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Creative Digital Mathematics

Creative Digital Mathematics. Morten Misfeldt ResearchLab: IT, Learning & Design Aalborg University . ResearchLab : IT, Learning & Design host for Danish GeoGebra institute . Emerging and existing themes Students as producers and designers Computer game research center

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Creative Digital Mathematics

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  1. Creative Digital Mathematics Morten Misfeldt ResearchLab: IT, Learning & Design Aalborg University Nordic GeoGebra Conference sept13

  2. ResearchLab: IT, Learning & Designhost for Danish GeoGebra institute • Emerging and existing themes • Students as producers and designers • Computer game research center • Organizational aspects of ICT in schools • Immersive and creative learning processes (including brain stuff) Nordic GeoGebra Conference sept 13

  3. Creative Digital Mathematics – what is it • Using GeoGebra to support a change in: • The typical student activity in primary math ed. towards producing and exploring with and within mathematics • Teacher collaboration and teacher roles, towards producing and exploring new learning situations in collaboration. Nordic GeoGebra Conference sept 13

  4. Project timeline - iterative approach Nordic GeoGebra Conference sept 13

  5. The learning environment 1.Welcome game builder2. Try GeoGebra3. Tasks 4. Game project 5. Test 6. Apply for work Nordic GeoGebra Conference sept 13

  6. Traditions and discussions that we build upon • World to school – school for the world • Epistemic games ad role playing (Shaffer, 2006) • Relation between societal mathematics and school mathematics • Didactical transposition (Chevallard, 2012) • Didactical domains (Hanghøj, 2013) • Mathematical competencies (Niss et al 2002) • Express and invent with and within mathematics • Constructionism (Papert, 1980, Resnick1996, diSessa 2000) • Mathematical creativity (Hadamard, 1954) • Semiotic and social semiotic approach and thinking as communication (Jewitt & Kress, 2003, Duval 2006) Nordic GeoGebra Conference sept 13

  7. Theoretical framework • For the analysis I build on concepts from the instrumental approach (Trouche, 2005, Rabardel& Bourmaud, 2003, Trouche 2005). • instrumental genesis • instrumentation: evolution of utilization and instrument-mediated action schemes • Instrumentalization: evolutions of the artifact • epistemic and pragmatic mediations • orientation of an instrumented mediation Nordic GeoGebra Conference sept 13

  8. Research question • Aim: to investigate how the use of GeoGebra for students board game design activities, support pupils appropriation of GeoGebra as a mathematical tool. • What types of mediations can be identified; epistemic mediations, pragmatic mediations, and mediations directed to task, self, and others. • What types of relations to various domains of knowledge can be identified in the pupils work with constructing mathematical board games with GeoGebra. Nordic GeoGebra Conference sept 13

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  12. Example of game The purpose of SP Game is that player number one throws a dice three times, and if you throw a “4“ you can move to the nearest next field. When get to a field with a multiplication calculation, you should do the calculation right, and then you can move all over the game board but not into the target zone. If you are next to the target zone you have to throw a 5 with the dice in order to get into the target. Nordic GeoGebra Conference sept 13

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  16. Data • Pre-project (fraction and multiplication crusher – 3 classes) • Observation of most teaching • Interviews with pupils • Teacher collaboration (minutes from meetings, discussions in classroom) • Main project (7 different materials about 25 teachers and 15 classes) • Survey of teacher ict skills (pre and post) • Survey of teachers experience (evaluation) • Observation of one lesson pr run through (approximately) • All the materials developed by the teacher (teaching material, description of intentions and learning goals, qualitative evaluation Nordic GeoGebra Conference sept 13

  17. data Int: … Have you used math to do that? Pupil: Yes, we have used mathematics. We have created the shapes of the game, we needed to make some shapes. Int: What kind of shapes? Pupil: Mostly squares, we have also made some circles and some pentagons. Int: Have you used any other mathematics than shapes? Pupil: Yes, we have also used calculations actually, when you landed on a field, then you might need to solve a task. Nordic GeoGebra Conference sept 13

  18. Some quotes from classroom discussions – from the teachers tape recorder • It's more fun than writing in books • It's fun to make games and decorate them • You use your brain in a different way - you think more • The book says exactly what to do - here you have to decide for yourself • Making the game is like playing (play) • You push yourself more, because the others will play (game) the game Nordic GeoGebra Conference sept 13

  19. I also play (game) GeoGebra at home • There is nothing that is wrong, it only happens in the book • You learn more about the program because you have to investigate it, and you'll also find new things in the program • It is nice/cozy to sit an work [together] with GeoGebra, in the book you are on your own • By trying things out, you learn it - it's the same with games for example. Wii Nordic GeoGebra Conference sept 13

  20. Results • Classroom situation is different and is experienced different • No significant effect with a standard test • Teachers reports that students are engaged and that some problematic students are able to work much better • Everyone ends up with a product • Technical issues is a major barrier • Teachers improve skills with GeoGebra • Teachers discuss ict and math learning Nordic GeoGebra Conference sept 13

  21. Analysis • How can the use of GeoGebra in an instrumented board game design activity, support pupils instrumental genesis with GeoGebra? • The pupils appropriate the tool to new needs (example: change color, remove points) • Builds their game with mathematical shapes • types of mediations; epistemic, pragmatic, and direction. • Direction to fellow pupils have some epistemic elements (making the game hard or easy) • Many pragmatic mediations toward both mathematical and software related actions • Identification and relation to domains of knowledge • Strong identification to kids universe and board-game universe. • Pupils considers activities very different from the normal teaching of mathematics, even though they recognize that they use mathematics Nordic GeoGebra Conference sept 13

  22. Epistemic frame/didactical domains • In this situation there is no simple didactical transposition of work life situation to school. There are many domains involved and the actual enactment and teaching allows different aspects to pop up as important. • The fact that several domains exists simultaneously seems to support meaning making and learning Nordic GeoGebra Conference sept 13

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