Geometry with a STEM and Gamification Approach: A Didactic Experience in Secondary Education
Abstract
:1. Introduction, Theorical Framework and General State of the Field
1.1. ICT as Educational Support Tools
1.2. Active Methodologies
2. Materials and Methods
2.1. Objective and Research Questions
2.2. Population and Sample
2.3. Tecniques for Collecting Information
2.4. Action Research Cycles
2.4.1. First Action Research Cycle
2.4.2. Second Action Research Cycle
Session 1: Initial Assessment [92] 
Elements Depending on whether the answers are correct or not, a scoring system is assigned so that students can interact with the platform and their Classcraft avatars, virtual mascots, and powers. 
Mechanism 

Dynamics 

Session 2: Classification of geometric solids 
Elements Group 1 used the virtual polyhedron pieces that appear in the NeoTrie VR immersive environment, while Group 2 used wooden polyhedron pieces (Figure 7). Points were awarded in Classcraft based on each team member’s success in ranking the different classification categories. 
Mechanism Students classify different geometric solids according to various criteria or categories of analysis in two phases. 
Dynamics In the first phase, the students determine the classification criteria (e.g., number of faces, vertices or edges, shapes of the polygons of equal faces, etc.). In a second phase, the students classify the shapes according to the criteria given by the teacherresearcher (e.g., regular, and irregular polygons, number of dihedral angles, etc.). 
Session 3: Regular polyhedra 
Elements Classcraft scoring, allocation of powers according to the number of regular polyhedra constructed. Polydron game. Virtual reality tool NeoTrie VR. 
Mechanism Group 1 used the immersive environment NeoTrieVR, while Group 2 used the polydron game as manipulative material. Students determined the number of regular polyhedra. 
Dynamic The students built the shapes until they could close them and make a regular polyhedron. Some students completed five platonic solids, while the remaining were irregular or remained open. 
Session 4: Analysis and deduction of Euler’s theorem 
Elements The Classcraft score depends on the correctness of the student’s analysis of the polyhedra (virtual, wooden, Zome game). Students who could induce Euler’s formula and write it on the worksheet were awarded an extra power as a badge on the Classcraft platform. 
Mechanism Analyses the number of faces, edges, and vertices of polyhedra. Based on the examples anlyzed, induce the formula of Euler’s theorem 
Dynamic With the help of wooden or virtual polyhedra and a fillable card, students indicated the number of faces, edges, and vertices of each, and after a process of investigation and analyzing numerous examples, some induced the formula of Euler’s theorem. 
Session 5: Research works [96]. 
Elements Classcraft scoring, badges according to work done. 
Mechanism The options, after research and documentation of each proposal, were: to build an origami of a known polyhedron; to create a video about polyhedra that can be found in nature, art, science, and human constructions; to create a drawing or work of art about polyhedra in three dimensions if possible; to create a video game or digital quiz about polyhedra in nature, art, science, and human constructions (Figure 8). 
Dynamic Upon their return from the Easter holiday break, each student presented their research work carried out during their break to the rest of the class. Each member of the cooperative learning team produced material based on their research concerning polyhedra, which would form part of the presentation. 
Session 6: Gamebased learning 
Elements A series of selfcreated manipulative games adapted to the content covered were used, combining math questions and the art, nature, and science content shown in the work of Session 5. The games included a “who’s who” memory game, Pictionary, and a quiz game (Figure 9). Participants received a Classcraft score depending on the correct answers. 
Mechanism Play the games and rotate them every 10 min between teams. 
Dynamics These games combined geometry questions about polyhedra that appear in nature, art, science, and human constructions, some of which appeared in the research videos shown in the previous session (viruses, molecules, minerals, polyhedra in sculptures, paintings, buildings, album covers, and the animal world, etc.). 
Session 7: Game development, design, implementation, and testing 
Elements Card with rules, dynamics, mechanics, elements, and blank board to design the game. In this case, the students themselves awarded the Classcraft points according to how they considered that the rest of their classmates had interacted with the game created by each team, and how fun and useful it was. 
Mechanism The students created a game on blank boards by adding their dynamics, game rules, and whatever else they felt was needed to create a game with the same STEM focus as in the previous session (Figure 10). 
Dynamic Once they had been created and implemented, each team tested the boards of the other groups. 
Session 8: Symmetry planes and duals. 
