Sharing Interactive Geometry in a Multilingual Europe

co-funded by the Community
programme eContentplus
©Paul-GeorgMeister/PIXELIO
Sharing Interactive Geometry
in a Multilingual Europe
Paul Libbrecht
Weingarten
University
of Education,
Germany

2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
about me
§ Paul Libbrecht
§ former mathematician
§ Switzerland, Canada
§ now informatician
§ DFKI & Uni Saarland, PH Karlsruhe, MLU Halle
§ Now at Weingarten University of Education
§ special focus: teacher pre-service teacher
§ primary, lower secondary
§ all branches taught at the school
§ pedagogy as a central topic
§ specialty of the state of Baden-Württemberg
2
Quelle:http://upload.wikimedia.org/wikipedia/commons/3/37/Weingarten_Basilika_von_Nordwesten.jpg(CC-BY)

menu
§ dynamic geometry
§ multilinguality and search
§ open educational resources
§ quality
§ i2geo experience
3
intro • dynamic geometry • search • OER • quality • experience

What is Interactive Geometry
§ A geometric picture: a single case
§ repeat? describe?
§ Manipulate a geometric construction:
§ let students or teachers explore
§ take to limits, verify hypotheses,
§ Since the 80s: JM Laborde, N Jackiw, R Mechling, …
§ Alive in many communities:
§ rather software and language-speciﬁc
§ one of the primary mathematics tool in schools
4
who uses
some?

Dynamic Geometry Example
5
Daniel Mentrard, Tableau de variation d’une fonction
http://i2geo.net/xwiki/bin/view/Coll_MD/Tableauxdevariationsinteractifs
French
speciﬁc?

Search for interactive resources
§ Dynamic geometry is very widespread
§ search for it?
§ French: triangle rectangle => rectangles
§ English: perpendicular bisector => angle bisectors
§ conceptual search is needed
§ and conceptual annotations
§ partly there at search engine (some languages)
§ I2geo’s approach: ontology of mathematical concepts
§ topics with ontological inheritance
§ competencies with relationships
6
demo

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Your search expanded to: (XWiki.AssetClass.trainedTopicsAndCompetencies:#Construct_perpendicular_bisector
XWiki.AssetClass.trainedTopicsAndCompetencies:#Perpendicular_Bisector)
Introduction à la médiatrice (6°)
En salle informatique les élèves manipulent et observent les propriétés géométriques associées a la ...
by Calpe Anne INRP-IREM Lyon (contributed by Anne Calpe INRP-IREM Lyon) (updated 2009-03-22 18:29)
Tracer une perpendiculaire a une droite qui passe par un point donne qui ne se situe pas
sur la droite
Animer la construction de la perpendiculaire a la droite AB passant par un point C en utilisant une ...
by Mike May, S.J.,
(http://www.slu.edu/classes/maymk/GeoGebra/)
(contributed by Carole
Dording)
(updated 2008-12-05
14:01)
Tracer la mediatrice d'un segment de droite
Animer la construction de la mediatrice dun segment de droite AB en utilisant une regle et un compas...
by Mike May, S.J., (http://www.slu.edu/classes/maymk/GeoGebra/) (contributed by Carole Dording) (updated 2008-12-05 14:00)
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Cross-curriculum Search and Annotate
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sur la droite
by Mike May, S.J.,
Dording)
(updated 2008-12-05
14:01)
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sur la droite
by Mike May, S.J.,
Dording)
(updated 2008-12-05
14:01)
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Curriculum Coverage
10
§ all educational levels of western Europe
are entered
§ some Curriculum linking
§ take ofﬁcial texts
and link it to ontology
§ satisﬁes teachers‘
wishes
§ all authored by
curriculum-experts (translations, additions)

Open Educational Resources
§ Dynamic Geometry Systems’ ﬁles are… ﬁles
§ that can be opened and played (with appropriate players)
§ that can be adapted
§ i2geo only has Open Educational Resources
§ delivered with a license
§ free to re-use, copy, share, republish
§ sometimes free to adapt or only outside commercial
§ easy to apply and re-use
§ the cost becomes
§ prepare to teach, pull from trusted resources
11

OER Quality… a long Quest
§ Free share may mean as cheap as free beer
§ Only from recommended authors?
§ Take time to evaluate everything on the web?
§ technical traps, mathematical issues, inconsistent behaviours
§ e.g. the outer-surprise
§ start: trust what others trust
§ => share quality evaluation
§ i2geo Quality: for dynamic geometry
§ usability, stability, ease of use… example: pyramid’s
§ displayed, and inﬂuences the search
§ many other approaches (even Facebook’s!)
12
After you get up and ru
about anywhere with th
 fa-extern
fa-external
 · Unicode: f08e · Cre
After you get up and running (../../get-started/), you can place Font Awe
about anywhere with the <i> tag:
 fa-external-link
<i class="fa fa-external-link"></i> fa-external-link
Looking for more? Check out the examples
(../../examples/).
fa-external-link
 · Unicode: f08e · Created: v1.0 · Categories: Web Application Icons

Quality is Social
§ consider How to create a class wiki
§ is it good?
§ I trust Neil’s comment… so I should trust it?
§ quality is a personal measure
§ may be leveraged by trust
§ social networks!
§ Open Discovery Space
§ large European project
§ social network and resources’ sharing in one
§ gather resources from many (~500’000)
13
After you get up and running (../../get-s
about anywhere with the <i> tag:
 fa-external-link
<i class="fa fa-external-lin
Looking for more? Check
(../../examples/).

Re-use? (sayings)
§ Preparation of Math-Bridge (1st attempt):
(partner, we)
§ p: Will there be an authoring tool?
§ w: Sure, but there will be content ready to use.
§ p: Mmh, but our teachers do not want to re-use.
§ w: why not?
§ p: these are proud men, they want to make their own.
§ Joke about German professors:
§ Re-use my colleagues course?
§ Rather his toothbrush!
14

Re-use?
§ i2geo.net hosts
§ ~3500 resources, ~2700 users
§ ﬁnal objective: help teachers apply
§ … use and re-use
§ observation of practices:
§ technicalities can still drown
§ incompatible format? not bad… just redo
§ dark re-use!
§ language crossing happens sometimes
§ mathematics may be the best there
§ but: different mathematical cultures!
15

Paul Libbrecht - CC-BY-SA 16
§děkuji,
§danke schön
§dank u wel
§muchas gracias, gràcies,
§merci,
§obrigado,
§thank you,
§dziękuję,
§спасибо,
§niżżik ħajr ..., dankon
i2geo.net

Sharing Interactive Geometry in a Multilingual Europe

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