Title Project Innovative Training for teachers and trainers in Math
Project Number 2010-1-IT1-LEO05-01062
Project Type Transfer of Innovation
The dissemination and promotion of the initiative was implemented on different levels: sectoral, provincial, regional and possibly national level. Each project partner will took care of the dissemination phase in their country of origin. Among the activities to disseminate the project results has been expected:
- Production of Brochures operational;
- Production of promotional material for the promotion of the downloadable PDF version from the Internet;
- Newspaper articles to promote national dimension, as well as at regional and local magazines of the sector;
- Organization of a meeting aimed at dissemination of results and comparison with industry experts;
- Organization of a Final Seminar aimed to disseminate the project results which will highlight the characteristics of training, the Network and the actions finalities.
Summary The scientific vocations crisis and the risulting mismatching between the demand for labour and the supply, cause, in their turn, of international competitiveness loss in the field of high technology, require a re-launch of scintific matters, in particular mathemetics. In this context, the project Il Giardino di Archimede was created to develop innovative methodologies an ricreational didattic tools to stimulate the student's interest and improve their performance in mathematics. The present project, named PITagorà, aimed to transfer the Il Giardino di Archimede model and dome tools, elaborated and tested in it, within a same but geographically different sector. Among the main objectives achieved there was the goal to train VET professionals in the use of innovative and attractive math teaching practices capable to offer to all students, in particular to the social and cultural weak ones, learning opportunities. The consortium permitted the optimal development of the project, because it was composed of, frst of all, four VET Vocational Training centre, PRAGMA Grouop Srl, Consorzio Nazionale PRO.GE.A. Formazione, Econometrica Ltd and Credij (linked to the French Ministry of Education - GIP Rectorat Paris - GRETA Network) and of a Universities consortium, Il Giardino di Archimede, that daily perform actions for the development skills and competences of VETprofessionals. Il Giardino di Archimede has had a critical role in the model transfer, in the training action of VET professionlas and in the supervision of its experimentation in three school in Basilicata. These Partners, with their results, had contributed, indirectly, to give a value to the methodology and the tools transferred. The tangible outcomes have been: an EUROPEAN KIT FOR TEACHING MATHEMATICS WITH PLAYFUL APPROACH, into English, Greek and French too; the results of the experimentation in Basilicata; publications, seminars and dedicated web site for the dissemination of results. As intangible outcomes, PITagorà, has developed in the VET professionals the awareness on importance and utility of the innovatove and attractive math teaching practices and, consequently, in the students, the awareness of the importance of the math as a determining subject for the individual delepoment and for an easier admittance in the working field. PITagorà has developed a strong impact on the European VET system, improving the learning quality and confirming the recreational didattic methodology at European level.
The project PIT.AGORA' aimed to transfer an innovative methodology for teaching and learning of mathematics, developed and tested by Consorzio Il Giardino di Archimede (Consortium of Universities of excellence such as the Scuola Normale of Pisa, the University of Pisa, University of Florence, University of Siena, the Italian Mathematical Union) based in Florence.
The project included the following phases of activity:
W.P.1 - Coordination and Process Management
Leader package: PRAGMA group s.r.l.
Ensure the correct and proper functioning of the project in the organization (coordination, logistics, manufacturing and documentary material) and administrative (reasonableness of costs and implementation of the regulations and parameters comply with industry regulations) to achieve the project objectives and the success of the the project.
As part of this phase 1st Transnational Meeting was carried out at the headquarters of the Consortium Il Giardino di Archimede, aimed to share the system design (path, working methods, time, cost, etc..) with European partners.
Start / End: October 2010/September 2012
W.P.2 - Monitoring and Evaluation
Package Leader: Consorzio Nazionale PRO.GE.A. Formazione
- Monitoring and verify the compliance of activities of the intervention strategy design. This phase was designed to take preemptive actions to counter and resolve differences on critical project objectives through the application of a model of monitoring and self-evaluation as a tool to support the management of operations, verification in progress and the final evaluation.
- Evaluation of the effects / results of the Experimentation, both on teachers (direct beneficiaries) and students (indirect beneficiaries)
Start / End: October 2010/September 2012.
W.P.3 - Adaptation
Package Leader: Il Giardino di Archimede
- Comparative analysis on the School systems of the 3 Countries involved (Italia, France and Greek). Research on the three school systems have been designed to check the specificity and implement a customization and "adaptation" of the method - product transfer consistent with the requirements of the systems and partners involved in the project.
