The questions we decided:

0.    We need a meta-pedagogy! – How to teach teachers/children?

1.     How do we deal with the different ways that teachers learn and the level of confidence they have in using technology?

2.     How do teachers overcome difficulties?

3.     Do we need different approaches with pre-service teachers and experienced colleagues?  How do we convince experienced teachers to try GeoGebra?

4.     What sorts of pedagogy are possible and appropriate when using GeoGebra?

5.     a)  How can certification best support teachers? (b) How can GeoGebra Institutes best support teachers?

6.     GeoGebra 4 – the new features/tools

7.     How to use assessment and GeoGebra together?

Notes from the TE discussion group, August 2011

0.     We need a meta-pedagogy! How to teach teachers/children?

     One possible model (used in a 30 hour, face-to-face course) uses three phases:

     Phase A: The teacher uses GeoGebra as their own tool

• do it at home
• make diagrams for printing on worksheets
• make mistakes in the privacy of their own home
• Support: face to face teaching during this stage. What do they need? Learn the tools, customize their work.
• Dynamic properties of GGB are not so important at this stage.
• Teachers are given a set of exercises: how to draw a square that stays a square

     Phase B: Teacher uses GGB as a presentation tool - the children watch.

• It is a tool for the teacher.  They have one computer and a projector.  The teacher has control of the mouse.
• It is a substitute for the blackboard.  The teacher knows their own computer and there is less opportunity for things to go wrong.
• Now the dynamics of the figures are important.
• “what if ...” questions can be answered.

     Phase C: Children work at a computer during a mathematics lesson or for homework.  

• Teach the children to use GGB
  
• They make a construction or get a premade construction from the teacher.

The face-to-face aspect of this course structure is important to ensure teachers don't just focus on technical issues.

NB:  In Phases A&B the teacher is using GGB.  In Phase C the children are using GGB.

1.     How do we deal with the different ways that teachers learn and the level of confidence they have in using technology?

• Teachers help each other
• Teachers are not pressed to go to the training
• When ICT follows conventions then it is easier to learn. Some people need/want more detailed instructions.

2.     How do teachers overcome difficulties?

• Show them the wiki/forum.  Have a Beginners' Forum
  
• Help them find a way to learn on their own (using the wiki, help, forum, autocomplete, collections of examples, GeoGebraTube, GeoGebra YouTube channel)
  
• Teach them to use the construction protocol
• How to support teachers after the three phases?  It is important to have the opportunity for on-going contact with the trainer and/or with each other (Luc Trouche). 
• Improve the sustainability of the innovation by having two teachers from the same school involved in training
• Have a group of certified trainers in the region for teachers to contact for support
• Active work by institutes
• Put together a starter package of materials for each subject/age-group

3.     Do we need different approaches with pre-service teachers and experienced colleagues?  How do we convince experienced teachers to try GeoGebra? What about non-specialist Mathematics teachers?

• Experienced teachers are concerned about time constraints, key questions, assessment.  Pre-service teachers are more anxious about behaviour management and assessment.
• Non-specialist mathematicians will find it more difficult
  
• Some teachers only use GGB for demonstrations (they don't get to Phase C)
• Is it necessary to revolutionize their teaching style? No, it is only another tool to be used.  Start from where the teachers are, and as they become more comfortable with the instrument (Paul Drijvers) then their style will evolve.  In this way GGB can help teachers to expand their teaching styles.
• In the beginning some teachers want/need more detailed construction instructions
• Mike May's "Shiny Toy" theory
• Introduce intriguing artefacts: show some files and applications to mathematics, science, STEM (Adrian Oldknow)
  

4.     What sorts of pedagogy are possible and appropriate when using GeoGebra?

• It depends on local issues.  GGB can be used within any pedagogy.  GGB can be an opportunity to expand your pedagogical approach.
• Compare pencil-and-paper methods with teaching with GeoGebra, what will be the benefits/drawbacks for the teaching and learning of STEM?
• Inquiry can be done without the use of technology but technology offers new opportunities
  
• Technology can be used for demonstration or investigation or motivation
  

5.     a)  How can certification best support teachers? (b) How can GeoGebra Institutes best support teachers?

• a) Can be important for status, quality control, motivation
• b) Can gather interested people, for example by establishing a local website in their own language
• b) Responding to local questions/concerns/suggestions
• b) Publishing a magazine - to show some "how to"s
  
• The IGI working group are likely to be able to advise further?
  

6.     Learning GeoGebra 4

• Beginners might be shown a perspective that is more like GGB3
• Can remove icons for beginners
  
• There is a need to support GGB3 users in learning GGB4
• There are more commands in GGB4 than appear on menus 
• Producing web applets is important
  
• NB: GGB4 has lots of extra help.  Please can future versions of this include examples of the syntax in use?
  

7.     How to use assessment and GeoGebra together?

• Need different type of questions if GeoGebra is used during examination
• It would be good to prepare some assessment materials and sample examinations (on the wiki)
• Use Mathlets (Mike Borcherds)

Open Questions:

1.     Would a Beginners' Forum be helpful?

2.     It is important to have the opportunity for on-going contact with the trainer and/or with each other.  How might this be possible?

3.     Should we upload materials on the wiki for sample examination material using GeoGebra?

4.     Could future versions of the GGB4 Help include examples of the syntax in use?