Elements Classcraft scoring. Virtual reality simulator tool NeoTrie VR. Zome Game. 
Mechanism Construct the planes of symmetry and the dual polyhedra of platonic solids. 
Dynamics Group 1 drew the symmetry planes and the dual polyhedra with the virtual reality tool NeoTrie VR. Group 2 used the hollow methacrylate pieces and cardboard to manipulate the planes and the Zome game to make the dual polyhedral (Figure 11). 
Session 9: Truncated polyhedra or Archimedean solids [94]. 
Elements Scoring on the Classcraft educational platform. Polydron game. Sheet of paper with truncated polyhedra. Smartphone and QR codes. An augmented reality application. Badges and powers to use with avatars on the platform. 
Mechanism The whole class group construct Archimedean solids (truncated polyhedra) from augmented reality figures with manipulative material polydron (they could also be seen in the sheet of paper). 
Dynamic Visualize the different truncated polyhedra with the augmented reality mobile application by reading QR codes. Replicating these polyhedra with the pieces of the polydron set (Figure 12). 
Session 10 and 11: Axes of rotation of regular polyhedra 
Elements Scoring in Classcraft. Virtual reality simulator tool NeoTrie VR. Badges and powers to use with avatars on the platform. 
Mechanism Construct the axes of rotation of regular polyhedra (platonic solids) with NeoTrie VR. 
Dynamic The axes of rotation were made using the NeoTrie VR tool by the whole class in two consecutive sessions. Simultaneously, a dynamic with the Kahoot! tool was also created to review the contents given during the subject. 
Session 11: Review Kahoot! 
Elements Kahoot! game 
Mechanism Using a mobile phone and clicking on the game link in the application, each student participates by registering with a code provided by the teacher. 
Dynamic Digital quiz (Appendix B) pointing to one of the four options offered by the class digital whiteboard, on their mobile phone. The student with the highest score for the most correct answers wins. The game application establishes a ranking of the top three and provides statistics on the correct answers given by each student. 
Session 12: Final assessment: Breakout EDU 
Elements Puzzles, hidden message pills, boxes, and padlocks, QR codes, wooden polyhedra, scissors, crossword, encryption wheel, Thanos gauntlet and infinity gems, invisible ink, UV torch, Classcraft platform scoring, final prize, and individual diplomas. The event also included: video games application and quiz questions; a poster exhibition of women scientists and mathematicians; model of the layers of the earth’s crust; an augmented reality application; smartphones; NeoTrie VR and virtual reality glasses with controllers; countdown timer. 
Mechanism An educational Breakout is a gamification activity in which students must overcome challenges or missions to open a series of padlocks or a closed box. It is an immersive game similar to an Escape Room, but educational in nature. The project’s main objective is for students to experience an adventure and solve a problem. The duration to reach the final prize is one hour. 
Dynamics The central narrative theme of the Breakout EDU was based on the students’ preferences. The theme chosen was the “Avengers”. Each student had already been assigned their role through the Classcraft platform and had interacted with their avatar throughout the sessions. The video presentation sent out by the “Avengers” asked for their help in overcoming a series of STEM focused tests and challenges to find the infinity gems, place them in Thanos’ gauntlet, and help save humanity. The first thing each team found was a puzzle card that they had to solve to read the first message. This message led them to a “pill or quark” hidden in one of the layers of the earth’s crust (models made by them in the geology course). Inside the quark was a hidden message with coordinates to find a box. Box 1 contained a QR code that took them to a mobile video game that they had previously created in Session 5, with questions on the topic of geometric bodies, and by answering these questions correctly they obtained the key to the first lock for Box 1. Box 1 contained a blank piece of paper, a word search or crossword puzzle, scissors, QR codes, and an encryption wheel (Figure 13). Following a series of challenges provided through QR, solving names of Archimedean solids and questions related to polyhedra that appear in nature in the form of Archimedean solids and platonic solids (polyhedric viruses, polyhedric minerals), the team obtained the clue to the location of the ultraviolet torch. The torch would help them to see what was written on the blank paper with invisible ink. It revealed a figure of the polyhedron dual drawn on the paper and visible to the naked eye, which led to the next clue (Figure 14). The clue was a word created by crossing the lines of the crossword puzzle. This word was the name of a polyhedron in augmented reality visible through a QR code (Figure 15). Cutting out the cipher circle and matching the letters of that name with numbers would be the combination for the lock that opened Box 2. The clue inside Box 2 led to panels displayed in the Institute of Women Scientists to find out about the first woman mathematician who taught polyhedra with manipulative materials (Grace Chilshom Young). Hidden with the text was the number combination to open the penultimate box, Box 3. Inside Box 3 was a plastic figure of a regular polyhedron, of which they had to figure out its axes of rotation with virtual reality, or simply by signing in the air as some of the team members did (Figure 16). Once figured out, if the number of axes of rotation were correct, it would reveal the number to open the last lock on the box. This number was the same for the whole class. This last lock could not be opened without the help of the remaining teams and their numbers obtained from axes of rotation of each figure. Inside the last box was the gauntlet of Thanos, to which they were to attach the gems each team had found, along with the wooden polyhedron. One student was to put it on and give the snap when the whole class was present and gathered around it. Thus, they received their prize, which was nothing material but the satisfaction of having achieved it with enthusiasm and joy, which could denote intrinsic motivation. 
