DecSys

DecSys is a game-based intelligent tutoring system for decimal numeration, which uses a BN for diagnosing student misconceptions and choosing what to present to the student. This has been included in V3.1 of the "Teaching and Learning about Decimals" CD-ROM, available since January 2006.

The teaching model used in this project incorporates a model of student misconception and task performance, represented by a Bayesian network. BNs have previous success in intelligent tutoring applications, offering an intuitive graphical representation with efficient probabilistic algorithms for updating beliefs in the light of new evidence. In this case study, the beliefs are the estimates of the probabilities that a given student has a particular misconception or will demonstrate certain behaviour when playing the games. We use a BN to model the interactions between students' misconceptions, their game playing abilities and their performance on a range of test items. Building the student model from misconceptions, rather than in terms of gaps in correct pieces of domain knowledge, is unusual, and was viable in this project because of the nature of the domain and previous extensive research on student understanding in the domain.

The computer game genre was chosen to provide students with an experience different from, but complementary to, normal classroom instruction, and to appeal across the target age range (Grades 5 to 10). A simple decimal comparison test (DCT) is given first to gain some initial knowledge about the student's understanding. Each game then focuses on one aspect of decimal numeration, thinly disguised by a story line.

• In the "Hidden Numbers" game students are confronted with two decimal numbers with digits hidden behind closed doors; the task is to find which number is the larger by opening as few doors as possible. Requiring similar knowledge to that required for success on the DCT, the game also highlights the place value property that the most significant digits are those to the left. The order in which doors are opened is monitored by the system. Some students successful on the DCT do not realise at first how they can play without opening all the doors.
  

  DecimAliens
• The game "Flying Photographer" requires students to "photograph" an animal by clicking when an "aeroplane" passes a specified number on a numberline. This task requires an understanding of the relative size of decimals, as well as their order as required in the DCT and Hidden Numbers. This task also requires understanding of decimal numeration and can be used to contribute to diagnosis of misconceptions. For example, clinical interviews confirm that whole number thinkers usually expect a number like 0.23456 to be very large and are surprised to see it close to zero.
• The "Number Between" game is also played on a number line, but particularly focuses on the density of the decimal numbers; students have to type in a number between a given pair. The main situation which produces errors is that many students are unable to insert a number between 3.46 and 3.47, as they think these are consecutive numbers.
• "DecimAliens" is a classic shooting game, designed to link various representations of the value of digits in a decimal number. For example, the 4 in the number 3.46 is to be identified as representing 4 tenths, 0.4, 4/10 as well as in more difficult representations requiring reunitising as 40 hundredths, 400 thousandths etc.

These games, together with a Decimal Comparison Test, address several of the different tasks required of an integrated knowledge of decimal numeration based on the principles of place value. Therefore, it is possible for a student to do well in one game or the diagnostic test, but do poorly in another; emerging knowledge is often compartmentalised.

Related Research Publications:

• K. Stacey, E. Sonenberg, A. Nicholson, T. Boneh and V. Steinle. A Teaching Model Exploiting Cognitive Conflict Driven by a Bayesian Network, in P Brusilovsky, A Corbett and F de Rosis (eds), Lecture Notes in Artificial Intelligence, Proceedings of the 9th International Conference on User Modelling UM-03, Springer-Verlag, Berlin, Germany, ISSN: 0302-9743, Vol 2702, pp 352-362.
• A. Nicholson, T. Boneh, T. Wilkin, K. Stacey, L.Sonenberg and V. Steinle. A Case Study in Knowledge Discovery and Elicitation in an Intelligent Tutoring Application In UAI01 -- Proc. of the 17th Conference on Uncertainty in Artificial Intelligence Seattle, 2001, pp. 386-394.
• Boneh, T.Nicholson, A. E.Sonenberg, E. K. Stacey and V. Steinle: DecSys: An Intelligent Tutoring System for Decimal Numeration, School of Computer Science and Software Engineering, Monash University, Melbourne, 33pp. Technical report 2003/134. Abstract available.