- Developed of a FEASIBILITY STUDY OF THE TRANSFER OF INNOVATIVE PRODUCT, taking into account the following parameters:
- Age of the children on which to perform the testing
- Skills of childrens and trainers
- Specificity of the geographical contexts involved in the transfer process
- Methodologies that were more suitable in the communication and evaluation of the proponent
Following the analysis of the specific characteristics of the beneficiaries of the transferring, the most suitable laboratories to be adapted and transferred in the geographical context were:
- Numbers and Calculations with the ancient Sumerians
- Numbers and Counting with the Hieroglyphs of the Ancient Egyptians
- Pythagorean Theorem in game form
- Rods for Multiplications and Divisions
They were assigned to the shools in this way:
- Elementary School (Primary School): Numbers and Calculations with the ancient Sumerians; Numbers and Counting with the Hieroglyphs of the Ancient Egyptians
- Middle School (Secondary School_lower education): Rods for Multiplications and Divisions; Numbers and Counting with the Hieroglyphs of the Ancient Egyptians
- Secondary School (Secondary School_higher) education: Rods for Multiplications and Divisions; Pythagorean Theorem in game form
Start / End: February 2011/June 2011
W.P.4 - Experimentation's Laboratory (Training Trainers)
Package Leader: Il Giardino di Archimede
- Developed of a "Trainers Training Kit" including the User Guide and application tools for each Laboratory of Mathematics, suitable to facilitate self-learning phase before the seminar and subsequent searches in the experimental phase;
- Activities of "TRAINING - INFORMATION" aimed to teachers / researchers identified by the individual partners involved in experimentation, to provide knowledge and skills appropriate to facilitate the application of the innovative methodology object of the transfer process.
The training program was structured as Course held by experts and in headquarters of the Il Giardino di Archimede. The course was preceded by a preparatory phase prior in which teachers, using the materials of "Trainers Training Kit", have carried out an initial self-training. The course was planned to complete the training of the teachers involved in the Experimentation, both the theoretical aspects and the use of instruments.
The training was divided into three sessions. Sessions were been established taking into account the different needs of beneficiaries. In particular:
- laboratories chosen for experimentation
- the language of the training course
- requirements associated with the school calendar and commitments of teachers
Each session was structured according to the program by providing the following main stages:
Welcome, compilation and distribution of forms
Historical introduction on laboratories
Distribution and compilation of forms and Conclusions
Courses Evaluation by the participants:
Answers to the questionnaires showed a high level of satisfaction of the participants with respect to the proposed contents, methods of communication used and the structure of the course.
Start / End: April 2011/September 2011
W.P.5 - Transferring Product Experimentation
Leather Package: Il Giardino di Archimede
METHODOLOGY EXPERIMENTATION of teaching mathematics developed by the Consortium Il Giardino di Archimede, in the different school contexts of the partners involved in this activity. This phase has expected:
Experimentation aimed to trainers / teachers involved in the project, made of self-study (with technical assistance from the Il Giardino di Archimede), in a perspective of lifelong learning and skills development for the teaching of Mathematics
Experimentation aimed to students
Evaluation of the relationship Teaching/ Learning, in relation to the application of the product transfer
Evaluation of Teachers/ Trainers skills
Evaluation of Student Learning Processes
Start / End: October 2011/June 2012
W.P.6 - Optimization and Innovative Experimentation Transfer
Package Leader: Il Giardino di Archimede
Verify the achievement of the expected results and take decisions and actions subsequent to the transfer of the product / model in action system partners;
This phase has expected:
Optimization of the results and the transfer of the product / model
Development of the European kit for teaching mathematics (product transfer with changes and integrations made by European partners)
The Enhanced Partnership through the strengthening and expansion of the network (other public and private entities interested in the subject of project)
Start / End: April 2012/September 2012.
W.P.7 - Dissemination of Results
Package Leader: Consorzio Nazionale PRO.GE.A. Formazione
Promoting the dissemination of the project results in order to introduce the project and its products to the largest number of end-users, stakeholders and actors in the system, so that they could be used in systems and practices in vocational training centre. Dissemination activities have expected:
Promotional items for the launch of the project on the newspapers at the regional and national level
Production of project brochure
Production of dissemination materials downloaded from the website, www.pitagoratoi.eu
Implementation of a Final Seminar, held on the 25.09.2012 in Matera at the school library room - Istituto comprensivo P. Minozzi.
Start / End: January 2012/September 2012.
