Learning geometry helps students develop their logical reasoning ability, which implies analyzing and elaborating arguments about spatial forms, shapes, and abstract math concepts [1]. However, geometry tends to be abstract, and many students encounter difficulties and show poor performance [2]. Some researchers claim that to improve students’ geometrical reasoning abilities, learning activities should keep the motivation and adaptation to their knowledge and psychological conditions [3,4].

Augmented reality (AR) is a technology that enhances the user’s actual physical surroundings by overlaying virtual elements such as images, videos, and virtual items [5]. AR technology might be useful both to facilitate the visualization of geometric shapes and to foster psychological states such as motivation towards learning. AR technology could help students easily understand basic geometry concepts, since it supplements their sensory perception of the real world through the addition of computer-generated content to the students’ environment in real-time [6]. Moreover, AR attracts attention to students due to its interactive possibilities [7]. In recent years, many researchers have focused their works on AR applied to education [8,9,10,11], particularly in areas of study such as science, technology, engineering, and mathematics [12]. Although AR has proven to foster motivation and engagement, it does not always positively impact learning outcomes. Consequently, some researchers suggest integrating AR technology into learning environments with the purpose of guiding learning activities in accordance with the knowledge or psychological state of students [13]. An effective choice for this integration is the incorporation of AR to an intelligent tutoring system (ITS) [14]. Intelligent tutoring systems are computer-based systems that provide personalized learning support to the student, according to their current (or projected) performance or skill in a task [15,16]. ITSs provide personalized and interactive help so that the content dynamically adapts to the student—who can “learn by doing” in realistic and meaningful contexts—providing feedback to the student [17].

ITSs have been built using different artificial intelligence (AI) techniques such as neural networks, Bayesian networks, data mining, and fuzzy logic, and they have proven their efficiency in many different fields of knowledge [18]. For example, in the field of English learning, the work of [19] combines a neural network with a fuzzy system to adapt learning content. In [20], a fuzzy-logic- and constraint-based student model (CBM) for an intelligent tutoring system was developed to teach Turkish students how to use punctuation correctly. In the field of computer programming learning, Ref. [21] implemented an intelligent multi-agent with a Bayesian technique for updating the student model, estimating the learner’s level of knowledge, and adapting the learning content. In the area of chemistry and molecular biology, Ref. [22] applied a data mining technique for learners’ evaluation and adaptive feedback. In the study field of the human circulatory system, Ref. [23] worked with intelligent multi-agents, neural networks, and different sensors for learners’ knowledge evaluation, automatic facial expression recognition, and emotion measurement. Finally, in the field of mathematics, Ref. [24] presented a Bayesian network for classifying the learner’s affective states and adapting the feedback generation. In recent years, ITSs have incorporated new technological strategies to give their operation more emotional intelligence and simulate empathy. Two examples of this kind of strategy are the incorporation of emotion recognition [25] and the inclusion of motivational techniques such as gamification [26].

AR allows users to interact in real-time with virtual elements in real contexts. This distinctive aspect of AR technology provides new opportunities to promote learning and allows the deployment of constructive learning environments [27]. The rapid development of smart mobile devices has increased the amount of AR applications in education, ranging from the use of AR for augmented books [28,29,30] to deploying inquiry-based learning activities [31,32,33] and fostering learning via exploration [34,35,36]. Regardless of the use of AR in developing learning activities, studies have demonstrated that AR allows students to learn new procedures in real conditions [37]; additionally, most of the studies claim that AR-enabled learning environments can enhance learning motivation, engagement, and learning effectiveness [38]. The use of AR in education can help students find the activities fun and interesting, monitoring them and increasing their interaction with the learning tool, making them understand abstract concepts, depending on their learning pace. Regarding teachers, they feel that AR enhances student creativity, participation, and attention to the academic work [39].

An application to help students learn programming using marker-based AR was carried out by [40]. This study focused on usability, efficiency, flow experience, and user perception. The efficiency of learning emphasizes the levels of competitiveness of the students to successfully solve the proposed exercises. To measure the efficiency of student learning, the authors recorded the number of tasks successfully completed by the student during the session using the system. On the other hand, [41] presented three AR-based applications to support students to understand and learn abstract concepts in probability and statistics. The authors examined the relationship between student performance and their attitudes when interacting with the application. They also evaluated the student learning gains when using their applications. The results reflected that the applications are useful for the learning achievements of the students and attitude improvement. An AR application for teaching geometry in middle schools was proposed by [42], where the students could create different segments by using two or more markers. They also made geometry solids using markers-based AR. The authors showed that by using AR in geometry lessons, they created conditions for positive emotional interaction between the student and the teacher.

