Developing personalized systems requires architectures that ensure adaptability, explainability, and ethical compliance while maintaining user engagement and trust. To assess whether a system meet these principles, this article puts to the test a novel framework, denominated CARAIX (Collaborative, Adaptive, and Responsible Artificial Intelligence -AI- assisted by eXplainability), designed to develop intelligent systems with a human-centered approach, to support real-time feedback and bias-aware AI decision-making. CARAIX is inspired by the principles of the Hybrid Intelligence (HI) paradigm and emphasizes the integration of explainable AI techniques in the development process to enhance user interaction and system reliability. This paper analyses, using a peer-validated rubric, howthe dimensions of the HI paradigm are integrated across four diverse and real-world learning scenarios, including intelligent tutoring systems, psychomotor skill acquisition, autonomous driving training, and acquiring occupational safety competences. CARAIX is designed for scalability and reuse, facilitating integration into various AI-driven educational domains. We aim to share its potential for sustainable and ethically sound AIenhanced multidisciplinary learning environments and for the assessment of whether a system complies with HI principles.

Providing effective and personalized support for students solving Math Word Problems (MWPs) in Algebra Intelligent Tutoring Systems (ITS) remains a significant challenge. Current help systems often rely on rule-based approaches limiting their adaptability to individual student needs and hindering proactive error detection. This work proposes a novel approach leveraging Hidden Markov Models (HMMs) to model user action sequences during MWP solving. We trained HMMs on a dataset of student interaction logs from an algebra ITS, where each action represents an observation and latent states represent the level of understanding. The HMM can effectively capture the dynamics of student's understanding level by probabilistically modelling the relationship between actions. The trained HMM models were evaluated on their ability to predict student actions and identify potential errors compared to the system's existing rule-based help and a Hidden Markov model. Results demonstrate that the HMM-based approach achieves significantly higher accuracy in predicting subsequent actions.

Knowledge Tracing (KT) enables adaptive learning systems to offer personalized learning experiences by modeling student learning behaviors. While recent studies in KT have shown promising results with attention-based models, the performance impact of the attention mechanism has not been sufficiently explored. To fill this gap, we aim to investigate the effects of different attention mechanisms in KT models. Through extensive experiments, we assess the strengths and limitations of five attention mechanisms across three benchmark datasets. Our results indicate that Talking-Heads Multi-Head attention outperforms the other four attention mechanisms, with the most significant improvements observed in terms of AUC, with an average performance increase exceeding 3

The potential benefits of introducing errors in problem solving has awakened interest in research into this understudied field. Here, we report the results of a quasi-experimental study with 85 third-grade students which examines whether erroneous examples might enhance students' problem-solving proficiency more effectively than worked ones. In the study, two conditions were established: a worked-example condition, where correct examples were presented before the students solved word problems, and an erroneous-example condition, where erroneous examples preceded word-problem solving. Our results demonstrate that post-test scores, after controlling the students’ prior level, are significantly greater for the erroneous-example condition than the worked-example condition. Therefore, the erroneous-example approach seems to be more effective in developing a learner’s problem-solving proficiency compared to a worked-example approach.

This research, following a sequential mixed-methods design, delves into metacognitive control in problem solving among 5- to 6-year-olds, using two floor-robot environments. In an initial qualitative phase, 82 pupils participated in tasks in which they directed a floor robot to one of two targets, with the closer target requiring more cognitive effort due to the turns involved. The results of this phase revealed that younger students often rationalised their decisions based on reasons unrelated to the difficulty of the task, highlighting limitations in children’s language and abstract thinking skills and leading to the need for a second quantitative study. In this subsequent stage, involving 117 students, a computerised floor-robot simulator was used. The simulator executed the students’ planned movements and provided feedback on their validity. Each participant had three attempts per problem, with the option to change their target each time. The simulator stored the information pertaining to the chosen resolution path, design of the plan, and re-evaluation of decision making based on the results and feedback received. This study aims to describe the criteria upon which students base their metacognitive control processes in decision making within problem-solving programming tasks. Additionally, through a comparative analysis focusing on age and gender, this research aims to assess the relationship between metacognitive processes and success in problem-solving programming tasks.

