1. Banff 2007: Innovations in Mathematics Education via the Arts Interactive Graphics Tools and Global Learning Mara Alagic & Glyn Rimmington Wichita State University

2. Banff 2007: Innovations in Mathematics Education via the Arts Outline L-Systems Turtle Graphics Rendering / Animation How people learn Standards-based Teaching Teaching for Understanding Examples

3. Banff 2007: Innovations in Mathematics Education via the Arts L-Systems Parallel Rewriting System axiom A rule A = AB rule B = A A AB ABA ABAAB ABAABABA ABAABABAABAAB

4. Banff 2007: Innovations in Mathematics Education via the Arts Turtle Graphics Fmove forward and draw fmove forward + -turn left or right ^ &pitch up or down roll clockwise or anticlockwise

5. Banff 2007: Innovations in Mathematics Education via the Arts Turtle Graphics Yaw Roll Pitch Z Y X + > &

6. Banff 2007: Innovations in Mathematics Education via the Arts Turtle Graphics F [ + F ] F 1 2 3 4 5 1 2,4 3 5 push onto branch stack pop off branch stack

7. Banff 2007: Innovations in Mathematics Education via the Arts Turtle Graphics F {. +g. +g. } 1 2 3 4 1 2 3 4 push onto polygon stack pop off polygon stack

8. Banff 2007: Innovations in Mathematics Education via the Arts How People Learn Developmental level Prior knowledge Learning styles Multiple Intelligences “How People Learn” (NRC, 2000)

9. Banff 2007: Innovations in Mathematics Education via the Arts Standards-based Teaching Mathematics (NCTM, 2000) Arts (http://artsedge.kennedy-enter.org/teach/standards/)http://artsedge.kennedy-enter.org/teach/standards/ Technology (http://www.iste.org/)http://www.iste.org/ BTTB ( http://www.education.wichita.edu/alagic/BTTB/BTTB.htm/ ) http://www.education.wichita.edu/alagic/BTTB/BTTB.htm/

10. Banff 2007: Innovations in Mathematics Education via the Arts Mathematics Standards Content Standards Process Standards – Problem solving –Reasoning and proof –Communication –Connections –Representations

11. Banff 2007: Innovations in Mathematics Education via the Arts Teaching for Understanding Perkins, 1993 Conceptual understanding Project-based learning Integration across curriculum Scaffolding (K to  ) Differentiating instruction

12. Banff 2007: Innovations in Mathematics Education via the Arts Plant Growth Animation

13. Banff 2007: Innovations in Mathematics Education via the Arts L-parser http://home.wanadoo.nl/laurens.lapre/ Global Dimension – exploring patterns and cultures Have fun!