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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.

Because of the Covid-19 pandemic, the need to promote digital education has been felt even more, bringing the DELTA Research Group to reflect on how digital education could optimally facilitate the creation of an educating community able to promote and support educational success exclusively through distance learning. In order to answer, in this paper the experience of the 2019/2020 edition of “Scuola dei Compiti” (a recovery project for secondary schools of the poorest suburbs of Turin) is analysed in the perspective of the priority strategies illustrated in the Digital Education Action Plan for the period 2021-2027. Results will show that this was a forerunner experience perfectly in line with the principles and directions outlined in the document. Moreover, thanks to digital education, even a peculiar edition of the project such as this one has been a success: in fact, it has allowed students to improve from a cognitive and metacognitive point of view, even during a time that was very difficult for some families.

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. Gaps or misunderstandings in basic knowledge can hinder the effort of students who attend technical high schools, where the core subjects are based on Mathematics. This paper deals with the design of a project conceived to strengthen mathematical competences of students attending the first year of a technical upper secondary school through an online course named “MATE-BOOSTER”. The online activities on the web-based platform have been developed using didactic methodologies founded on constructivist assumptions, as problem posing and problem solving, collaborative learning, learning by doing, automatic and adaptive formative assessment. In this work the process of design of MATE-BOOSTER is shown, the methodologies chosen are discussed, and the online activities are analysed from a constructivist perspective.

Automatic Assessment Systems empowered by mathematical engines allow the development of online assignments for Mathematics, which goes beyond multiple-choice modality. Automatically assessed assignments, used with formative purposes, can support teaching and learning from several perspectives, such as conceptual and procedural understanding, metacognition, enactment of adaptive strategies, and teachers’ management of the class. This paper reports on an experimentation where automatic assessment has been used in a blended modality according to a model of formative assessment and interactive feedback to enhance learning. The experiment involved a total number of 546 students of 8th grade in the town of Turin (Italy). The use of the automatic assessment is shown and exemplified. Data from learning tests, questionnaire and platform usage are analyzed and used to show the effectiveness of the interactive materials for enhancing mathematical understanding and self-assessment skills. Moreover, a profile of the students who did not use the online opportunities, defined as “reluctant users”, is drawn and discussed.

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.

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.

Enhancing language skills is a duty for many institutions, schools and universities; Information and Communications Technology is nowadays supporting language teaching, heading also to the integration of foreigners. According to previous studies, the use of a Technology Enhanced Learning Environment can foster language competences through online tests. The goal of this paper is to show and discuss different typologies of automatically evaluated questions useful to learn languages and designed with an Automatic Assessment System, already successfully used for teaching STEM disciplines: Science, Technology, Engineering and Mathematics. This work has been carried out thanks to the collaboration between the Department of Mathematics and the Department of Foreign Languages. Five different typologies of questions are analysed: "Combining sentence elements" asks to combine given elements to form at least three correct and meaningful sentences; "Find the mistake" asks whether a sentence is grammatically correct and to explain why; "The Target puzzle" asks to join words together using precise links; "Scrambled text" asks the student the correct sequence of sentences in a scrambled text; "The Encrypted Crossword puzzle" is a crossword puzzle without definition clues. Linguists consider these question types effective to develop language competences and have already used them profitably in traditional teaching and language learning. To engage the learner and increase motivation, we will develop an implementation where the questions are self-evaluated, always available, with immediate and interactive feedback. These tools could be used in online language courses and in all those teaching activities that are carried out remotely by the student alone. All questions are outlined with the explanation of the grading code and a triplet of descriptors; they describe the Performance, Requirements and Objectives of each question and allow further studies on automatic detection of the relatedness between different language learning objects, in order to construct adaptive language tests.

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.

