). For each of the qualified users 11 user models were computed: with 0% to 100% of example browsing activity "blended" to the problem solving (by % here we mean numerical weighting not item filtering).

Metrics

• Accuracy was used to measure the resulting user model quality
• For every user - the "best blend" - blended model (with 10% or more of example activity added) having the highest accuracy; if there is more than one such model, the smallest % of the blend is taken
• For each user - number of "best blends" - number of blended models (with 10% blend of example activity or more), where the accuracy is the highest

Results

Example of blend accuracies for 5 users

Distribution of number of users for different "best" blends

• While looking at users' individual preferences, the best user blend seems to be superior to the 0%-blend: t = -5.38, p-value<.001
• Comparison of uniform blends for all users to a 0%-blends, shows that 40% and 50% blends were significantly better than 0%-blend: t = -for both 2.05, p-value = .023
• User separation into groups by the number of best blends yielded the following results
  • Low. 1 best blend only, 2 users. No further investigation performed.
  • Medium. 2-4 best blends. 22 users. Here 90% blend had the highest significant edge over 0% blend: p-value = .037
  • High. 5-9 best blends. 17 users. This group follows the global trend with 40% and 50% blends having best significant edge over 0% blend: p-value = .049
  • No difference. 10 best blends (all blended models have same accuracy). 15 users. No further investigation performed.