Currently, most AR-based learning systems have two main limitations. First, they promote distraction probably due to the novelty effect [32,43,44]. Second, they provide instructions linearly with no feedback about any eventual mistake [45]. To alleviate these problems, some researchers are including scaffolding approaches in their AR learning environments [46,47], while others provide intelligent tutoring systems to guide students through the learning process in a more accurate way [45,48,49].

The field of ITSs supported with AR has been scarcely explored, and most of the currently published work focuses on finding learning activities that may be convenient and relevant to be carried out in the new interactive environments, with possible help for students in relation to the activities that they perform or with basic scaffolding techniques [12,50].

Intelligent tutoring systems use artificial intelligence techniques to represent the knowledge that is essential in the teaching–learning process such as domain knowledge, pedagogical strategy knowledge, and knowledge about the student’s present state [51]. Instruction and learning support delivered using an ITS tend to provide higher learning gains than the classroom and static instruction. The effectiveness of ITSs is tied to their capabilities to adapt themselves to the characteristics of the students.

Some researchers claim that ITSs based on a desktop computer paradigm disconnect the real world and the tutoring instruction, thus degrading the interest and motivation of students [45,52]. In this regard, AR technology has been used in education or training as the main interface module to support the rest of the ITS components (student and pedagogical modules). For example, the Motherboard Assembly Tutor (MAT), designed by [48], integrates AR technology to provide an adaptive training experience for students. In their work, students learn the process of assembling components such as a RAM, CPU chip, or heat sink on a motherboard guided by the MAT tutor, which overlays the assembly parts on the motherboard using AR technology. The results showed that MAT users improved test scores by 25% and found the solution 30% faster compared with users who trained without the ITS. One limitation of this work was the small sample of participants. Similarly, the project ARTWILD proposed by [53] used the Generalized Intelligent Framework for Tutoring (GIFT) with Markov decision processes for inferences made by the intelligent tutoring system. Authors used Metaio Creator and Unity 3D to support military training tasks in environments that are not specially designed to support combat training. They developed a software architecture that provides a standard messaging interface between the apprentice, the sensor, the tutor, and the pedagogy module. Additionally, [54] presented IARTS, an ITS using AR working together with the assistance of a virtual tutor and an adaptive guide for solving math problems. The learning tool engages the student in a variety of interactive ways, enhancing the student with rich content unique to three-dimensional learning environments. The tutor combined with AR technology uses a head-mounted display to guide students through the cabling of a network topology by overlaying arrows and digital icons on the ports of the hardware. The messages are displayed only when the learner experiences difficulties, allowing learners to remain motivated by practicing themselves. Likewise, AdapTutAr is a project designed by [55] to be an adaptive task tutoring system that enables experts to record machine task tutorials via embodied demonstration and train learners with different AR tutoring contents adapting to each user’s characteristics. The system enables an expert to record a tutorial that can be adaptively learned by different workers. For this purpose, it uses a convolutional neural network for machine state prediction based on bounding boxes. The authors evaluated the accuracy of the low-level state recognition on a mockup machine with nine component types, and further evaluated the overall adaptation model via a remote user study in a VR environment.

The combination of augmented reality technology and fuzzy logic in an ITSs has the potential to significantly enhance student learning in several ways by engaging different cognitive mechanisms. Firstly, AR can capture students’ attention by overlaying digital information on the real-world environment [56], while fuzzy logic can use rules and reasoning to adapt the presented information to the student’s level of understanding, making the content more engaging and relevant to individual learners [16]. Secondly, AR can provide visual and spatial cues that help students understand complex concepts by visualizing abstract ideas [56]. Fuzzy logic can also personalize the learning experience by adapting the content presentation based on the student’s prior knowledge and current performance [57]. Lastly, AR can provide students with opportunities to solve problems and make decisions in a real-world context [58]. Fuzzy logic can assist students in making informed decisions by analyzing data and providing feedback on the best course of action [59].