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Adaptive teaching is defined as applying different teaching strategies to different groups of students so that the natural diversity prevalent in the classroom does not prevent each student from achieving success. Some of the strategies for adaptive teaching are formative assessment, feedback, and self-regulated learning. For the application of these strategies, technology plays a fundamental role. Our research group has developed and tested a model for automatic formative assessment and interactive feedback for STEM using an Automatic Assessment System to allow adaptive teaching. This article presents the design, the implementation, and the analysis of adaptive teaching activities carried out by secondary school teachers of STEM disciplines during a training course. Teachers designed the transformation of questions created for standardized assessment into formative assessment questions, reflecting on how to adapt the requests to students’ different needs and how to create guided learning paths. In this paper, all the steps of the training activity carried out will be analyzed using some representative examples: the design of the questions with an analysis of the adaptive teaching strategies adopted; the reflections of the teachers at the end of the course; carrying out activities with students and analyzing their responses; the reflections of the teachers at the end of the activity.

The health emergency due to COVID-19 has highlighted the need of new and flexible digital methodologies for learning and teaching Mathematics, which can support the individual student’s needs and help shape education. In this paper, we propose to use Automatic Formative Assessment (AFA) activities designed according to an innovative model, framed on the theories of formative assessment and feedback. The model includes: availability of the activities and multiple attempts; algorithmic questions; open mathematical answers; contextualized tasks; immediate and interactive feedback. We analyzed an experience using AFA in a blended module in Mathematics for 96 first-year students in Biotechnology. We collected data from the platform on grades and attempts of AFA activities and cross-checked them with the final exam grades. The results show that the feedback gained from AFA helped students improve their performance and supported them in the exam preparation. In light of these results, we can conclude that similar activities can be an effective solution to support students’ self-study during and after the pandemic.

Problem solving and computational thinking are the key competences that all individuals need for professional fulfillment, personal development, active citizenship, social inclusion and employment. In mathematics, during contextualized problem solving using Maple, the differences between these two skills become thinner. A very important feature of Maple for problem solving is the programming of animated graphs: an animation obtained by generalizing a static graph, choosing the parameter to be varied and its interval of variation. The first objective of this research is to analyze the computational thinking processes behind the creation of animated graphs for the resolution of a contextualized problem. To this end, we selected and analyzed some resolutions of problems carried out by fourth-grade students of upper secondary schools in Italy (grade 12). The paper shows some examples in which different processes of computational thinking have emerged, which reflect resolutive strategies and different generalization processes. From the analysis it emerged that all the processes underlying the mental strategies of the computational thought useful for solving problems are activated in the creation of animated graphs. In the second part of the article we discuss examples of animations created during training activities with secondary school teachers, and how animations can support the learning of scientific concepts. It is very important to train the teachers in this regard, both to understand the processes that the students would activate during the creation of animated graphics and to enrich the theoretical or practical explanations with animated representations.

In the transition from lower to upper secondary education, Italian students are expected to have achieved a level of competence which allows them to use knowledge and abilities to model and to understand scientific and technical disciplines. National standardized tests show that especially students who attend technical high schools often have gaps or misunderstandings in their basic knowledge, which may hinder them in learning scientific technical disciplines, which are at the core of their curriculum. In this paper we start from items designed for summative assessment which highlight the main difficulties that students face with Mathematics at this stage, and discuss how it is possible to adapt them to automatic formative assessment through a process of expansion and digitalization, with the aim of helping students fill the gaps and develop mathematical competences. The activities are part of an online course, called “MATE-BOOSTER”, conceived to strengthen mathematical skills of students attending the first year of a technical upper secondary school. In this paper the process of design of MATE-BOOSTER, rooted on constructivist assumptions, is outlined; the design of tasks for automatic formative assessment is discussed in details, and some examples of online activities are analyzed in light of a theoretical framework.

In an Italian and European context, one of the fundamental skills in Mathematics is the ability to solve problems in everyday situations, often linked to everyday life. For this reason, the problem posing and solving methodology plays a fundamental role in the process of teaching and learning Mathematics. This paper presents the results of the immersive experience "Mathematical Exploration with Problem Posing and Solving", included in the teacher training activities proposed by the national PP&S - Problem Posing & Solving - Project of the Italian Ministry of Education, which aims at enhancing the teaching and learning of Mathematics by using new methodologies and technologies. In particular, the focus will be on the work and considerations of the 50 teachers who took part in the project, from both primary and secondary school. They were guided through the individual step-by-step creation of a contextualized problem, following a process guided through stimulus-based questions. This immersive experience brought about the production of valid problems and was full of very stimulating teachers' considerations on the various phases of the problem posing and solving.

