Interoperable Interactive Geometry for Europe: an introduction
Ulrich Kortenkamp
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Colette Laborde
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C. Laborde LIG,
Universite Joseph Fourier
, BP 46, 38042 Grenoble Cedex,
France
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U. Kortenkamp (&) CERMAT,
University of Education Karlsruhe
, Postfach 11 10 62, 76060 Karlsruhe,
Germany
1 Introduction
Interactive or dynamic geometry is one of the three major
software pillars of technology-based mathematics
education, next to computer algebra systems (CAS) and
spreadsheets. We can trace back the roots of this great tool
for visualization and interactive manipulation to the work
of Sutherland (1963), a system called Sketchpad which laid
ground in computer science and human computer
interaction. Since the introduction of Cabri-Geome`tre (Baulac,
Bellemain and Laborde, 1988) and Geometers Sketchpad
(Jackiw 1991), we could see several generations of such
tools applied in mathematics education. During the last
20 years, interactive geometry software could establish a
settled position in the mathematics education community,
and for many researchers it is no longer a question whether
to use these tools or not, but how to use them.
However, what has convinced many in the academic
field of mathematics education has still not become a
standard in mathematics teaching in the classrooms
(Intergeo Consortium 2008). While the lack of availability of
computers in some schools or the cost of licensing might be
reasons for the apparent underrepresentation, this cannot be
the only reason. In particular, in Europe, most schools can
offer access to networked computers, and there are several
interactive geometry packages available free of cost. Also,
there are thousands of web pages containing sketches,
examples, activities and exercisessubsumed as
resourcesusing dynamic geometry.
An initiative of Christian Mercat back in 2006 started
what became the Intergeo project (Kortenkamp et al.
2009), funded through the eContentplus program of the
European Union between October 2007 and 2010. This
project intended to bring together teachers at all school
levels from K-12 to university teaching and the wealth of
resources available on the internet. By assembling the
consortium and associate partners of the project from
several major interactive geometry software producers
from Europe (among them Cabri, Cinderella, GeoGebra,
GEONExT, Geoplan-Geospace, TracenPoche, WIRIS and
Z.u.L/C.a.R.), it was possible to include not only more than
3,000 resources contributing to the project, but the project
could also strive for a common exchange format, a lingua
franca for interactive geometry. A necessary condition for
a true re-use of a resource lies in the possibility of using the
resource in the environment familiar to the user regardless
of the particular system used to create the resource.
In addition, it was not clear how teachers can find
exactly the content needed for his or her particular
classroom situation. Helping people in this search for a specific
content usually means adding to the resource itself
metadata providing information about the resource. Then search
engines can identify material based on keyword searches.
The task is not trivial for mathematics and in particular
geometry, as information cannot be extracted from a
formula or graphical representation as easily as from a text.
Adding a European dimension makes the situation even
worse: the names of theorems or notions in mathematics
are not consistent throughout different languages, and even
translating them does not help. A famous example is
Thales theorem, which can be a theorem about
rightangled triangles inscribed in circles or about rays that
intersect parallel lines, depending on whether you are
talking about el teorema de tales, den Satz des Thales, le
theore`me de Thale`s, or o Teorema de Tales. Another
illustration comes from statistics: A camembert would not
be the correct word if you are translating pie to French for a
recipe book! For mathematics it is.
The only solution to add enough information to
resources to make them browsable and searchable for
teachers from all over Europe is to base the metadata on an
ontology, a formal representation of concepts from
mathematics. In Intergeo, an ontology of concepts, topics and
educational regions (Libbrecht et al. 2008) was created and
used by the search engine in order to help the users find
exactly what they need, even if it is only available in a
language different from the query formulated by the user.
But Intergeo did not only address the technical hurdles of
finding and using interactive geometry resources. If there
are more than just a few resources but several dozens as a
result for a query, then it is necessary to rank them according
to quality criteria. It is a difficult task to create such quality
criteria, as they depend on several factors. Also, even if there
are such criteria, the evaluation of the resources is
timeconsuming and an additional burden to those who just want
to use them. With the available funding, the project could
give limited support to in- (...truncated)