Although nowadays AR has been incorporated to many educational practices [ 11 ], different aspects have to be explored in order to complete the implementation of AR-based activities in real class situations. In particular, this work pretends to explore the applicability of AR-based activities for the learning of 3D-geometric contents in a 6-grade Primary classroom.

As we will describe in the next section, the use of AR can support the learning of specific domains regarding to geometric and spatial abilities. The key point is that AR enhances the students’ visual perception. An AR-based activity allows us to manipulate virtual objects as well as to physical objects in the real world [ 14 ]. Thus, students can move around a 3D-virtual figure and view it from any vantage point, just like a real object. Different researchers have delved into the geometric and spatial abilities developed by students when using AR-based activities from Primary to High Education levels [ 14 22 ]. In particular, the 3D-activities based on AR in which the students have to represent and manipulate spatial and virtual objects are depicting promising results for extending the resources used in the Mathematics classroom [ 23 ].

The AR has been applied with different goals to medicine, engineering, psychological treatments, etc. [ 17 ]. Concerning the educational approach, the benefits of AR applications had been told to strengthen the comprehension of complex concepts, supporting the contextualisation [ 11 ]. In this line, the use of the AR-based technologies allows an individual learning for each student and the manipulation of both tangible and virtual objects in an enhanced and motivational scenery. In spite of the generalised though that AR is an expensive resource, the integration of AR devices in the classroom does not imply a high cost because of the mobile devices. Different educational studies are providing clues to implement AR-based proposals at different ages [ 10 19 ].

These AR-based learning environments reinforce the significant learning through new possibilities and motivational practices [ 6 7 ]. The AR has been considered as a technological tool capable to permeate on the teaching and learning mechanisms providing significant impact on both processes. Due to the affordability and the ease of use, AR has been reported as a mid-term technological adoption (2–3 years) for K-12 levels and High Education levels [ 8 9 ]. Possibilities for AR applications in research are also promising. Different studies had demonstrated the AR usefulness for increasing the student motivation, as well as for enhancing a wide variety of learning domains [ 3 16 ]. In particular, the meta-analysis provided by [ 4 ] among JCR publications on the state of AR applications in the Education field, concludes that there is a increasing trend, specially during the last 4 years, on the Science and Humanities & Arts areas.

In the last decade the use of the technological tools linked to the Information and Communication Technologies (ICT) has acquired a big importance, both as a didactic tool and as well as a provider of new environments for promoting the learning. Different authors are reporting the learning effects of a significant use of technological environments in the classroom, specially those regarding to the Augmented Reality (AR) [ 1 3 ]. Although, AR has been defined from different perspectives [ 4 ], we understand an AR environment as a system that allows for combining real world objects with virtual objects or superimposed information. As a result virtual objects seem to coexist in the same space with the real world [ 5 ].

2. AR for Geometric and Spatial Learning

Geometry comprises those branches of mathematics that exploit visual intuition (the most dominant of our senses) to remember theorems, understand proofs, inspire conjectures, perceive realities, and give global insight. (Zeeman, quoted in [ 24 ], p. 12)

spatial reasoning , underlying the most geometric thought, is defined as a vital capacity for human action and thought, not always supported in school curricula ([ geometric reasoning consists on the inventions and the use of formal conceptual systems that allows us to investigate the space and the shape in a mathematical way ([ Historically, spatial abilities have been addressed from a psychological standpoint [ 25 ]. Nowadays, the recent research on teaching and learning of Geometry covers geometric and spatial thinking among other content domains, as the geometric measurement or the teacher development [ 26 ]. In one hand, the, underlying the most geometric thought, is defined as a vital capacity for human action and thought, not always supported in school curricula ([ 27 ], p. 3). On the other hand, theconsists on the inventions and the use of formal conceptual systems that allows us to investigate the space and the shape in a mathematical way ([ 28 ], p. 843).

The learning of Geometry at Primary levels can be exciting and fun for those pupils who are engaged with Mathematics, but the same cannot be told for those pupils showing less interest in Mathematics [ 29 ]. Usually, the geometric ideas in the curriculum are reduced to the identification of 2D- and 3D-geometric shapes, related to area and volume measurements, not taking to much time on developing spatial reasoning and visualisation contents [ 26 ]. This approach does not fit the international guidelines, that claim the use of visualisation, spatial reasoning, and geometric modelling to solve problems [ 30 ]. In this line, Duval in 1998 stood up for a teaching of Geometry beyond the arithmetic operations, in which three cognitive processes are involved: visualisation, construction and reasoning [ 31 ]. This position has strong implications on the teaching of Geometry, in the sense of involving spatial reasoning tasks on the Geometry teaching proposals. Moreover, has been stated that the interaction with technological environments improves the visualisation and spatial reasoning on the students [ 30 32 ].

The use of manipulatives in the Mathematics classroom is not new. In the longstanding history different kinds of physical materials have been used in order to explore, acquire, or investigate mathematical concepts or processes and to perform problem-solving activities drawing on perceptual (visual, tactile, or, more generally, sensory) evidence [ 33 ]. Nowadays, the technological progress is providing a big amount of virtual materials that, combined with the physical ones, offer a wide variety of possibilities to explore teaching activities in new and motivational manners. In particular, the AR-based learning experiences produce as physical benefits as virtual benefits [ 23 ].

Concerning the AR-based educational implementations related to Mathematics, these can be a powerful tool to strengthen the spatial visualisation. From a Mathematical Education approach, the spatial visualisation is determined as a set of mental skills that allow individuals to act in the context of mathematical graphical representations, taking this context in a broad sense that includes the usual representations in the different mathematical fields such as Geometry, Algebra, Arithmetic or Statistics [ 34 ]. In this line, the manipulation of AR 3D-geometric shapes enhances the spatial visualisation ability, in the terms described by Gutiérrez [ 35 ], by means of the use of visual or spatial elements, developed to solve problems or demonstrate properties.