3. Analysis and Results
3.1. Analysis of the Context of the Experience
3.2. Comparison of Final Scores between Edmodo and Classcraft
3.3. Data Obtained from Kahoot!
3.4. Comparison of Final Assessment Sessions of the Two Action Research Cycles
3.5. Analysis of the Final Questionnaire on the Second Action Research Cycle
3.6. Analysis of the Cycle Student’s Comments from Classcraft’s Chat and Teacher’s Diary
3.7. Analysis of the Design of the First and Second Action Research Cycles
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
 What are regular polyhedra called?
 Are Platonic solids truncated, regular, irregular, or semiregular polyhedra?
 Which of the following are truncated polyhedra?
 The dual of a hexahedron is a…
 Which scientistmathematician proposed that an excellent way to learn geometry was to manipulate geometric shapes?
 The dual of an icosahedron is a…
 How many planes of symmetry does a cube have?
 Which of the following are truncated polyhedra?
 Which of the following geometric bodies are not bodies of revolution?
 The dual of an octahedron is an…
 C + V = A + 2 What is this Theorem called?
 What is the order of the axes of rotation of a cube?
 To make the axes of rotation of a cube, I can draw them… (Available options: from face to vertex, from face to face, from edge to face, etc.).
 The dual of a tetrahedron is a...
 A cuboctahedron has… (available options: different options between the shape of the polygons that form the faces and the number of faces of each)
 A truncated icosahedron is formed by… (available options: different options between the shape of the polygons that form the face and the number of faces of each one).
 If a polyhedron has six faces and six vertices, how many edges does it have?
 The polyhedra are classified as…
 Semiregular polyhedra are…
 If a polyhedron has 20 faces and 30 edges, how many vertices does it have? Is it regular?
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Cooperative Learning Role  Assignment Criterion  Objective  Avatar on Classcraft  Percentage Match Cooperative Role/ Avatar Role Classcraft 

Coordinator  Responsible, welldeveloped academically and empathetic pupils.  Manage the work and the team, but always taking everyone’s opinion into account.  Healers (recovering lives in the game, responsible role, students with good academic results).  100% 
Assistant or person in charge of equipment  Students who demonstrated creative skills.  Help choose the materials to be used during the experience.  Wizards (Maintains team powers and skills, role with socialisation problems, shyness). Healers  83% 17% 
Secretary  Restless, disruptive pupils.  Establish habits by being accountable for work to peers.  Warriors (Defend the team, active role).  100% 
Controller  Less attentive pupils.  Promote an atmosphere of concentration and responsibility.  Warriors Wizards Healers  66.7% 16.7% 16.6% 
Spokesperson  More shy and reserved pupils, with less social interaction.  They relate Unwittingly through its role with the rest of colleagues.  Wizards  100% 
First Challenge  Parallel Sessions 
The first challenge was to find polyhedra in the real world and everyday life, to bring some of these polyhedra from home to the classroom as they would be part of the activity of classifying geometric solids and the activity of inducing Euler’s theorem.  Sessions 2–4 
Second challenge  Parallel sessions 
The second challenge of this experience coincided with the Easter break and was launched in the holiday period. It consisted of using the social network Twitter, and each student had to tweet polyhedra that they saw in the real world with a photo, according to a series of hashtags and specific rules for retweets and likes [95].  Session 5 
Third and Fourth challenge  Parallel sessions 
Given that there was an exhibition about women in science, technology, and mathematics, in every corridor of the school, which had gone unnoticed by the students for years, the third challenge was the search for such women. The fourth challenge occurred at the end of Sessions 8–10, with a dynamic to build polyhedra through shadows. The shadows created with the light of the projector and the hands of the different members of each group tried to form the different geometric solids.  Sessions 6–11 
Fifth challenge  Parallel sessions 
The fifth challenge was a competition involving the creation of a video presentation with the theme and narrative for the start of the Breakout EDU. This competition was submitted to a vote by the students, and the video was chosen at the start of Session 12. It was the final challenge before facing the final assessment.  Session 12 
Final Position in Kahoot!  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18 

Number of correct answers  19  18  17  17  15  15  14  14  14  13  13  12  12  12  10  10  8  7 
Variables  Cycle 1 Gymkhana  Cycle 2 Breakout EDU 

Working system  Collaborative teams  Cooperative learning teams 
ICT  Virtual maps, smartphones  Smartphones, augmented reality, virtual reality and 3D glasses, video game apps with quizzes, QR codes. 
