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REFERENCES

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INTELLIGENT TUTORIAL SYSTEMS
Gerhard Holland
Gießen
1. INTRODUCTION
The following is an attempt to contribute to the topic of intelligent tutorial
systems (ITS) as an object of research in mathematics education and devel-
opment. In the debate in mathematics education about the use of advanced
software for mathematics instruction, tutorial systems have only a low
status beside mathematical tools like DERIVE and mathematical
microworlds like Cabri géométre. There are at least two reasons for this:
1. As far as ITS are available, very few will run on school computers, are
adaptable to the requirements of countries and school systems other than
those for which they were developed, and are offered additionally at prices
within the reach of schools.
2. Because of negative experience with programmed instruction in the
1960s, and subsequently with simple and low-yield drill and practice pro-
grams for simple skills, many mathematicians have a general distrust
toward tutorial systems.
My contribution will have met its goal if it succeeds in initiating a quali-
fied debate about the significance of tutorial systems for mathematics in-
struction and for research into mathematics education. After explaining the
classical architecture of intelligent tutorial systems (section 2), the system
HERON for solving word problems (by K. Reusser) is presented as an ex-
ample (section 3). Subsequently (section 4), the paradigm of ITS as a pri-
vate teacher is contrasted with the concept of a mathematical microworld
with tutorial support. Finally, I give an extensive presentation of a general
concept that can be used to subsume a large number of (potential) tutorial
systems for mathematics instruction and is intended to contribute toward re-
ducing the development cost for ITS (section 5).
2. INTELLIGENT TUTORIAL SYSTEMS
The primary theoretical motive in using methods of artificial intelligence
(AI) to develop "intelligent" tutorial systems, which yield the same perfor-
mance as a private teacher, has been an objective for more than 10 years in
advanced research in the still recent field of artificial intelligence and edu-
cation. This, however, is unaffected by the illusion of revolutionizing the
R. Biehler, R. W. Scholz, R. Sträßer, B. Winkelmann (Eds.),