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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>mathematical skills in children with learning dificulties: design and evaluation of NumbersPlayRoom VR</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Matteo Noro</string-name>
          <email>matteo.noro@studenti.unipd.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ombretta Gaggi</string-name>
          <email>ombretta.gaggi@unipd.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="editor">
          <string-name>Virtual Reality, Serious Games, Dyscalculia, Learning math</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Padua, Department of Mathematics</institution>
          ,
          <addr-line>Padua</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>This paper presents NumbersPlayRoom VR, a virtual reality serious game designed for children with learning dificulties, such as developmental dyscalculia. Based on cognitive theories of numerical processing, it leverages VR's immersive potential to enhance numeracy skills through interactive mini-games targeting visuospatial and symbolic components of mathematical reasoning. Preliminary evaluations show high usability and engagement, highlighting immersive technologies' potential for inclusive education.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        The acquisition of numerical skills involves complex cognitive mechanisms that engage multiple
processing modalities. Children with developmental dyscalculia (DD) experience persistent dificulties
in learning and manipulating numbers, and require more support and motivation[
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. DD is a learning
disability that directly afects the processing and understanding of numerical information, and it can
involve dificulties in estimating quantities, manipulating symbols, and performing basic arithmetic.
      </p>
      <p>
        The cognitive basis of numerical processing is fundamental in creating efective supportive tools,
especially when dealing with new technologies such as Virtual Reality (VR). Cognitive models, such
as Dehaene’s Triple Code [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ][
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], describe numerical cognition as the interaction of three systems:
the analog magnitude system, the visual-Arabic code, and the verbal code. Deficiencies in the analog
code, specifically the visuospatial representation of number, i.e., the mental number line, are seen as a
hallmark trait of DD. Evidence from phenomena, such as the distance and SNARC efects, supports the
importance of spatial-numerical associations in early number understanding[
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. In addition, children
with Developmental Dyslexia often show deficits in visuospatial working memory and executive
functions, which further hinder calculation skills and algebraic manipulation[
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. Many serious games
have been developed to support children with dyscalculia, but almost the totality of them rely on
traditional gaming experiences and platforms.
      </p>
      <p>
        Despite existing studies highlighting VR’s educational potential[
        <xref ref-type="bibr" rid="ref6">6</xref>
        ][
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], the use of VR in this domain
remains limited. Current research is mostly confined to laboratory settings and lacks comparison
with standard methods or other game-based solutions[
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. If properly validated and implemented
in teaching activities, VR can efectively provide immersive, interactive environments that support
visuospatial reasoning and focused engagement. In this context, immersive technologies ofer an
opportunity not only to simulate engaging learning environments but also to activate multisensory
processing that supports both cognitive and emotional engagement. Extended Reality (XR), especially
in the form of VR, enables the embodiment of mathematical concepts through direct manipulation and
      </p>
      <p>CEUR
Workshop</p>
      <p>
        ISSN1613-0073
spatial interaction, which can be especially beneficial for learners with numerical cognition dificulties.
Moreover, the afective and motivational components of immersive learning environments may help
reduce math-related anxiety and encourage a more positive learning experience. These features align
with Mayer’s Cognitive Theory of Multimedia Learning[
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] as the integration of verbal, visual, and
kinesthetic channels can reduce extraneous cognitive load and promote richer learning. In particular,
embodied interaction and intuitive feedback may enhance engagement and retention, especially for
children who struggle with abstract or symbolic representations in traditional settings.
      </p>
      <p>To this end, the proposed VR game ofers several key benefits for children with learning dificulties.
By leveraging immersive virtual reality, it provides:
1. Increased engagement and motivation through playful interaction;
2. Dedicated training on visual-spatial and symbolic numerical components;
3. Reduced math anxiety thanks to a safe and exploratory environment;
4. Integrated multisensory feedback (visual, auditory, haptic) that reduces cognitive load and
promotes the encoding of mathematical concepts through multimodal channels.</p>
    </sec>
    <sec id="sec-2">
      <title>2. The NumbersPlayRoom VR Approach</title>
      <p>
        NumbersPlayRoom VR was developed as a serious game designed to address specific cognitive
dificulties frequently observed in children with DD[
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. These challenges guided both the selection
of numerical tasks and the implementation of VR interactions, with the goal of creating a supportive,
engaging learning environment tailored to learners’ needs. The game consists of a virtual space designed
to be friendly and engaging, encouraging focused interaction while minimizing cognitive overload.