Manipulative Elements  Paper, tape measure  Paper, geometric shapes, invisible ink, ultraviolet light, boxes, padlocks, message pills, Thanos’ gauntlet, and infinity gems. 
Mechanism  Tracks via smartphone and on paper  Clues and challenges through initial video, QR, augmented reality, paper (crossword puzzle, message), apps, panels of women mathematics and scientists, and virtual reality. 
Dynamics  Repetitive same tools  Nonrepetitive and always with different tools and elements. 
STEM content  Inaccessible heights with mirrors and technology  Technology, polyhedra in nature, art and science, and human constructions, layers of the earth’s crust, atoms, geology, etc. 
Factor 1 
1. Using my mobile phone in class helps me learn (0.605) 
2. I like to learn more through games than through textbook activities (0.890) 
7. VR activities are easy for me (0.887) 
8. I can count the order of the axes of rotation better when I see it in Virtual Reality than with the textbook (0.898) 
9. It is easy to make symmetry planes. I would be able to make them right now with VR (0.639) 
10. VR helps me visualise objects I didn’t understand before (0.598) 
Factor 2 
3. I learn better by working as a team with my colleagues than on my own (0.941) 
11. The way I work these days makes it easier for me to communicate with my colleagues (0.598) 
Factor 3 
4. The class flies by when I work with maths games (0.645) 
5. I learn more when I have fun and participate more actively (0.628) 
Factor 4 
6. Over the last few days, I was able to confirm whether what I was doing was right or wrong (0.547) 
12. I have acknowledged my failures (0.514) 
ITEM  1  2  3  4  5  6  7  8  9  10  11  12 

Media  3.36  3.73  3.50  3.76  3.80  3.43  3.26  3.73  3.50  3.46  3.56  3.43 
Deviation  0.69  0.52  0.77  0.43  0.40  0.62  0.58  0.44  0.77  0.57  0.56  0.50 
Variance  0.47  0.27  0.60  0.18  0.16  0.39  0.34  0.20  0.60  0.32  0.32  0.25 
Statements  1. Strongly Disagree  2. Disagree  3. Agree  4. Strongly Agree 

1. Using my mobile phone in class helps me learn  0%  7%  50%  43% 
2. I like to learn more through games than through textbook activities  0%  3%  20%  77% 
3. I learn better by working as a team with my colleagues than on my own  3%  7%  27%  63% 
4. The class flies by when I work with maths games  0%  0%  20%  80% 
5. I learn more when I have fun and participate more actively  0%  0%  20%  80% 
6. Over the last few days, I was able to confirm whether what I was doing was right or wrong  0%  7%  43%  50% 
7. VR activities are easy for me  0%  7%  60%  33% 
8. I can count the order of the axes of rotation better when I see it in Virtual Reality than with the textbook  0%  0%  20%  80% 
9. It is easy to make symmetry planes. I would be able to make them right now with VR  3%  7%  27%  63% 
10. VR helps me visualise objects I didn’t understand before  0%  3%  47%  50% 
11. The way I work these days makes it easier for me to communicate with my colleagues  0%  3%  37%  60% 
12. I have acknowledged my failures  0%  0%  57%  43% 
Category  Indicators  Number of Comments  e.g., 

M (Motivation)  Interest in learning Rewards Participation Fun  Classcraft’s chat 54% Teacher’s diary 45%  “The classes have flown by, the bell goes off, and I say... are we done already?” “I’m going to miss the classes and making the shapes in virtual reality because you could see everything much better, and then you remember.” “I like to work like this in maths classes. It’s easier. When will we do it again with another topic?” “Of course, I would repeat this experience. Everything is much clearer.” 
