iMath - An Intelligent System to Learn Mathematics

iMath project motivation was deeply connected to the experience and follow up activities of MathE project during which some of the iMath partner organisations developed an e-learning platform dedicated to the improvement teaching and learning of Math subjects at higher education level. The original MathE tool (https://mathe.ipb.pt) offers a variety of multiple-choice questions to help students understand their level of knowledge of different Math concepts and guiding them in improving their skills and reinforce their confidence through practice and learning materials. The MathE platform randomly provided students with questions only taking into account the chosen math topic. With the involvement and testing of the platform (carried out in 2020 involving more than 50 lecturers and 650 students), the need for a more powerful functionality able to select the questions and materials more appropriately, emerged. iMath motivation is therefore to answer to students and lecturers needs by developing a new intelligent learning system that using artificial intelligence techniques at its core, offers the best possible personalized learning pathways, defined according to personal profiles and tailored to the related characteristics.

The general aim of the iMath project was to make full use of advanced technology and data analysis systems and solutions to fully exploit new and alternative approaches of teaching Mathematics able to adapt to the evolving expectations of learners, offering inexpensive, personalized educational environments and support higher education students through their learning path. Specific objectives were: SO 1: Fully explore the state of art in terms of academic publications and exemplary practices of the use of artificial intelligence and algorithm based tools in education for the identification of the student needs and behaviors SO 2: Pursue the development of an intelligent system to support the learning path of student through the planning, drafting and testing a fully operative AI-based algorithm able to map each student’s individual learning paths, their strengths and weaknesses, identify subjects that are more challenging and those that are easily assimilated, to then create personalized learning paths and environments SO 3: Provide academic Math lecturers and students with ready to use tools, guidance and tips on how to use visual and AI based approaches to teach and learn Math topics

The main concrete outputs produced are, of course, the three Results: Project Result 1 - Literature review about optimization, learning methods and models The first main Result of the iMath project fully explores all issues and provides best features, examples and best practices of algorithms with optimization strategies to be used in learning contexts as well as scientific material that can support researchers/students in their exploration on optimization and machine learning topics Related contents available and freely usable on the iMath Portal are: - A Library of more than 76 relevant scientific and academic publications (https://imath.pixel-online.org/gp_Library.php) including books, web articles and scientific papers addressing the themes of Benchmarks, Data Analytics, Machine Learning and Optimization. - A set of 45 selected algorithms (https://imath.pixel-online.org/gp_Algorithms.php) reviewed, commented, and related to machine learning and optimization. - A set of 34 benchmarks related to learning and optimization algorithms are available for free use (https://imath.pixel-online.org/gp_Benchmarks.php). Benchmark sets have the purpose to compare the performance of different algorithms. - A set of 18 selected and reviewed learning indicators (https://imath.pixel-online.org/gp_LearningIndicators.php) to be used by lecturers to evaluate their student’s progress. Project Result 2 - Developing the method OptLearn and its incorporation into a case study platform The OptLearn is a hybrid algorithm that combines machine techniques and optimization procedures to identify the students learning path. The enhanced system is now integrated in the MathE platform by dynamically adapting the learning experience to meet each student's unique needs and preferences. The OptLearn algorithm considers the collective and individual performance of the students, and also the lecturers’ feedback to categorize the questions into different difficult levels. Besides, it uses the student profile information combined with the student’s past performance to select the most appropriate question for the student in each moment. The algorithm allows for a more tailored approach to student learning, ensuring each student receives questions appropriate to their skill level. Several videos explain how the platform supports the personalized learning path for a given student (see: https://www.youtube.com/watch?v=X9GgQx-mxXg&t=1s). The MathE platform has been also enriched with more than 170 video-based learning materials added to the existing ones and students can count on more than 8 times more learning sources than previously available and can count now on more than 1400 tested different math questions questions, covering 26 math-related topics and subtopics. The implemented algorithm is also freely available for use on other e-learning platforms. Project Result 3 - Online Resources: The Result provides academic Math lecturers and students with ready-to-use tools, guidance and tips on how to use visual and AI-based approaches to teach and learn Math topics. Contents are fully available and freely usable on the dedicated section of the iMath Portal that contains: - At https://imath.pixel-online.org/gp_Applets.php a collection of 7 Applets, that is, small programs embedded in web pages that can run when the pages are viewed and can be used for educational purposes, enabling hands-on practice for those mathematical contents whose teaching can rely strongly on visualization - At https://imath.pixel-online.org/gp_Tips.php, a wide range of tips (42), suggestions and case scenarios on how to use artificial intelligence in an educational context. The tips are designed to offer guidance on how to integrate artificial intelligence into educational settings. - At https://imath.pixel-online.org/gp_Algorithms.php 6 new algorithms developed by the project partners are available to be applied in the educational field for teaching Math. Intangible but fundamental achievements of the iMath project are also: - The creation of a wide community of 1700 students and more than 160 lecturers that benefited from the use of the iMath results for strengthening Math teaching and learning and are interested in fully exploring Math teaching and learning with advanced technologies and artificial intelligence based approaches. A community that actively involve users in the further follow up and sustainability of the project activities and results and that will allow further evolution of the algorithm. - Reaching the conditions of scaling up and mainstreaming project achievements and results into the universities part of the consortium, in higher education institutions that joined as associated partners and in the higher educational system at large by the involvement of decision and policy makers in a common reflection on the innovation and personalization of teaching offer through new technologies