Recent Large Language Models (LLMs) demonstrate problem-solving capabilities suitable for educational use. This paper investigates using LLMs to create virtual agents that mimic student behavior and interact with learning platforms. Testing a modest-sized LLM on an Intelligent Tutoring System for word problem-solving revealed that the LLM could fully solve 92% of single-step problems, although their performance decreased to 14% when attempting more complex problems.

This article introduces a set of teaching strategies to enhance second language learning for students with Down syndrome (DS) enrolled in an English course covering material from the first two years of primary school. A set of instructional support strategies has been defined and integrated into an online learning software, developed ad hoc to teach the basic vocabulary of the English subject syllabus of the two first courses of primary school. A controlled experiment was carried out with 20 students with DS, who were divided into two groups: control and experimental. The control group was given a simplified version of the software, while the experimental group had access to the complete software with personalized instruction. Prior to the experiment, all participants undertook the same level test (pretest) in order to assess their initial knowledge level of English. After finishing the learning stage, a posttest was provided to the students to assess their learning. In both groups, results in the posttest were consistently better than in the pretest, supporting the positive effect of the learning software as an instructional tool. In addition, learning gains were significantly higher in the experimental group, that used the proposed instructional aids.

In this article, we analyze the potential of conversational frameworks to support the adaptation of existing tutoring systems to a natural language form of interaction. We have based our research on a pilot study, in which the open-source machine learning framework Rasa has been used to build a conversational agent that interacts with an existing intelligent tutoring system (ITS) called hypergraph-based problem solver (HBPS). This agent has been seamlessly integrated into the ITS to replace the previously available button-based user interface and allow the user to interact with HBPS in natural language. Once appropriately trained, the conversational agent was capable of identifying the intention of a given user utterance and extracting the relevant entities related to the message content, with average weighted F1-scores of 0.965 and 0.989 for intents and entities, respectively. Methodological guidelines are provided to generate a realistic training set that enables the creation of the required natural language understanding model and also evaluate the resulting system. These guidelines can be easily exported to other ITS and contexts to provide an enhanced interaction based on natural language processing methods.

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in which both control and experimental groups participated in a teaching sequence based on mathematical problems. In each session, both groups used audience response systems to record their responses to mathematical tasks about fractions. After each session, students from the control group were given generic homework on fractions-the same activities for all the participants-while students from the experimental group were given a personalised set of activities. The provision of personalised homework was based on the students' errors detected from the use of the LA-based formative assessment. After the intervention, the results indicate a higher student level of understanding of the concept of fractions in the experimental group compared to the control group. Related to motivational dimensions, results indicated that instruction using audience response systems has a positive effect compared to regular mathematics classes. Practitioner notesWhat is already known about this topic Developing an understanding of fractions is one of the most challenging concepts in elementary mathematics and a solid predictor of future achievements in mathematics.Learning analytics (LA) has the potential to provide quality, functional data for assessing and supporting learners' difficulties.Audience response systems (ARS) are one of the most practical ways to collect data for LA in classroom environments.There is a scarcity of field research implementations on LA mediated by ARS in real contexts of elementary school classrooms.What this paper adds Empirical evidence about how LA-based formative assessments can enable personalised homework to support student understanding of fractions.Personalised homework based on an LA-based formative assessment improves the students' comprehension of fractions.Using ARS for the teaching of fractions has a positive effect in terms of student motivation.Implications for practice and/or policy Teachers should be given LA/ARS tools that allow them to quickly provide students with personalised mathematical instruction.Researchers should continue exploring these potentially beneficial educational implementations in other areas.

