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

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

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

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

 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

 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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: CARRYING OUT AND EVALUATING THE ACTIVITY

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

5- GROUP PHOTO

5- GUESSING THE KEYS

5- COLLECTING THE NECESSARY DOCUMENTS

5- ONE OF THE TEACHERS GIVING THE KEYS

5- FOLLOWING THE MAP

5- PHOTO OF THE PHOTOGRAPHER

5- WAITING AT ONE OF THE BASE CAMPS

5- ORGANISING THE DOCUMENTS

5- WAITING FOR THE STUDENTS

5- WILL ANYONE COME TO MY BASE CAMP?

5- VIDEO REPORTER READY TO GO

5- HAVING AN ICE-CREAM ON THE JOB

5- MEASURING THE TILES

5- YOU MEASURE AND I WILL WRITE THE RESULTS

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

5- GETTING IN-VOLVED IN THE WATER

5- COUNTING CUBES

5- MEASURING THE DEPTH – DON’T FALL IN

5- I THINK WE HAVE THE ANSWER

5- WHERE IS MY MOBIL TELEPHONE?

5- VIEWING OF THE VIDEO

5- PRIZE GIVING CEREMONY

5- RECEIVING THE DIPLOMA

5- GIVING OUT THE DIPLOMAS

5- EVEN THE TEACHERS RECEIVE A DIPLOMA

5- ALL GOOD FUN

5- POSING FOR THE CAMERAS

5- TEAM PHOTO

More information of the activity at: as 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