1. MATHEMATICS GYMKHANA THROUGH ZARAGOZA Teachers Schools Mª Ángeles Arroyo García CPR Nº2 JUAN DE LANUZA J. Carlos Gil Mongío IES ELAIOS Emilio P. Gómez García IES PILAR LORENGAR Manuel Hernández Rodríguez IES FÉLIX DE AZARA Fernando Herrero Buj IES FÉLIZ DE AZARA Mª Luz Mayoral Gastón IES MEDINA ALBAIDA Teresa Royo Muñoz IES ELAIOS José Mª Sorando Musas IES ELAIOS

2. 1- Previous considerations. 2- Characteristics of the activity. 3- Preparation of the activity. 4- Carrying out and evaluating the activity. 5- Visual documentation of the activity. 6- Further information. GUIDE FOR THE PRESENTATION OF THE EXPERIENCE

3. Mathematics has been developed throughout history being interrelated to other area of knowledge The specific language developed through mathematics has led to an isolation of the subject in the classroom and conceived as being ABSTRACT and unconnected to the real world. Many students see the utility of Mathematics confined to the school environment. 1- PREVIOUS CONSIDERATIONS

4. In this context we must make our students become aware of :  The cultural value of Mathematics throughout their own history and of the interrelation with other areas of culture. 1- PREVIOUS CONSIDERATIONS

5.  Its functionality in daily life: the citizen needs knowledge, procedures and values in order to resolve problems from different areas.  Its use in other areas of knowledge.  Its potential for taking part in the development of abilities of reasoning, abstraction, deduction, reflection, analysis … 1- PREVIOUS CONSIDERATIONS

6.  In order to achieve all of this it would seem to be necessary to present a subject which goes much further than its language and its abstract rules. 1- PREVIOUS CONSIDERATIONS

7. At the same time, the methodology used to teach Mathematics can help to create critical and democratic citizens. 1- PREVIOUS CONSIDERATIONS

8. SOME GENERAL CHARACTERISTICS:  This is an activity that can easily be transferred to other areas or levels.  It allows the ordinary context of the class to be changed. 2- CHARACTERISTICS OF THE ACTIVITY

9.  Mathematics related to the city is carried out.  Therefore related to daily life.  Mathematics in significant contexts. 2- CHARACTERISTICS OF THE ACTIVITY

10. The problems include references to:  The history of the city,  art,  urban landscapes,  commerce... 2- CHARACTERISTICS OF THE ACTIVITY

11. Regarding the mathematical work:  Develop different problem solving strategies to those of trial and error.  They begin to apply mathematics to the real world. 2- CHARACTERISTICS OF THE ACTIVITY

12. Regarding the type of activity:  This is a voluntary extracurricular activity.  There are so many base camps and problems that the students cannot possibly carry them out. This is in order to disperse the students.  Each group performance in solving the problems is evaluated.  The identifying T-shirt and badges make it easier to locate the students. 2- CHARACTERISTICS OF THE ACTIVITY

13. Objectives of the activity: 1. Apply the contents of the subject area of Mathematics to situations and objects which can be found around us in our daily lives outside the classroom, in this case in the city of Zaragoza. The students have greater freedom to use the academic knowledge acquired in class. 2- CHARACTERISTICS OF THE ACTIVITY

14. 2. Achieve a more in-depth knowledge of the city with the mathematical perspective taking first place as well as the historical, artistic, sociological or economic. 3. Motivate the students by taking Mathematics out of the classroom and onto the street. 2- CHARACTERISTICS OF THE ACTIVITY

15. 4- Strengthen the students teamwork skills. 5- Develop the students’ autonomous investigation skills in problem solving strategies. 2- CHARACTERISTICS OF THE ACTIVITY

16. MATHEMATICS GYMKHANA THROUGH ZARAGOZA  Organised by CPR 2 “Juan de Lanuza” by the “Mathematics Gymkhana through Zaragoza” seminar.  Teachers and Students from five different Secondary Centres in Zaragoza have participated. 3- PREPARATION OF THE ACTIVITY

17. Two areas: - Teamwork through individual and collective work at the meetings held at the CPR. - The educational limits of the centre of each one of the teachers which is dealt with by the students in problem solving and teamwork. 3- PREPARATION OF THE ACTIVITY