AP (Academic Performance)  Qualifications STEM Competencies Reasoning  Classcraft’s chat 25% Teacher’s diary 27%  “I will always remember the symmetry planes of a cube.” “With virtual reality, you see things for real…clearer…I can imagine what they are like.” “I have never seen polyhedrons so close and so real. Now I can see them; before, I didn’t understand them. You can even get inside, and it’s as if you were doing it yourself, it’s easier, and I like it.” 
E (Emotions)  Satisfaction Tolerance Positive attitude Success  Classcraft’s chat 13% Teacher’s diary 20%  “Making polyhedra with virtual reality is easier, and I like it.” “I love working with my colleagues like this because if I don’t know something, I can ask them, or they can ask me, and we all help each other.” “When will we do this again, to learn a maths subject like this?” “I have done all the symmetry planes the first time.” “I have come up with a super cool drawing and origami.” “I have helped my partner when she has asked me, and we have learned together” 
Others  Interaction with ICT Others  Classcraft’s chat 8% Teacher’s diary 8%  Not relevant 
Motivation (M) 
M.1. Intrinsic motivation (interest in learning) 
M.2. Extrinsic motivation (Rewards) 
M.3. Participation 
M.4. Interactive platforms 
M.5. Novelty, fun, discovery 
Academic performance (AP) 
AP.1. Qualifications 
AP.2. Acquisition of STEM skills 
AP.3. Abandonment reduction 
AP.4. Meaningful learning and reasoning 
AP.5. Social networking: shortterm performance 
Commitment/Participation (CP) 
CP.1. Facing challenges 
CP.2. Permanence and engagement with ICT 
CP.3. Attendance and submission of work 
CP.4. Persistence after achieving goals, perseverance 
C.P.5. Common objectives 
Emotions (E) 
E.1. Tolerance of mistakes 
E.2. Positive mood 
E.3. Low level of anxiety 
E.4. Satisfaction 
E.5. Group success 
Group cohesion/cooperation (GC) 
CG.1. Unity, sense of belonging 
CG.2. Social skills 
CG.3. Contribution of all members 
CG.4. Altruism, cooperation, enrichment of approach 
CG.5. Interaction and communication with ICT 
Variables Associated with M  Point 0 Traditional  Cycle 1 Approximate Model to a Gamified Approach to STEM  Cycle 2 Complete Gamified STEM Model  

M.1. Intrinsic motivation (interest in learning)  Not applicable  Video research work on geometric proportionality made by students.  Evidence of research work from Session 5 (origami, videos, drawing, etc.) Results in Table 9 (M).  
M.2. Extrinsic motivation (Rewards)  Not applicable  Edmodo badges. Points and powers cards.  The entire Classcraft reward system (avatars, virtual mascots, powers, badges, challenges or quests, etc.).  
M.3.Participation  Traditional master class. Passive students.  12 sessions (2 master class and 10 practical). More active students.  12 practical sessions. Active students. Virtual interactions on the Classcraft platform. Results in Kahoot!  
M.4. Interactive platforms  Not applicable  Edmodo (homework and badge delivery).  Classcraft with a fully gamified system.  
M.5. Novelty, fun, discovery  Not applicable  Gamesbased learning (GBL), challengebased learning (CBL).  Gamebased learning (GBL), challengebased learning (CBL), narrative, simulators VR (NeoTrie VR), AR, apps, social media (Twitter), full STEM gamification.  
Variables Associated with AP  Point 0 Traditional  Cycle 1 Approximate Model to a Gamified Approach to STEM  Cycle 2 Complete Gamified STEM Model  
AP.1. Qualifications  2 “A Grades” (outstanding), 1 “B Grade” (very good), 10 pass grades, 15 fails grades.  8 “A Grades” (outstanding), 13 “B Grade” (very good), 7 pass grades. (Edmodo data points).  15 “A Grades” (outstanding), 13 “B Grade” (very good), 2 pass grades. (Classcraft data points).  