Formative assessment is a practice aimed to enhance teaching and learning and to develop self-regulation. Among the strategies for activating formative assessment, the provision of feedback is one of the most studied: good feedback helps close the gap between actual and desired performance and it promotes self-regulation. Automatic Assessment Systems can improve the practice of formative assessment, especially for the immediacy of feedback and the flexible solutions for questioning. In this context, the Department of Mathematics of the University of Turin has developed a model for automatic formative assessment using an automatic assessment system suitable for STEM disciplines. The key features of the model, grounded on the models from the literature, are: availability, algorithmic questions, open answers, immediate feedback, interactive feedback, and contextualization. These are detailed and discussed through evidence gained from three experimentations, involving the total number of 553 students. In particular, it emerges that the use of interactive feedback ensures that students process the information from the feedback and use it to improve their performance, thus solving the major problem raised in the literature that feedback are not useful when students do not read them.

Teachers need, in a lifelong learning dimension, occasions that provide them with opportunities to reflect on the activities done by themselves, to learn how to use the newest and most advanced technologies in their teaching, to exchange ideas, to confront themselves on the updated didactic methodologies. Only in this way can they enhance their professional competences and keep the motivation for their job high. Online contexts seem to be the most appropriate option for in-service teacher training because teachers work fulltime in school and, having personal and family responsibilities, it is difficult to find time for scheduled meetings. In this paper we will discuss online asynchronous collaboration within the virtual community of the Italian teachers of Mathematics of secondary schools who participate to the national Problem Posing and Solving (PP&S) Project of the Italian Ministry of Education. One of the main goals of PP&S, which started in 2012, is to enhance teaching and learning Mathematics and Informatics using new methodologies and technologies. The community lives on an e-learning Moodle platform integrated with several tools. Using a multi-method approach, we analyse the online forum discussions among teachers and tutors collected in the last three years; in particular, we explore which kind of activities they suggest to adopt in their real-world classes and the nature of the interactive processes activated in the community. This collaboration among teachers is a peer support and facilitates the process of transformation of practices and of construction of new professional knowledge and competences. Some implications for the training of teachers in pre-service are discussed.

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.

This paper will analyze an educational model for automated formative assessment developed at the Department of Mathematics of University of Turin for learning and teaching Mathematics and scientific disciplines. The model is provided through an automated grading system which, empowered by the engine of an advanced computing environment, allows the creation of algorithmic variables and open mathematical answers, recognized in all their equivalent forms. The adoption of automated formative assessment brings many advantages to learning. Easily available assignments, immediate feedback, adaptivity, the chance of learning from mistakes turn assessment into a fundamental enhancement in education; the intrinsic “rigidity” of technology can also have positive results on students’ path to knowledge. Automated assessment brings innovation into teaching: time saved in grading can be used to improve materials and activities, teachers easily get information about students’ learning, they need to change their approach and to attend trainings; sharing and collaboration among teachers are facilitated. Results obtained by the application of automated formative assessment in several class experiences are discussed and data about emerged satisfaction and criticisms are shown.

Assessment of learning and assessment for learning are at the core of the research on new teaching strategies involving the use of new technologies recently performed by University of Turin. The practice of automated assessment in Mathematics using the grading system Maple T.A. Has been introduced in many undergraduate scientific courses and, after the initial success, it has been diffused in high-schools through several projects aimed to improve Maths teaching and learning. The following paper is intended to describe the effectiveness of automated assessment as a learning tool, the strength of Maple T.A. For grading Mathematics and its integration in a learning content management system, and the results obtained at University and in high-schools.

This paper will analyze Orient@mente, a project developed by the University of Turin since the 2014/2015 academic year. The project's main purpose is to support students in their choice of the most appropriate university study course. An educational model for university guidance has been developed and applied in the creation of a self-paced MOOC. It is provided through a learning management system integrated with an advanced computing environment, an automated assessment system and a web conference system. In the platform students can find accessible activities such as interactive resources, information, orienting material about 15 scientific courses, automatically graded tests, review courses. As a result, the University of Turin has recorded enrollment growth in scientific courses. Students’ feedback has shown high appreciation of these innovative teaching methods and digital devices for learning Mathematics and other scientific subjects. In the next future, the University of Turin is interested in extending a similar service oriented towards other courses, especially courses which provide a highly selective admission test and requires a specific background of knowledge.