The questions we decided:

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

- How do we deal with the different ways that teachers learn and the level of confidence they have in using technology?
- How do teachers overcome difficulties?
- Do we need different approaches with pre-service teachers and experienced colleagues? How do we convince experienced teachers to try GeoGebra?
- What sorts of pedagogy are possible and appropriate when using GeoGebra?
- a) How can certification best support teachers? (b) How can GeoGebra Institutes best support teachers?
- GeoGebra 4 – the new features/tools
- How to support teachers to follow through the things they say they want to do?
- How to use assessment and GeoGebra together?

Notes - TE discussion group 2011-08-30

The questions we decided

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

A. We can use GeoGebra in many ways as a tool to prepare worksheets. This is not complicated.

B. Use as a presentation tool – students watch

C. Have students use – make construction or get a premade construction from the teacher.

- Give clear examples of cases where what you see isn’t always “the mathematical truth”

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

- Mostly need to worry about people that have the difficulty
- Teachers help each other

2. How do teachers overcome difficulties?

- Show them the wiki
- Help them find a way to learn on their own
- Teach them to use the construction protocol

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-Mathematics teachers?

- In the beginning need all the steps for something
- Need to make it their own tool

http://dmentrard.free.fr/GEOGEBRA/Sciencephy.htm

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

- It depends on local issues – no change –
- Compare the traditional method with teaching with GeoGebra, what will be the benefit for the student?

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

6. GeoGebra 4 – the new features/tools

7. How to support teachers to follow through the things they say they want to do?

8. 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 sample examinations
- Mathlets – from a talk by Michael Borcherds

Wishlist:

1. A beginners forum would be nice

2. A place in the wiki for sample examination material using GeoGebra (or is this already there?)

Notes from Tues pm:

1. Learn to make geogebra your tool, do it at home, 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 it. Dynamics is not so important at this stage. Teachers are given a set of exercises: how to draw a square that stays a square

2. Tool for my teaching: to be in one computer with control of the mouse with one projector. Substitute of the blackboard. I know my own computer and have less opportunity for things to go wrong. Now the dynamics of the figures are important. With that “what ifs” questions can be answered.

3. Pupils working in a computer lab or with dynamic worksheet.

Does this model need a stage 2½ ? File for the pupils to manipulate with key questions or worksheets.

It is important for pupils to have the opportunity to explore with GGB.

Different pedagogies come from different understandings of what mathematics is (eg whether it is a body of knowledge to transmit…). For our purposes, we are working with teachers who already have some sympathies with the aims of GGB.

How to support teachers after the three phases? It is important to have on-going contact with the trainer.

Create a pioneer in each school? Or do we need at least two people to work together? In Florida there was a network of GGB specialist teachers to support teachers with questions/difficulties.

Sustainability of innovation?

It is important to stress that we are not putting extra things into the curriculum (and we cannot influence the curriculum, even though we would like to) but changing the way it is done.

Confidence is important - there may be things that go wrong, but the results are so important that the technical difficulties are worth overcoming.

Notes from Wed morning

Curriculum is asking pupils to do computations by hand, we don’t need to spend so much time on the calculations

More important to have conceptual understanding

Curriculum not connected with the evolution of technology

Technology is seen as an addition, an extra activity to the curriculum but not as a replacement or changing the pedagogy.

Inquiry can be done without the use of technology but technology makes it easier to have open-ended problems

Technology used as demonstration or investigation

Technology supports to structure the lesson: introduce lesson, form small groups, discussions. Teachers can get to the objective of the lesson

New technology is a good support to manage the lesson and support

Use technology in certain tasks

If replacing some tasks with technology, some of the paper and pencil skills can be lost. Students should not always rely on technology for their skills.

How dependent is one on technology? Replacing the skill of finding the sine of an angle or to solve a quadratic equation. Distinction of having knowledge or having a skill to solve it.

What is the importance of solving a quadratic equation? Practice skills, appreciate structure

Use of existing geogebra files depends on the content knowledge of the teachers

When teachers have a didactical problem (students did not understand or lean a concept) then technology is useful.

Evolution of a file: same file (like the inscribe circles) can change from the idea of circles to talk about rounding and continuity of decimal numbers.

When teachers feel they want to improve their way of teaching, then technology is useful.

Teachers must feel a fascination with technology

Technology can change the way the curriculum is introduced as well as the order of the concepts introduced.

Technology can also bring misconceptions like “point moving on a curve” and seeing the tangent move on the curve. Other misconception: rotation is a transformation bringing one shape into another and not a continuous motion.

These discussions are important to have with colleagues. What skills do I give away? If using technology, will we have to show the use of a compass? What are the good skills to have and which one will vanish?

There is no need to use the technology every single time, use it in excess.

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

Teachers are not pressed to go to the training

We should not deal with the problems of the reluctant teachers

Some teachers only use it for demonstrations

Is it necessary to revolutionize their teaching style? No, it is only another tool to be used.

When technology has commonalities then it is easier to deal with them. Some people need more detailed instructions.

Some teachers are fascinated by transforming formulas and not by pictures. Are we a special group? Is for us math a collection of pictures? Are we showing students what is in our heads? If a teacher is in favor of more dealing with formulas, then that teachers might not find technology that fascinating. With the use of sliders then parameters of equations can be changed.

People can see problems in different ways. Seeing proofs in a more pictorial way can do the transformation for an algebraist. How can a problem be seen in a more geometrical way?

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