This paper presents a model for school remedial, focusing on improving the digital materials sharing process for the diversification of tutoring strategies. The model involves the characterization of materials for automatic assessment shared within a community of tutors. The characterization expects materials to be linked with natural language descriptors explicating their intended instructional objectives. The possibility of implementing a recommendation system on the basis of natural language processing techniques is discussed taking in consideration an analysis of the application of the model within a local-scale project. Clustering techniques searching for materials that have the same educational purposes but involve the activation of different cognitive processes are proposed, in order to continuously extend the database of shared materials in favour of the effectiveness of ongoing tutoring actions. The results collected from questionnaires submitted to students, tutors, and teachers involved in the project are shown, and clustering data are discussed highlighting the feasibility of the application of the model.

Supporting students in the transition from secondary school to university is an important action to be taken in order to increase the number of people with tertiary education degrees; it has positive consequences on the citizens’ working perspective and on the national economic growth. To this purpose, in the academic year 2014/2015 the University of Turin started the Project Orient@mente, a platform of self-paced open online courses aimed to guide students in the choice of a scientific university program. This paper focuses on the design of the Realignment Course in Mathematics, provided by the platform and aimed at the self-paced review and integration of knowledge that students are required to acquire during secondary school. Materials are created and structured according to the User Experience Design for Learning, with the aim of providing a valuable learning experience to students. Contents are delivered through an accessible learning management system integrated with an advanced computing environment and an automatic assessment system. Data from the usage of the activities and from the results of the online tests are analyzed in order to validate the design choices and the coherent structure of the course.

This paper presents an ontological model for defining competency paths in STEM education, designed for the implementation of an adaptive system integrated in virtual communities. The model is applied for clustering materials for automatic assessment and the results are discussed.

This paper shows the model developed by the University of Turin to support students that must face the transition from the last year of secondary school to the first year of University. Integrations that are specifically designed for Learning Management Systems help sustain three effective actions conducted in synergy: increase students’ awareness in the choice of the future course of study, support them in taking the admission tests and the first-year exams, allow the autonomous administration of admission tests led by the University. The methodological strategies adopted are presented and discussed based on the analysis of the data of the years 2015 and 2016.

This paper shows a model of teacher training developed by the XXX of the ZZZ, aimed at introducing teachers to the use of innovative methodologies for learning Mathematics and for developing disciplinary and cross-cutting competences. The learning methodologies proposed are mainly based on Problem Posing and Problem Solving, the use of an Advanced Computing Environment, of a Virtual Learning Environment and of an Automated Assessment System. The training model, designed in blended modality, mainly relies on the creation of an online community of practice, where teachers, supported by tutors, collaborate in the creation of interactive learning materials for their classes. They acquire competences not only in the use of learning technologies, but also on sharing and collaborating in virtual environments; they learn how to develop self-tailored didactic methodologies. The key strengths of this model are highlighted and the results, achieved after the experimentation in several projects, are discussed, showing the effectiveness of the model.

[EN] The paper shows how problem solving competences can be developed by solving contextualized problems using an Advanced Computing Environment (ACE). An ACE is a computer system which enables its user to perform numeric and symbolic computations, graphical representations in two and three dimensions, insert embedded components and create interactive worksheet, all in the same user-friendly environment. An ACE allows students to approach a problematic situation in the way that most suits their thinking, to use different types of representations according to the chosen strategy and to display the whole reasoning together with verbal explanation in the same page: in other words, they can fulfill all the processes that problem solving involves. This paper analyzes a problem solving activity with an ACE proposed by the XXX of the ZZZ, and clarifies, also through examples, how the use of the ACE makes it possible to solve real and relevant problems, facilitates the comprehension of the situation and of the Mathematics laying behind and enhance critical thinking., The authors desire to thank the Fondazione CRT of Turin, in particular dott.ssa Daniela Tornielli for the support given for the Project Digital Mate Training and for her remarkable dedication and passion.

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.

Adaptive teaching consists in a teaching style aimed at overcoming inner differences among learners by providing them tailored ways to achieve outcomes according to their learning style, culture and needs. ICTs play an important role in supporting teachers with the adoption of adaptive strategies. Adaptive teaching acquires relevance in contexts of scholastic remediation and in reducing failures. The paper presents and discusses how adaptive teaching is used within "Scuola dei Compiti", a project proposed by the City of Turin (Italy) in collaboration with the University and the Polytechnic of Turin, aimed at reducing the drop-out rate and at enhancing scholastic success. University students help groups of 5-6 students aged 13-15 with their difficulties in the main subjects (Mathematics, Italian Language, Foreign Languages). Part of the Mathematics courses adopt a set of innovative computer based methodologies developed by the Department of Mathematics of the University of Turin, including a virtual learning environment integrated with an advanced computing environment, an automatic assessment system and a web-conference tool, which supports adaptive teaching. The project has involved over 7500 students in the last 5 years, the results achieved, discussed in the paper, show the effectiveness of these methodologies with respect to traditional teaching methods.