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
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 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
"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
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,
- 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