Abstract-The Project PP&S, Problem Posing & Solving, is part of a set of initiatives promoted by the General Directorate of the Italian Ministry of Education, Research and University, aimed to support the many innovations in the High School. Its main goal is to enhance teaching and learning Mathematics and Informatics using new methodologies and technologies, like an elearning platform integrated with an Advanced Computing Environment and with a web conference system. This integrated environment makes available to teachers and students a powerful set of features for collaborative learning, e-tutoring and eassessment.

In modern societies, life itself is a problem solving. OCSE-PISA defined the problem-solving competence as the capacity to engage in cognitive processing to understand and solve problem situations where a method of solution is not immediately obvious. Hence in teaching Mathematics, and in general scientific subjects, it becomes important to adopt new methods centred on student learning, which are able not only to deliver knowledge but also to enhance the competence in problem solving. It is essential to start from simulated real-life problem situations in order to explain new concepts, since it enables students to understand the application of Mathematics as well as to enhance their ability to regulate problem-solving processes. The University of Turin has adopted problem solving digital methodologies using a virtual learning environment integrated with an advanced computing environment, automatic assessment and a web conference system. This set of technologies promote interaction among students and help teachers guide and coach their students in creating, conjecturing, exploring, testing and verifying. In the Erasmus+ Project SMART – Science and Mathematics Advanced Research in good Teaching - the University of Turin shared these methodologies with other European partners (Strategic Partnership Key action). The aim of this exchange of best practices is to obtain Mathematics and Science teachers who are more involved in the methodology and consequently students who are better equipped to develop coherent mental representations of problem situations, more flexible in incorporating feedback and in reflecting. In the paper, examples of interactive material produced and tested in the Project are presented and the results of the experience are discussed.

Problem solving, i.e. the ability to model concrete situations in mathematical terms and to solve the problems connected to them, plays an important role in teaching and learning Mathematics to and by students at every level of education and is one of the basic skills for the training of citizens. By learning problem solving in Mathematics, students acquire ways of thinking, creativity, curiosity, collaborative skills and confidence in unfamiliar situations, from which they will benefit also outside the Mathematics classroom. The use of digital technologies helps in both representing and exploring mathematical tasks. Technologies also provide a range of tools and opportunities to structure and support learning environments in which students continually interact to build knowledge and solve problems. The national PP&S - Problem Posing & Solving - Project of the Italian Ministry of Education aims to enhance the teaching and learning of Mathematics and Informatics using new methodologies and technologies. One of the methodologies is problem solving through the use of an Advanced Computer Environment (ACE). An ACE is a system that allows one to perform numerical and symbolic calculation, make graphical representations in 2 and 3 dimensions and create mathematical simulations through interactive components. Moreover, it is able to support students in reasoning processes, in the formulation of exit strategies and in the generalization and re-adaptation of the solution in different contexts. The goal of this paper is to discuss the results of an immersive workshop, entitled "Mathematical Exploration with Problem Posing and Solving", involving 50 secondary school Maths teachers, who were invited to reflect on the role of an ACE in learning and teaching Mathematics through problem posing and solving. During the workshop were presented the problem solving methodology used in the PP&S project and an example of a contextualized problem solved with the use of an ACE. The results emerged from the analysis of the questionnaires (initial and final) compiled during the workshop and a study of the works delivered by the teachers, who were asked to design a problem, its resolution and generalization through the use of an ACE. They are useful to understand teachers' reflections on the methodologies proposed and on the impact of new technologies on teaching.

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