Within this virtual environment, the user will be able to access a series of mini-games (Figure 1 and
Figure 2). Two of the available mini-games are listed below:
• Mental Calculation: The player is presented with simple arithmetic expressions based on
the chosen type and dificulty level. It must then identify the correct result among the
spatially distributed options (Figure 2 top left and right). This activity reinforces symbolic number
comprehension and verbal retrieval, taking advantage of virtual reality-based interaction;
• Column Counting: The player must correctly solve an operation on the board using cards to put
the number in the right position. The type of the operation and the dificulty are selected by the
user (Figure 2 bottom left and right). This activity is designed to assist the user in correctly carrying
out and completing operations, reinforcing their visuospatial skills in algebraic manipulation.
The game is implemented using Unity, OpenXR framework and optimized for standalone VR headsets
(e.g., Meta Quest 2). The game mechanics were deliberately kept simple, with short trials, minimal text,
and multimodal feedback to accommodate children with attention or language dificulties, ensuring a
smooth and inclusive user experience.
      </p>
      <p>An optional tutorial was also implemented to assist users new to the game or unfamiliar with
interactions in VR (Figure 1 bottom right and left). Designed as a short game sequence, this section
uses narrated instructions and visual cues to introduce basic actions such as teleportation, object
manipulation and interaction. Each stage guides the user progressively, with clear visual cues and
allowing them to learn by doing in a controlled and engaging manner. In the final stage, players must
combine all previously introduced actions to complete a simple task, reinforcing learning through
playful exploration before entering the main experience.</p>
      <p>A synthesized voice provides instructions to children without overloading the screen with text,
greatly improving the efectiveness of information comprehension. Users move around the room
using a teleportation system, chosen to minimize the risk of motion sickness, while interacting with
virtual objects through grabbing, positioning and pointing actions. Each interaction is reinforced by a
combination of multimodal feedback: visual cues (such as raycast highlights), subtle tactile responses
via controller vibrations, and context-specific audio signals. For example, picking up an object generates
a sound and a tactile impulse, as well as pressing a button in the UI.</p>
      <p>Similarly, correct responses are accompanied by positive sound efects and subtle vibrations, while
incorrect actions trigger discreet auditory and tactile feedback that signals the error without creating
frustration or stress (allowing the user to try again). Short musical stingers are also used to signal success
at the end of each mini-game session, increasing the user’s sense of satisfaction. These audio-tactile
feedback mechanisms have been carefully designed to be informative, discrete, and positive.</p>
      <p>The environment has been created to engage multiple sensory channels while maintaining a relaxing
and reassuring atmosphere. The color combinations have been selected to provide high contrast between
interactive elements and background areas, improving object recognition and visual orientation while
also making the environment playful (Figure 1). The lighting has been balanced to avoid excessive
contrasts or flickering that could distract or overwhelm users with sensory sensitivity, and is adjusted
to keep the eye focused on the main area of interaction, while ensuring a pleasant graphic efect that
significantly enhances the perception of the virtual world.</p>
      <p>The application underwent multiple iterations based on informal feedback and design testing before a
formal validation with target users. These refinements aimed to reduce potential cognitive load, clarify
interaction mechanics, and ensure that all game elements were accessible and comprehensible to young
users. This iterative, user-centered process allowed us to better align the mechanics and pacing of the
mini-games with both the cognitive profiles and attentional rhythms of the target population.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Preliminary Evaluation</title>
      <p>The development of NumbersPlayRoom VR was accompanied by three evaluation phases aimed at
assessing usability, engagement, and educational potential. An initial informal phase involved educators,
researchers, and relatives. These preliminary tests helped to verify comfort, interaction flow, and overall
understanding of the in-game mechanics. Feedback led to initial refinements, such as simplifying
interfaces, improving interaction feedback, and adding on-screen instructions and optional tutorials.</p>
      <p>The second phase involved 33 young adult participants who completed both a SUS (System Usability
Scale) questionnaire and a short evaluation survey. The results showed high usability and clarity
(with an average SUS score of 84.17), with users reporting a good sense of engagement and immersion.
Participants also perceived the mini-games as meaningful and well aligned with educational goals,
suggesting potential for efectiveness. In this phase, the aim was not to evaluate the educational
efectiveness of the game, but rather to test its usability, comfort and technical stability before using it
with children. Involving users with greater technological familiarity enabled us to quickly collect bug
reports, measure the learning curve for the controls and calibrate audio-haptic feedback, reducing the
risk of frustration during subsequent school trials.</p>
      <p>The third and most significant phase was conducted in a primary school with 34 children aged 8
to 12, including some with learning dificulties. The children played selected mini-games under adult
supervision, and their experience was recorded via an emoji-based survey, co-designed with a
psychologist, administered on tablets. The results were very encouraging: most reported positive emotions, low
frustration, total engagement, willingness to use the application again, and full task comprehension.