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in which both control and experimental groups participated in a teaching sequence based on mathematical problems. In each session, both groups used audience response systems to record their responses to mathematical tasks about fractions. After each session, students from the control group were given generic homework on fractions—the same activities for all the participants—while students from the experimental group were given a personalised set of activities. The provision of personalised homework was based on the students' errors detected from the use of the LA-based formative assessment. After the intervention, the results indicate a higher student level of understanding of the concept of fractions in the experimental group compared to the control group. Related to motivational dimensions, results indicated that instruction using audience response systems has a positive effect compared to regular mathematics classes. What is already known about this topic What this paper adds Implications for practice and/or policy

The use of the algebraic method for solving word problems is a challenging topic for secondary school students. Students’ difficulties are usually associated with extracting the problem’s network of relationships between quantities and with formalizing these relationships into algebraic language in a problem model. Both sources can coexist and interact; thus, it is usually not possible to determine which source of difficulty is more relevant. In addition, there are specific errors, such as the error by multiple referents for the unknown, which are directly linked to the wording of the problem text, and in which the same two sources of error coexist. In this work, we present the results of an experiment conducted with 255 secondary school students assessing the effect of two common difficulties on the accuracy of problem models and on the rate of multiple referents for the unknown. The first difficulty is the use of algebraic language in the construction of the problem model; the second is the use of the same expression to designate different quantities within the problem text. We used a 2 × 2 between-between design, with one factor related to the symbolic language (algebraic or arithmetic) in which the problem model is constructed, and the other factor related to the actual language features of the text problem. Our results indicate that overall, the main source of difficulty for students is the use of algebraic language to formalize a problem model, representing a large effect size.

In this paper, we present and evaluate the recent incorporation of a conversational agent into an Intelligent Tutoring System (ITS), using the open-source machine learning framework Rasa. Once it has been appropriately trained, this tool is capable of identifying the intention of a given text input and extracting the relevant entities related to the message content. We describe both the generation of a realistic training set in Spanish language that enables the creation of the required Natural Language Understanding (NLU) models and the evaluation of the resulting system. For the generation of the training set, we have followed a methodology that can be easily exported to other ITS. The model evaluation shows that the conversational agent can correctly identify the majority of the user intents, reporting an f1-score above 95%, and cooperate with the ITS to produce a consistent dialogue flow that makes interaction more natural.

In the last years, the educational field has been influenced by technological advances. The digital transformation in educational environments allows the incorporation of virtual teaching-learning environments, which allow or facilitate learning opportunities for students, showing, for example, where they make mistakes and providing personalized help whenever they require it. In addition, these systems provide permanent access availability whenever it is possible to access the Internet. Traditionally, simultaneously many students learn word problem-solving skills in the classroom through instruction from only one educational professional. The Intelligent Tutoring System (ITS) Hypergraph Based Problem Solver (HBPS) is capable of tutoring the whole process of solving arithmetic-algebraic word problems, in a personalized way and without imposing any restrictions on the resolution path. Nevertheless, the student-system interaction is performed through a traditional interface by selecting items from a drop-down menu and clicking on buttons. Since dialogue is the fundamental communication mechanism for human-human, we propose use a framework to improve the interaction of the HBPS using a conversational user interface that allows performing the same actions more easily using natural language as the main means of interaction. My thesis research focuses on two main topics. The first one is related to the incorporation of a conversational agent using an open source machine learning framework that is fully configurable. The second one in concerned with testing and modifying different neural architectures to improve performance in intent classification and entity extraction, in such a way that it can be exported to other mathematical domains.

Patterning, as a component of early mathematic knowledge, is a common activity carried out at elementary levels in which children are not equally successful. This study aimed to measure different variables affecting performance on patterning tasks in early childhood. For this purpose, the success of Pre-K (N = 33), K (N = 31) and first-grade (N = 33) children when solving 14 repeating-pattern tasks, which varied in complexity, was analysed. The results revealed no significant differences between core-2 and core-4 length patterns, and greater success with patterns involving size. The study also introduces distractors, as a novel factor, in the patterning activities related to the presence of contradictory or surplus data. The impact of each factor and the relations between complexity and difficulty on the patterning tasks are discussed in order to contribute to the design of teaching itineraries.

