1. Working Group D Notes of Day 2

2. Participants 27 person 12 countries 3 continents

3. Materials Topics – Solid geometry – Model of the solar system created by students – Investigating transformations and trig functions, inverse trig functions – Locus lines Shear – Local solution “Naver café” as a temporary solution before GeoGebra wiki and forum – Embedding GeoGebra applets in online classes

4. Methodology Prerequisites for Teaching with GeoGebra Need to change the curriculum for new, technology- supported mathematics Groups of students of different skill levels / ages in one class, different ways of “understanding” and “explaining”

5. Trainings How do we teachers make want to use GeoGebra? Using videos / screen recordings of best practice examples Creating files “live” during teaching, instead of black- box principle (e.g. applets) GeoGebra workshops with Interactive White Boards Design of workshop materials Assess local accomodations (computer labe vs. laptop computers, IWB or not, Internet connection?,…)

6. Group 1 Compare GeoGebra with painting, – tool like a brush to make pictures, – teacher makes an ornament and pupils color it, – or they use the tool to be creative

7. Group 2 – I. Design Features Consistency – doing things for students consistent across applets Not too much in each applet (1 idea per applet) Simple to work with Clear purpose Multiple formats Issues of range of tools features, open vs. closed option as a teacher tool, student tool purpose and learner developmental needs are important

8. Group 2 – II. Wiki – difficult to find items, categories like use, teacher use, student use, topic Need list of tags – standard list plus other Liked the solar system applet because students needed to find information as background to create tool Needs to be annotation, explanation to help deconstruct/construct Brings up the issue of when is a proof a proof? Some way of capturing explanation/”proof”, steps Many teachers do accept the “black box”, don’t have time to think about what is under the hood How much scaffolding vs. how much challenge, what specific skills are needed (or combination of skills)

9. Group 3 What is most important in the creation of resources? Randomisation of examples (now we can use command ‘RandomBetween[a,b]’ where a and b are integers) Use of checkboxes to show answers (graph or algebra) Whole lesson for students, with text and applets, as a webpage Get students to use GeoGebra application for themselves (as quickly as possible) (Allow them to teach you!) This depends on the particular class/students Video tutorials – learn maths in English as a foreign language! There is a lot of work for us to do over the next month.

10. Group 4 I Wish list: Can Locus interact with other objects and tools, e.g. Intersect, Tangent,… Concern with simple v. elaborate applets, which are better for what puprose? Essential to think o the objective of a particular applet in its design / motivatin factors for students – Autnonomy – Collaboration – Competence (Andreas Krapp) Give students a variety of different types of applets (simple to elaborate). Need to consider assessment, What did students actually learn from an applet? Objectives of a particular applet

11. Group 4 II Questions to ensure that students slow down with experimenting and use the applet the way it’s intended to be used. Use of prepared applets vs. GeoGebra as a tool Designing applets with open questions for students to explore, even if hey cannot make a formal proof at this stage What will happen to the quality of GeoGebra applet once text books are going to include them? Allow for student discovery

12. Wish List IWB Presentation mode: increase sensitive area of sliders and checkboxes Alternative way of right-clicking, since it is not supported by all white boards Wishlist for GeoGebra 3D wish list directly to Matthieu (Temel Kösa, Turkey) Grid for Polar coordinates Intersection of locus wit geometric objects Constructions protocol should include the toolbar icons Different kinds of toolbars for different math topics Creation of dynamic applets Print buttons for applets Possibility to change font size of html page Include a back and next button to create a series of dynamic worksheets Templates for dynamic worksheets (e.g. text next to applet,…) Ability to take notes within an applet (e.g. explanations, proof,…), maybe having a formula editor (e.g., Formulator MathML Weaver) available as well