In particular, children diagnosed with dyscalculia or ADHD showed greater concentration and high
success rates, often completing tasks accurately and independently.</p>
      <p>Teachers provided additional observations, highlighting that some children who typically struggle to
complete similar exercises in the classroom—particularly those with ADHD—performed significantly
better in the VR setting. In several cases, they noted that students completed tasks such as the column
counting game with focus and accuracy, whereas they would normally require assistance or abandon the
activity. The immersive nature of the environment, combined with its game-based structure, may have
played a key role in sustaining attention and reducing performance anxiety, allowing these learners to
remain engaged and self-directed for longer periods than usual.</p>
      <p>During the sessions, a generally positive attitude and increased confidence were also observed in
many children, especially those with learning disabilities. Many participants spontaneously asked to
repeat activities, and some expressed pride in having successfully completed tasks without help. The
playful tone of the environment seemed to support this, helping to reduce the stress typically associated
with math tasks.</p>
      <p>These findings might also reflect, in addition to motivational aspects of game-based learning, the
benefit of multisensory feedback from an attention and emotional regulation standpoint. The instantaneous
auditory-haptic feedback, intuitive spatial tasks and embodied interactions may have helped to establish
the user’s focus and promote psychological safety and gratification in the learning environment.</p>
      <p>At the same time, some usability issues were encountered suggesting directions for future refinements
in VR interactions. Although teleportation, the most commonly used system, was adopted as a movement
strategy to minimize motion sickness, some children, particularly those with ADHD, found it unintuitive
or frustrating. In response, they switched to continuous locomotion, more in line with traditional
video game routines. Although this provided a more familiar control experience, it also increased the
risk of dizziness. This feedback highlights the necessity of hybrid locomotion models that merge the
intuitiveness of free movement with the comfort of structured transitions, hence taking a step beyond
the standard systems ofered by XR development libraries. For example, the implementation of a fluid
directional teleportation with short fade-to-black transitions can ofer a balanced solution that suits
diferent user profiles without compromising safety.</p>
      <p>Further insights into physical interaction emerged from observing how participants behaved after
completing their tasks. In some cases, it was found that some participants preferred to throw objects
around the room after completing a task, perceiving it as a form of reward. This behavior suggests an
opportunity to expand the use of active, physical dynamics in future iterations. Enhancing gamification
through reward-based movement mechanics could further increase motivation and engagement,
especially for children with high energy levels or attention problems. In addition to the structured feedback,
teachers and support staf expressed interest in the potential use of the app in inclusive learning contexts,
and asked about the possibility of replicating the experience in a concrete and continuous way as well.
Although further controlled studies are needed, these results suggest that serious games in VR can ofer
valuable support for inclusive learning, particularly for students with attention or numerical processing
dificulties. The encouraging responses gathered in these early stages indicate the feasibility of adopting
immersive technologies as complementary tools in real-world educational settings.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusion</title>
      <p>This research introduces an under-investigated and targeted approach to inclusive numeracy education,
combining cognitive theory with the immersive potential of virtual reality. Designed to address specific
dificulties encountered by children with dyscalculia and attention disorders, the tool demonstrates
how spatial interaction and embodied learning in these immersive environments can improve the
understanding of numerical concepts beyond traditional methods.</p>
      <p>Initial observations from young adult and classroom testing highlight its potential as an engaging
and efective resource that can complement existing educational practices. Rather than replacing
conventional teaching, this virtual reality-based tool ofers a new way to reach students who benefit
from alternative formats and reduced cognitive interference. While digital interventions for dyscalculia
already exist, few are designed from the ground up to leverage the unique afordances of VR. This work
does not aim to replicate existing activities in a new medium, but to explore how immersion, embodied
interaction, and controlled spatial environments can actively support cognitive functions that are often
compromised in these learners.</p>
      <p>We actively support the ongoing development of immersive educational technologies and the research
that underpins them, with a particular focus on inclusion. Although our pilot project confirms the
efectiveness of NumbersPlayRoom VR and its ability to engage students who typically struggle with
traditional mathematics, two limitations must be acknowledged. First, the study did not include a control
condition based on traditional activities or 2D games, so it is not yet possible to isolate the specific
contribution of virtual reality to learning progress. Secondly, the outcome measures (in terms of cognitive
improvement) were mainly observational and qualitative, based on teacher assistance; no standardized
pre/post assessment of numerical competence was carried out. We are therefore considering a follow-up
study comparing the current VR experience with tablet exercises and worksheets with in-app analysis,
in order to obtain a clearer picture of cognitive improvement and retention. Such evidence will guide
the refinement of game mechanics and provide further insights into how immersive technologies can
best support inclusive mathematics education.</p>
    </sec>
    <sec id="sec-5">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author(s) used GPT-4o in order to: Formatting assistance. After
using these tool(s)/service(s), the author(s) reviewed and edited the content as needed and take(s) full