Partners involved on the Project were:
- PRAGMA Group s.r.l. - Matera (Italy)
Contact: Dr. Rosalba Dragone
- Consorzio Il Giardino di Archimede - Florence (Italy)
Contact: Prof. Dr. Enrico Giusti
- Credij (Regional Centre for local development, training and insertion of young people) - Paris (France)
Contact: Dr. Maria Edwige Rudowski
- Econometrica Ltd - Athens (Greece)
Contact: Dr. Maria Manda
- Consorzio Nazionale PRO.GE.A. Formazione - Potenza (Italy)
Contact: Mr. Domenico Sangiacomo
- Direzione Didattica Statale "P.G. Minozzi" I Circolo - Matera (Italy)
Contact: Teacher Patrizia Di Franco
- Scuola Media "N. Festa"- Matera (Italy)
Contact: Teacher Gerardo Desiante
- Istituto Tecnico Industriale Statale "A. Einstein"- Potenza (Italy)
Contact: Teacher Rocco Colonna.
From 1 September 2012, as a result of recent and new measures in the regional school system (Basilicata), it became effective the merger of two educational institutes (Direzione Didattica Statale "P.G.Minozzi" I Circolo and SCUOLA MEDIA N. FESTA), consolidation that has created a new single entity known as "Istituto Comprensivo Padre Minozzi". This new entity has included resources and activities of these institutions which have ceased to operate.
This has resulted in a change in the partnership, as the partners Direzione Didattica Statale "P.G.Minozzi" I Circolo and SCUOLA MEDIA N. FESTA from 1 September 2012 are no longer active and were replaced by a new subject/ partner who is the Istituto Comprensivo Padre Minozzi. Following a request for an amendment, the consortium included partners n. 8 in the Report form.pdf - Istituto Comprensivo Padre Minozzi, which didn't receive budget as tasks assigned to partner Direzione Didattica Statale "P.G.Minozzi" I Circolo and SCUOLA MEDIA N. FESTA in the original project were completed by 30 August 2012.
In closing activities and preparation of the Final Report, the transfer of funds relating to the budget assigned to partners involved in the merger, therefore, were assigned to the new partner.
The project lasted 24 months.
Utilization and distribution of results
Open and distance learning
Access for disadvantaged
Activities of Extraterritorial Organisations and Bodies
Professional, Scientific and Technical Activities
Arts, Entertainment and Recreation
Public Administration and Defence; Compulsory Social Security
procedure for the analysis and prognosis of the vocational training requirement
open and distance learning
program or curricula
material for open learning
Products implemented are:
- Project Web Site: This is the website of the Project, www.pitagoratoi.eu, where you can view the presentation of the project, activities and planned work packages, documents and products, plan and dissemination activities and exploitation of the project.
The Product has contributed and contributes first of all to promote the communication of the project and the results achieved, as well as to facilitate contacts with a wide audience potential user and the fruition of the implemented products, including the European kit for teaching mathematics with playful approach-teaching, as prominent final product. Has also contributed to the sharing of documents between the partners and the publication and systematic updating of the work program through the preparation of a database.
- Database: This is an electronic archive of documents, communications and products prepared for the Project's management. Database has been divided into two macro-areas DOCUMENTS available to all users and RESTRICTED AREA-> CONFIDENTIAL DOCUMENTS, accessible only by the project partners.
The purpose of the Product has been sharing documents and immediate availability of equipment to carry out the tasks and activities by each partner. In this sense, it has contributed to the success of the project.
- Survey Questionnaires: The product, made in Italian and English, consists of n.3 types of survey questionnaires for mapping of educational systems, professional needs in the three Countries involved on the Project (Italy, France, Greek). The survey questionnaires were addressed to three different target:
- Teachers / Trainers;
- Social parts,
and contain items that have facilitated the recognition of the role and the importance of mathematics in school contexts, entrepreneurial and social.
This product has contributed to the preparation of the report on the educational systems of the three Countries involved, as instruments of data gathering and informations. Purpose of the administration of the questionnaires was measuring the level of correspondence between the education system school and the real professional needs in the Countries involved. Therefore it has contributed to the achievement of the outcome of the report on education systems, which in turn has formed the information basis for the process of transferring and adaptation of the innovative product.
- National School systems Report: The product in question is a Research Report on Education systems of the three Countries involved (France, Italy and Greece);it is a comparative research on education systems of the three Countries and in particular on educational courses, educational programs and internal organization. This mapping of educational systems was crucial to define the customization and adaptation of innovative methodology and tools to the different geographical contexts.
The Product has been functional for the verifying of the conditions and characteristics of the cultural and geographic context of the partners who were involved in the transfer process. Therefore it has contributed to the preparation of the Feasibility Study of the transfer process, helping to achieve the project objectives.
