Search

This paper is focused on understanding if the use of interactive activities based on problem solving and automatic formative assessment in a blended learning environment can promote the development of engagement in Mathematics for students of grade 8. In this context, engagement is characterized as a multidimensional construct composed of an emotional component, a cognitive component and a behavioral one. The discussion is based on the results of a didactic experimentation conducted with 299 students of grade 8 who, during one entire school year, had access to an online platform rich in interactive learning materials used in blended modality. Through an initial and a final questionnaire, evolutions in their engagement levels were measured. We found that the initially most disengaged students and those coming from lowest social classes are those who mainly benefitted of the interactive activities in order to improve their engagement levels.

Studies show that gamification enhances the mathematics learning experience by increasing student engagement. Gamification can be successfully used in higher education contexts, primarily when it comes to distance learning. It can compensate for the lack of interaction and create a student-centered, customizable, and autonomy-promoting environment. The use of adaptive learning and interactive feedback can be seen as strategies to improve student access and success in open online courses. In particular, a mathematical modelling module for undergraduates developed inside the project start@unito uses such strategies. Moreover, it is taught entirely in English. The Mathematical Modelling course inside the Erasmus+ Project SMART represents another source for research. The purpose of the chapter is to discuss the possibility of combining adaptive learning with gamification techniques to enhance and facilitate the English-mediated learning process while teaching of mathematics, adding the linguistic and STEM education challenge.

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. 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.

Engagement is one of the most powerful driving forces that moves learners forward in a learning experience. The effects of engagement are related to satisfaction, learning results, and reduction of drop-out rates. School engagement can be positively influenced by problem solving and technology-enhanced learning activities. This paper discusses how online interactive activities can promote engagement in Mathematics at school level. After discussing a theoretical framework for defining and measuring engagement, the potentialities of activities with automatic formative assessment used in a blended environment are illustrated. The activities have been experimented with 299 students of grade 8 in Italy; their effects on student engagement are evaluated through questionnaires administered before and at the end of the project. The activities resulted particularly effective with regard to the increase of the engagement level of students who showed a low interest in Mathematics at the beginning of the project.

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.

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.

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.

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.