The aim of this pre-experimental study is to evaluate the acquisition level of counting skills of a 3-year-old classroom made up of 14 children through a specific instructional design. To this end, an instructional proposal to improve these mathematical skills was designed. Before and after the intervention, we measured the students’ level regarding counting skills through an evaluation of their counting abilities. The results indicate that the designed intervention increased the acquisition level of skills related to counting principles, constituting an effective instrument to enhance counting skills for 3-year-old children. In particular, after the intervention children improved significantly in skills related to the one-to-one correspondence principle and the order-irrelevance principle, both showing a large effect size in their observed differences. The cardinality principle, stable-order principle and abstraction principle also showed gains, but the differences were found to be statistically non-significant. Finally, the role of the age of the participants was also analyzed in relation to their acquired counting skills, indicating that children in the older age range improved their counting skills more than children in the younger group.

The COVID-19 pandemic led to the lockdown of schools in many countries, forcing teachers and students to carry out educational activities remotely. In the case of mathematics, developing remote instruction based on both synchronous and asynchronous technological solutions has proven to be an extremely complex challenge. Specifically, this was the case in topics such as word problem solving, as this domain requires intensive supervision and feedback from the teacher. In this piece of research, we present an evaluation of how technology is employed in the teaching of mathematics, with particular relevance to learning during the pandemic. For that purpose, we conducted a systematic review, revealing the almost complete absence of experiments in which the use of technology is not mediated by the teacher. These results reflect a pessimistic vision within the field of mathematics education about the possibilities of learning when the student uses technology autonomously. Bringing good outcomes out of a bad situation, the pandemic crisis may represent a turning point from which to start directing the research gaze towards technological environments such as those mediated by artificial intelligence. As an example, we provide a study illustrating to what extent intelligent tutoring systems can be cost-effective compared to one-to-one human tutoring and mathematic learning-oriented solutions for intensive supervision in the teaching of word problem solving, especially appropriate for remote settings. Despite the potential of these technologies, the experience also showed that student socioeconomic level was a determining factor in the participation rate with an intelligent tutoring system, regardless of whether or not the administration guaranteed students' access to technological resources during the COVID-19 situation.

Problem solving is often regarded as one of the most essential cognitive functions in our daily lives, and, for that reason, educational theorists have long stressed the need for its development. As cognitive flexibility is a fundamental characteristic necessary throughout the problem-solving process, the purpose of this study is to analyse students' problem-solving performance after following intra-task flexibility-based training mediated by an intelligent tutoring system. With this aim, 110 fifth and sixth grade students took part in a quasi-experimental study that included six forty-five-minute flexibility-based training sessions preceded and followed by test sessions in order to evaluate eventual problem-solving proficiency improvements. The findings show that intra-task flexibility training enhances students' ability to solve arithmetic word problems, especially when flexibility-related activities are completed sequentially in the same session and not in different sessions. Furthermore, the proposed instruction is particularly helpful in improving girls' problem-solving competence, which can minimize eventual gender gaps and strengthen their STEM vocation. Practitioner notes What is already known about this topic Cognitive flexibility is beneficial in finding appropriate problem-solving strategies. Exposing students to a variety of problem-solving methods or strategies can improve their cognitive flexibility. Boys are more likely than girls to flexibly apply multiple solution paths while solving problems, which leads to gender differences in mathematics. By contrast, girls are more prone to take advantage of instructional advice when using intelligent tutoring systems (ITS). What this paper adds Prompting students to apply multiple resolution strategies within the same problem (intra-task flexibility instruction) is comparatively more efficient than standard instruction in promoting problem-solving performance. It is more effective in terms of problem-solving proficiency to ask students to find different resolutions for a problem sequentially in the same session than to do so in separate sessions. Effectiveness of ITS-mediated flexibility-based training leads to the promotion of problem-solving proficiency, particularly in the case of female students. Implications for practice and/or policy The use of the ITS HINTS has the potential to promote the use of multiple solutions in problem solving by monitoring the resolution paths of the student, which can be difficult in a traditional classroom setting. ITS-mediated flexibility-based training is especially effective in improving girls' problem-solving competence, which can minimize eventual gender gaps and strengthen their STEM vocation.