1. Individualizing a cognitive model of students’ memory in Intelligent Tutoring Systems Maria Virvou, Konstantinos Manos Department of Informatics University of Piraeus

2. Introduction In this study we will describe the student modelling module of an educational application. This module measures-simulates the way students learn and possibly forget by using principles of cognitive psychology concerning human memory

3. Student Model the student model takes into account: How long it has been since the student has last seen a part of the theory How many times s/he has repeated it How well s/he has answered questions relating to it

4. Test Bed To test the generality of our approach and its effectiveness within an educational application we have incorporated it in a knowledge based authoring tool. The authoring tool is called Ed-Game Author (Virvou et al. 2002) and can generate ITSs that operate as educational games in many domains

5. Cognitive model (Ebbinghaus, 1998) t: is the time in minutes counting from one minute before the end of the learning b: the equivalent of the amount remembered from the first learning. c and k : two constants with the following calculated values: k = 1.84 and c = 1.25

6. Learning Process Whenever a students encounters a new part of the theory, the date and time are stored in the system’s database (TeachDate). Whenever a student “uses” a part of the theory, the date and time of this action is also stored in the system’s database (LastAccessDate)

7. Retention Factor (RF) The Ebbinghaus’ model is generic. To personalize it we will use the Retention Factor. The RF is a base percentage of the how much of the fact a student actually remembers The RF is modified based on the student’s profile and progress during the test

8. Retention Percentage b is the result of Ebbinghaus’ power funtion if we set t=Now-TeachDate X is the Retention Percentage If we want to know how much of a fact (Retention Percentage) a student remembers at a specific moment then we use the following formula

9. Custom Retention Factor To customize the Retention Factor of a student we will introduce two new factors: Memorize Ability Factor Response Quality Factor

10. Memorize Ability Factor Based on the student model we define the memorize ability factor, a constant number with the following values: 0  Very Weak Memory 1  Weak Memory 2  Moderate Memory 3  Strong Memory 4  Very Strong Memory

11. Memorize Ability Factor (2) The new range for the RF is from 90 (very weak memory) to 100 (very strong memory) Memorise Ability Value Retention Factor Modification 0RF` = RF – 5 1RF` = RF – 2 2RF` = RF 3RF` = RF + 2 4RF` = RF + 5

12. Response Quality Factor During the test, depending on the student’s answer we define the Response quality factor, a constant number with the following values: 0  No memory of the fact 1  Incorrect response; the student was “close” to the answer 2  Correct response; the student hesitated 3  Perfect Response

13. Response Quality Factor (2) At that point the RF is again modified as shown in the following table RQModification 0 RF’ = X – 10, set TeachDate=Now 1 RF’ = X – 5, set TeachDate = Now 2 RF’ = RF + (MA + 1) * 3 3 RF’ = RF + (MA + 1) * 4

14. Response Quality Factor (3) When a student gives an answer, the modification of his/her Retention Factor depends on his/her Memorise Ability factor In the end of a “virtual lesson”, the final RF for each fact is calculated. If this result is above 70 then the student is assumed to have learnt the fact, else s/he needs to revise it.

15. Conclusions We have described the part of the student modelling process of an ITS authoring tool that keeps track of the students’ memory of facts that are taught to him/her For this reason we have adapted and incorporated principles of cognitive psychology into the system In this way the system may know when each individual student may need to revise each part of the theory being taught