18. Two edged work by the teacher: - Mathematical: in the search and preparation of mathematical problems taken from the data of our city. - The teaching: in the preparation of the students and in the discussion of the appropriate strategies in order to work with them. 3- PREPARATION OF THE ACTIVITY

19. STAGES: 1st Stage: Elaboration of the event and didactic aspects related to it. 2nd Stage: Discussion of criteria and relative rules for the organisation of the event. 3rd Stage: Carrying out the event. Evaluation, conclusions and improvement proposals. 3- PREPARATION OF THE ACTIVITY

20. 1st Stage:  Limit the area and choose the position of the base camp.  Look for localizations.  Elaborate questions.  Adapt other pre-existing problems.  Selection.  Revision and Modelling. 3- PREPARATION OF THE ACTIVITY

21. Elaboration criteria:  The level the activity is aimed towards.  The problems must belong to different mathematical blocks (not all Geometry)  Include problems of different levels of difficulty.  Look for problems linked to the localisations. 3- PREPARATION OF THE ACTIVITY

22. 2nd Stage:  Establish the organisation of the event.  Elaborate the pertinent documents:  Leaflet for students. Leaflet for students  Instructions. Instructions.  Registation card Registation card  Keys sheet. Keys  Sheet of answers. Sheet of answers  Control sheet. Control  Codified question sheet.question  Folders.  Ask for permission, material and contract school insurance policy.  Distribute the tasks among the teachers.  Distribution of material: T-shirts, identification cards.T-shirts cards 3- PREPARATION OF THE ACTIVITY

23. 3rd Stage: 1- Carrying out the event. 2- Correction of the event by the Seminar. 3- Giving out prizes and diplomas to the students at the CPR. 4- Evaluation of the activity. 4- CARRYING OUT AND EVALUATING THE ACTIVITY

24. Carrying out the event:  Previous meeting of the teachers.  Students’ meeting with the students at the starting point.  Distribution of material among students and final instructions.  Initiation of the event at 9:30.  Development.  Collection of solutions at the starting point at 13:30. 4- CARRYING OUT AND EVALUATING THE ACTIVITY

25. Giving out prizes and diplomas:  Attendance of the students and teachers at the CPR.  Watching the video.  Giving out diplomas.  Giving out prizes.  Looking at the photographs.  Sending-off and thanks for the valuable participation of all involved. 4- CARRYING OUT AND EVALUATING THE ACTIVITY

26. 5- GROUP PHOTO

27. 5- GUESSING THE KEYS

28. 5- COLLECTING THE NECESSARY DOCUMENTS

29. 5- ONE OF THE TEACHERS GIVING THE KEYS

30. 5- FOLLOWING THE MAP

31. 5- PHOTO OF THE PHOTOGRAPHER

32. 5- WAITING AT ONE OF THE BASE CAMPS

33. 5- ORGANISING THE DOCUMENTS

34. 5- WAITING FOR THE STUDENTS

35. 5- WILL ANYONE COME TO MY BASE CAMP?

36. 5- VIDEO REPORTER READY TO GO

37. 5- HAVING AN ICE-CREAM ON THE JOB

38. 5- MEASURING THE TILES

39. 5- YOU MEASURE AND I WILL WRITE THE RESULTS

40. 5- NO DESK TO USE, JUST HAVE TO USE THE FLOOR

41. 5- GETTING IN-VOLVED IN THE WATER

42. 5- COUNTING CUBES

43. 5- MEASURING THE DEPTH – DON’T FALL IN

44. 5- I THINK WE HAVE THE ANSWER

45. 5- WHERE IS MY MOBIL TELEPHONE?

46. 5- VIEWING OF THE VIDEO

48. 5- PRIZE GIVING CEREMONY

49. 5- RECEIVING THE DIPLOMA

50. 5- GIVING OUT THE DIPLOMAS

51. 5- EVEN THE TEACHERS RECEIVE A DIPLOMA

52. 5- ALL GOOD FUN

53. 5- POSING FOR THE CAMERAS

54. 5- TEAM PHOTO

55. More information of the activity at: http://es.geocities.com/mundo_matematic as http://es.geocities.com/mundo_matematic as ARROYO, M A Y OTROS (2005): Rutas matemáticas I Gymkhana Matemática x Zaragoza, Ed. Área de Educación y Acción Social del Ayuntamiento de Zaragoza, Zaragoza. 6- MORE INFORMATION