This document summarizes Paul Libbrecht's presentation on sharing interactive geometry resources in a multilingual Europe. The presentation introduced dynamic geometry as a tool for exploring mathematical constructions. It discussed the i2Geo platform's approach to enabling cross-curricular search of resources through an ontology of mathematical concepts. The presentation also covered i2Geo's focus on open educational resources, efforts to ensure resource quality, and challenges around encouraging reuse of resources across languages and cultures.
2. 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)
3. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
menu
§ dynamic geometry
§ multilinguality and search
§ open educational resources
§ quality
§ i2geo experience
3
intro • dynamic geometry • search • OER • quality • experience
4. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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?
intro • dynamic geometry • search • OER • quality • experience
5. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
Dynamic Geometry Example
5
Daniel Mentrard, Tableau de variation d’une fonction
http://i2geo.net/xwiki/bin/view/Coll_MD/Tableauxdevariationsinteractifs
French
specific?
intro • dynamic geometry • search • OER • quality • experience
6. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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
intro • dynamic geometry • search • OER • quality • experience
7. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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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)
showing 3 of 3
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NSORS
platform is brought to you by
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uropean commission and by
ers.
Intergeo | eContentPlus
TURED MEMBER
Cross-curriculum Search and Annotate
7
intro • dynamic geometry • search • OER • quality • experience
8. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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Become
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English
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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)
showing 3 of 3
login name
password search
rivacy Policy | Help | Contact Us | All content licensed Creative Commons | Terms of Use | Copyright
ME
FIND
CONTRIBUTE
CONNECT
HELP
ABOUT I2GEO PROJECT
NSORS
platform is brought to you by
ntergeo project, funded under
Content Plus programme of
uropean commission and by
ers.
Intergeo | eContentPlus
TURED MEMBER
Cross-curriculum Search and Annotate
8
intro • dynamic geometry • search • OER • quality • experience
9. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
Go »
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Become
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English
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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)
showing 3 of 3
login name
password search
rivacy Policy | Help | Contact Us | All content licensed Creative Commons | Terms of Use | Copyright
ME
FIND
CONTRIBUTE
CONNECT
HELP
ABOUT I2GEO PROJECT
NSORS
platform is brought to you by
ntergeo project, funded under
Content Plus programme of
uropean commission and by
ers.
Intergeo | eContentPlus
TURED MEMBER
Cross-curriculum Search and Annotate
9
intro • dynamic geometry • search • OER • quality • experience
10. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
Curriculum Coverage
10
intro • dynamic geometry • search • OER • quality • experience
§ 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)
11. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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
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intro • dynamic geometry • search • OER • quality • experience
12. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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!)
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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
intro • dynamic geometry • search • OER • quality • experience
13. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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)
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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/).
intro • dynamic geometry • search • OER • quality • experience
14. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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!
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intro • dynamic geometry • search • OER • quality • experience
15. 2014-09-11 MetaMath & MathGear Meeting Saarbrücken
Paul Libbrecht - CC-BY-SA
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!
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intro • dynamic geometry • search • OER • quality • experience