- Feasibility Study for the transfer of the methodological model: The product consists of a feasibility study of the innovative product transfer process, outlining the strategies and methods of carrying out this process. Analysis of the data provided by the Report on Education Systems, in fact cultural differences between the countries involved and between the same project partners have emerged, differences that have required different product transfer strategies. Then, since it was the transferring a teaching methodology consists of several Mathematics Laboratories, it was necessary to analyze the technical specifications of these laboratories with the characteristics of each partner to which the product transfer was directed. The Feasibility Study has therefore developed a hipothesis of transfer of products with the definition of "which products to who."
This hipothesis has taken into account:
- The specific characteristics of each Mathematics Laboratory (Product Transfer)
- The specificity of target and transfer context
- The aims of the project (and in particular facilitate the dissemination of products)
- The possible ways of execution of trainers training (defined and implemented in a later phase of the project).
Based on these considerations, each partner has been assigned Laboratory of Mathematics adapted to their characteristics and in particular to those of the direct beneficiaries (teachers and trainers) and indirect ones (students).
The product, having defined the methods and contents of the product transfer process, has contributed to the optimization of this process. Partners involved was given in fact a guide for the experimental program development and guidelines for management activities.
In this sense, the product has been a strategic document fundamental to the achievement of project objectives.
- Trainers Training Kit: Trainers Training Kit is the product of transfer of an innovative way to teach Maths based on a ludic-educational and Laboratory approach (with the help of Learning of Mathematics Laboratories appropriately assigned to the Partners involved), developed and tested by the Consortium "Il Giardino di Archimede".
Each Laboratory of Mathematics, with manuals and tools, has specific characteristics with differences regarding content, methodologies, tools and subdivision of the subjects according to levels of difficulty appropriate for ages). Direct beneficiaries of the transfer were Teachers and Trainers involved in testing; indirect beneficiaries, instead, were pupils of the schools and students who participated in the testing.
As defined in the Feasibility Study of the product transfer process, Kit has included some Mathematics Trainers Training Workshops, selected and adapted to the characteristics of the partners involved. The selection of the Laboratory of Mathematics also took into account the possibility of exchange of experience between the partners involved, so hence the strategic decision to define and assign n.4 laboratories, of which n.2 same for partners Elementary School P. Minozzi and Econometrica, and n.2 same for partners ITIS Einstein - De Lorenzo, Middle School N. Festa and Credij.
Trainers Training Kit were prepared in:
- Italian Language;
- French language;
- Greek language.
The product has been in fact a training document and available for Teachers and Trainers, as support of the actions and activities carried out during the Experimentation phases and in particular for the implementation of the new methodology.
Trainers Training Kit has therefore contributed to the achievement of project objectives, having provided the scientific information needed for the performance of own professional role.
Compared to the initial project plan, Partners decided to postpone the implementation of the English language version of the European Trainers Training Kit in the WP6; conducting trainers training activities and experimentation they preferred to use the Italian language version and own languagge version, namely French and Greek. In the context of W.P. 6 - Transfer Optimization in fact, the innovative European kit for teaching mathematics in game form was implemented, enhanced and/ or supplemented by additions or modifications to the Transfer Product to which Partners were able to report during the testing of the Product. Therefore, it has been appropriate to pospone the implementation of the English version until the transfer product was tested and considered final.
- Trainers Training Seminars: Trainers Training Seminars were intended for Teachers and Trainers involved on the project, organized at the headquarters of Il Giardino di Archimede - Florence, that has the know-how and scientific equipment and materials necessary for such training. Product provided:
- The material for the preparation of seminars;
- Trainers Training program;
- Trainers Evaluation.
The product has provided to the teachers and trainers involved in the process of experimentation, knowledge and skills for the application of the new methodology of teaching mathematics with playful approach (Product Transfer). This activity was preliminary to the Experimentation's phase of the Product Transfer - W.P.5.
The product has contributed to the achievement of the project objectives, providing to the teachers and trainers involved new mathematical knowledge and the ability to use the new teaching methods, raising the level of professional quality.
- Experimetal Lab Report: The product is a report on the activities related to the preparation and implementation of Trainers Training Seminars.
As such, the product contributed to provide information and qualitative and quantitative data on training activities, being a useful document for programming the experimentation's phase and preparation of supporting documents.
- Online Support: Product is a report of the activities of technical and scientific experimentation conducted by Il Giardino di Archimede and addressed to the teachers/trainers involved in the Experimentation activities.
In the Experimentation phase the role of TIl Giardino di Archimede was to assist, guide and coordinate the teachers activities.
- Preparation and submission to teachers of guidelines and timelines abuot activities they carried out,
- Online support through e-mail exchanges for advices, explanations, updates, resolution of questions and problems,
- Telephone support in addition to the e-mail exchanges,
- Use of an Internet platform so that each participant had the opportunity to check the progress of the Experimentation,
- Access to the materials prepared by Il Giardino di Archimede,
- Uploading their materials,
- Consulting the materials of their colleagues.
