The Problem Posing an Solving Project: National Project on Mathematics Prof. Marina Marchisio University of Turin

What is it? It is the Strategic Italian Key Action to Enhance Teaching and Learning Mathematics and Informatics in the High School born in 2012 promoted by the General Directorate of the Ministry of Education, Research and University, aimed to contrast the critical situation of Italian school and to bring innovation in teaching to sustain the transition from "programs specified by the Ministry of Education” to “National Guidelines for High Schools, Technical Schools and Vocational Organizations”

Partners Italian Association for Automatic Computing (AICA) National Research Center (CNR) National Industrial Unions University of Turin Polytechnic of Turin High School Carlo Anti of Villafranca di Verona (National pole high school)

Principal Aims To build a culture of problem posing and solving (activity based on the formalization, quantification, simulation and analysis of problems of various complexity) To found education processes combining Logic, Mathematics and Computer Science To ensure growth of computer science-based training of teachers To adopt a significant amount of social network activity and virtual learning environment, sharing learning materials

History of PP&S : numbers September 2012: 100 schools, 150 teachers and students of the last 3 high school years September 2014: 800 active teachers, more the 400 schools and 12000 students, and it opened to all the 5 high school years

History of PP&S 2012-2013: attention focused on Mathematics, on how to use new technologies in order to build new teaching plans in Mathematics in the logic of problem posing and solving Faculty of Science of the University of Turin put its big experience in this field at service of the Project, in particular the asset based on Moodle integrated with an ACE and a web conference system

History of PP&S September and November 2012 brief training in presence in Verona Creation of a community on Moodle, and teachers began to practise a strong collaborative learning Careful and precious service of tutoring was activated through Moodle, addressed to the teachers February 2013: were born 150 communities of students 2013-2014: a community of Computer Science teachers was born on the platform

Mathematics and Computer Science strong interaction core of the scientific method applied in all the other subjects

PP&S and ICT PP&S Project is not a “technology project”, but a project which uses new technologies in order to develop problem solving skills and favour the employability

the address e-learning platform Moodle of the Project is Web site of PP&S the address e-learning platform Moodle of the Project is www.progettopps.it

Best Practice Communities best practice communities of teachers and students on the e-learning Moodle platform

Community of teachers Teachers in the community improve their skills through the collaborative learning They have access to synchronous (i.e. real time)and asynchronous (with discussion forums) tutorings which help them with the difficulties with the new methodologies and technologies Tutors are constantly present and well-prepared to answer any doubts and motivate teachers in their work There is also a helpdesk service provides immediate technical support at any time

Community of teachers They can share with their colleagues interactive files, question banks and assignments for self-assessment They can also practise the cross-coursing visiting other courses and analysing how resources and activities are proposed They can exchange experiences, new ideas and teaching strategies The collaborative learning allow to break the physical distance Feeling part of a community reduces the sense of failure

Tutoring in real time Web tutoring with Adobe Connect

Community of students Constituted by the classes participating to the project Teacher plays the role of tutor with his class Students have access to resources, as files and videos, made available by their teacher They can complete Moodle interactive activities, assignments and test for evaluation and self-evaluation They can solve problems with their class mates, discuss through forums Everyone gives his personal contribute in the logic of cooperative learning

Work of the Communities Working in platform allows to go beyond the rigidity of scholastic timetables and outside the class room Key factor capable to turn learning into a lifelong, lifewide and lifewise process

ACE for Problem Solving In the Problem Posing and Problem Solving methodology, didactic activities are heavily based on the use of an Advanced Computing Environment (ACE) Maple Suite (since University of Turin has successfully adopted it for years for the didactics)

ACE for Problem Solving Maple Suite consists of 4 software components Maple: the Mathematical Engine capable to do symbolic and numerical computations and geometric visualisation in 2D and 3D MapleNet: Maple worksheets can be made available on the web (implementation on Moodle, developed by University of Turin) and interactive files can be added in the Moodle courses maintaining their interactivity

ACE for Problem Solving Interactive component Maple worksheet

ACE for Problem Solving MapleSim: a virtual laboratory designed to the physical modelling and mathematical simulation. It is appreciated especially in technical institutes. A spring with MapleSim

ACE for E-assessment Maplesoft Testing and Assessment (Maple T.A.): web application studied for the e-assessment and particularly suitable for Mathematics; thanks to the Maple Engine behind, it is able to evaluate mathematical expressions; Mathematical answers are accepted in all the equivalent correct forms; integrated with Moodle

ACE for E-assessment Graded and commented answer with Maple T.A.

ACE for Labs and Lessons All schools joining the project have been provided with Maple licences, so that part of Maths lessons can be held in the computer lab and with the use of Maple Students, who are mainly digital natives, learn quickly how to work in an ACE The use of the computer makes Maths lessons stimulating and Mathematics more attractive It also facilitates the learning, which can be freed from heavy computations, leaving time for dedicating to the deep comprehension of topics and connections between different parts of the subject

Computational Thinking Problem Posing and Problem Solving methodology is strictly connected to Computational Thinking Definition given by G Wing: ”Computational thinking is the reasoning processes involved in formulating problems and their solutions so that the solutions are represented in a form that can be effectively carried out by an information-processing agent” Living Lab approach Pyton

E-training for teachers In 2014 the Italian Ministry of Education promoted a strong action of training directed to all Italian teachers other 1700 teachers started the training through blended courses some brief session of training in presence, in the geographical area of residence and then on line training (through the e-learning platform Moodle of the project)

E-training for teachers Statistics of the distribution of teachers in training in the Italian regions

E-training for teachers great effort and investment of time, but refunded by personal and professional development major satisfaction in learning and in the results of the students average age of Italian teachers 51 years old worry and anxiety of teachers, especially when they realise that they will have to confront with students, who are more familiar with new technologies.

E-training for teachers teachers learn how to use Moodle, Maple, Maple TA and MapleSim training courses are held by University professors or by expert teachers who have already been trained strong tutoring conducted by PhD students appropriately trained (aged 22-25 years old resulted winning) The training format model resulted to be really effective!