responsibility for the publication’s content.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>We would like to express our gratitude to Salvatore Gatto for actively supporting this work from its
early stages, and to Valentina Fietta for her valuable consultation on the psychological aspects during
the test sessions. We also thank the students and PhD candidates who collaborated on the project for
their valuable assistance. Special thanks are extended to the Belluno primary school for their warm
welcome and crucial cooperation, which made the field study possible.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>I. C. M.</given-names>
            <surname>Daniela Lucangeli</surname>
          </string-name>
          ,
          <article-title>Psicologia della cognizione numerica</article-title>
          ,
          <source>FrancoAngeli</source>
          ,
          <year>2010</year>
          . URL: https: //francoangeli.it/Libro/Psicologia-della
          <string-name>
            <surname>-</surname>
          </string-name>
          cognizione-numerica?Id=
          <fpage>18406</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>S.</given-names>
            <surname>Dehaene</surname>
          </string-name>
          , Varieties of numerical abilities,
          <source>Cognition</source>
          <volume>44</volume>
          (
          <year>1992</year>
          )
          <fpage>1</fpage>
          -
          <lpage>42</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>S.</given-names>
            <surname>Dehaene</surname>
          </string-name>
          , L. Cohen,
          <article-title>Towards an anatomical and functional model of number processing</article-title>
          ,
          <source>Mathematical Cognition</source>
          <volume>1</volume>
          (
          <year>1995</year>
          )
          <fpage>83</fpage>
          -
          <lpage>120</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>J.</given-names>
            <surname>Bachot</surname>
          </string-name>
          ,
          <string-name>
            <given-names>W.</given-names>
            <surname>Gevers</surname>
          </string-name>
          ,
          <string-name>
            <given-names>W.</given-names>
            <surname>Fias</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Roeyers</surname>
          </string-name>
          ,
          <article-title>Number sense in children with visuospatial disabilities: Orientation of the mental number line</article-title>
          ,
          <source>Psychology Science</source>
          <volume>47</volume>
          (
          <year>2005</year>
          )
          <fpage>172</fpage>
          -
          <lpage>183</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>D. B.</given-names>
            <surname>Berch</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E. J.</given-names>
            <surname>Foley</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. J.</given-names>
            <surname>Hill</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P. M.</given-names>
            <surname>Ryan</surname>
          </string-name>
          ,
          <article-title>Extracting parity and magnitude from arabic numerals: Developmental changes in number processing and mental representation</article-title>
          ,
          <source>Journal of Experimental Child Psychology</source>
          <volume>74</volume>
          (
          <year>1999</year>
          )
          <fpage>286</fpage>
          -
          <lpage>308</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>M.</given-names>
            <surname>Belter</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Lukosch</surname>
          </string-name>
          ,
          <article-title>Towards a virtual reality math game for learning in schools - a user study</article-title>
          ,
          <source>in: 2022 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW)</source>
          ,
          <year>2022</year>
          , pp.
          <fpage>808</fpage>
          -
          <lpage>809</lpage>
          . doi:
          <volume>10</volume>
          .1109/VRW55335.
          <year>2022</year>
          .
          <volume>00255</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>P.</given-names>
            <surname>Acevedo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. J.</given-names>
            <surname>Magana</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Benes</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Mousas</surname>
          </string-name>
          ,
          <article-title>A systematic review of immersive virtual reality in stem education: Advantages and disadvantages on learning and user experience</article-title>
          ,
          <source>IEEE Access 12</source>
          (
          <year>2024</year>
          )
          <fpage>189359</fpage>
          -
          <lpage>189386</lpage>
          . doi:
          <volume>10</volume>
          .1109/ACCESS.
          <year>2024</year>
          .
          <volume>3489233</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>T. A.</given-names>
            <surname>Mikropoulos</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Natsis</surname>
          </string-name>
          ,
          <article-title>Educational virtual environments: A ten-year review of empirical research (</article-title>
          <year>1999</year>
          -2009),
          <source>Computers &amp; Education</source>
          <volume>56</volume>
          (
          <year>2011</year>
          )
          <fpage>769</fpage>
          -
          <lpage>780</lpage>
          . URL: https://www.sciencedirect. com/science/article/pii/S0360131510003052. doi:https://doi.org/10.1016/j.compedu.
          <year>2010</year>
          .
          <volume>10</volume>
          .020.
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>R. E.</given-names>
            <surname>Mayer</surname>
          </string-name>
          , The Cambridge Handbook of Multimedia Learning, Cambridge University Press,
          <year>2005</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>M.</given-names>
            <surname>Noro</surname>
          </string-name>
          ,
          <article-title>Numbers playroom: a vr serious game to enhance children's engagement and numeracy skills</article-title>
          ,
          <year>2025</year>
          . Available on https://thesis.unipd.it/handle/20.500.12608/84821.
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>