Purpose of the product was:
- Facilitate the application of the methodology, following both the program planned and the monitoring of results;
- Facilitate the exchange of information between the participating teachers to receive help and advice.
The product therefore contributed to the success of the experimentation and its planned goals.
- Reports for analysis and evaluation of the Experimentation: Product is a report on the Experimentation phase conducted, under the scientific direction of Il Giardino di Archimede, by teachers/ trainers involved on the project. The aim of this document was to detect and verify data and information on activities carried out and in particular on the results of the application of the innovative methodology of mathematics developed by Il Giardino di Archimede in different geographical and cultural contexts which partners involved operated in. This report provides information on the impact of the new methodology both on the direct beneficiaries (teachers / trainers) and on the students too, detecting and evaluating possible changes and / or improvements the relationship Teaching / Learning.
The product, therefore, together with the two following reports on the skills acquired by the teachers and the learning achievements of students, has been a strategic document to evaluate the achievement of the project objectives and to implement the Dissemination Plan and dissemination of results. The report was prepared on the basis of data processed by Il Giardino di Archimede, who developed special questionnaires and monitoring sheets given to the direct and indirect beneficiaries of the partners involved (P. Minozzi Elementary School, Middle School N. Festa, Itis Einstein - De Lorenzo, Credij and Econometrica).
The product has therefore contributed both to provide self-evaluation tools by teachers / trainers and by students and to present the test results on the same, providing reliable information on the achievement of project objectives. In addition, the product has helped to facilitate networking between the participants and the exchange of information provided by each.
- Evaluation Report on the new skills of teachers: The product is a report on the results of testing with particular reference to the objectives achieved by the direct beneficiaries of the project, the teachers and trainers who have been involved in the Experimentation. This report is part of a more general Reports for analysis and evaluation of the Experimentation that should be consulted for the necessary conditions.
This report has provided data and information on new mathematical skills acquired by teachers and trainers and the ability to use new methods, including both national and European level.
The report was prepared by Il Giardino di Archimede who developed special questionnaires and monitoring sheets given to the direct beneficiaries of the partners involved (P. Minozzi Elementary School, Middle School N. Festa, Itis Einstein - De Lorenzo, Credij and Econometrica).
Purpose of the evaluation activities recorded in this report was to analyze all the stages in which teachers were able to apply, in their professional roles, new knowledge and teaching tools acquired. The product, therefore, helped to provide reliable data and information on the achievement of project objectives.
- Evaluation Report on Students Learning: The product is a report on the results of experimentation with particular regard to the achievment of the project objectives by indirect beneficiaries of the project (students who have participated in the mathematics workshops, product transfer, assigned to each partner involved).
This report has provided data and information on the level of appreciation of the new methodology, the level of learning and on any changes in their approach to the study of mathematics, including both national and European level.
The report was prepared by Il Giardino di Archimede who developed special questionnaires and monitoring sheets given to indirect partners involved (P. Minozzi Elementary School, Middle School N. Festa, Itis Einstein - De Lorenzo, Credij and Econometrica).
The product made it possible to verify objectives by students who participated in the laboratory testing phase of the project.
Purpose of the evaluation activities recorded in this report was in fact to analyze the levels of learning achieved and the attitudes adopted by the students in the course of the Experimentation. The product, therefore, helped to provide reliable data and information on the achievement of project objectives.
- European kit for teaching mathematics with playful approach: This product is a kit that includes the Product Transfer, namely Trainers Training Kit already experienced in W.P.5 and related Mathematics Workshops complete with Manuals and Tools.
The European Kit has been the final product of the project and it has been the result that outcomes from applications and experimentations performed by the different partners.
At the end of the project, in fact, the product of transfer was enhanced in terms of usability towards end user (the direct and indirect), becoming an even more available tool for future transfers in different contexts (schools, colleges, VET Vocational Training centre, etc..) also at European level.
All the mathematics laboratories object of transferring were translated into English to allow the widest possible dissemination of the kit in a European context.
kit includes European manuals and tools necessary for the application of the methodology of teaching mathematics based on 'playful approach and the concept of "learning by playing."
Therefore, the EUROPEAN KIT FOR TEACHING MATHEMATICS WITH PLAYFUL APPROACH, in the English version, has represented and represents a usable product, spendable and transferable to a wide audience of potential users and stakeholders in Europe.
This product has helped and thus contributes to the achievement of the objectives of dissemination and dissemination of project results at European level, also helping to promote new transfer processes of the product.