AP.2. Acquisition of competences STEM  S (Science)  Not applicable  Reflection and refraction rays are used to measure inaccessible heights through a mirror in an escape room. Geography in Gymkhana.  Geology (e.g., layers of the earth’s crust in Breakout EDU). Elements of nature related to polyhedral shapes (viruses, atoms, minerals, etc. in activities). 
T (Technology)  Not applicable  Use of interactive maps and mobile apps  Use of mobile apps (creation of quiztype video games in session 5). NeoTrie VR for the development of spatial visualisation skills (sessions 8, 10,11). Social networks (Twitter in second challenge). Use of augmented reality with QR codes (session 9). Participation in the virtual world of Classcraft.  
E (Engineering)  Not applicable  Construction of models of the classroom tables using scales.  Construction of polyhedra through origami, with and without face structure with paper and with games such as Zome and Polydron. Construction of polyhedra in NeoTrie VR.  
M (Mathematics)  Mathematics with blackboard and notebook  Mathematics (geometry) with mixed method: blackboard and notebook, introduction to active methodologies.  Mathematics (geometry) with active STEM methodologies gamified with Classcraft.  
AP.3. Abandonment reduction  Passive, bored pupils in the classroom. Absenteeism.  Active pupils, participation in the classroom. No absenteeism.  Active students, participation in the classroom and outside the classroom on the platform. No absenteeism.  
AP.4. Meaningful learning and reasoning  Not applicable  Demonstration of the Pythagorean theorem with puzzles. Selfinitiated calculation of inaccessible height with indirect methods as the day was cloudy and could not be done with shadows.  Deduction of the existence of only five Platonic solids, induction of Euler’s theorem, solving all the trials in the final assessment Breakout EDU. Statistical data results of hits from Kahoot! Results Table 9 (AP).  
AP.5. Social networking: shortterm performance  Not applicable  Not applicable  Using Twitter to develop spatial visualisation skills with a photo contest (number tweets, retweets, likes).  
Variables Associated with CP  Point 0 Traditional  Cycle 1 Approximate Model to a Gamified Approach to STEM  Cycle 2 Complete Gamified STEM Model  
CP.1. Facing challenges  Not applicable  Sporadic offline challenge.  Table 2 of weekly challenges and sessions.  
CP.2. Permanence and engagement with ICT  Not applicable  Not applicable  Extra NeoTrie VR sessions during break times. Twitter activity.  
CP.3. Attendance and delivery of work  Homework, often without feedback  Delivery in Edmodo or externally on platform.  Integrated Classcraft platform delivery, daily interaction with powers and avatars. Delivery of challenges and work in the sessions.  
CP.4. Persistence after achieving goals, perseverance  Not applicable  Not applicable  Construction of Archimedean polyhedra (football—truncated icosahedron) at the end of the class. When the next group came in, nobody moved until they had finished building it. They didn’t want to leave.  
C.P.5. Common objectives  Not applicable  Gymkhana for each group  Breakout EDU could not be resolved without the participation of all groups. Teams in Classcraft and the interaction between them and their components. Results Table 8. Results in Kahoot!  
Variables Associated with E  Point 0 Traditional  Cycle 1 Approximate Model to a Gamified Approach to STEM  Cycle 2 Complete Gamified STEM Model  
E.1. Tolerance for mistakes  Not applicable  Pythagorean puzzles attempted to the level reached by each team.  All sessions (e.g., attempting to create the polyhedra repeatedly with the construction games until they came out, giving wrong answers in the games but still participating and improving).  
E.2. Positive mood  Not applicable  They expressed enthusiasm for the methodological change proposed and showed interest in continuing the experience.  At the end of the Breakout EDU, the whole class applauded and hugged each other as a group, having managed to finish the task before the onehour time limit. The mood was very positive throughout the whole experience. Results Table 9 (E).  
E.3. Low level of anxiety  High level of anxiety (comments from students such as: “I can’t wait for this to be over, let’s see if I pass maths.”) “I’m getting desperate because I don’t know anything.” “I don’t want to be put on the board because I don’t know how to do it.” “I’m bored.”)  Medium level of anxiety (comments from students such as: “I’m nervous about the exam.” “What do I have to do to pass maths? We’re not doing exams.”)  There is hardly any anxiety. (There were no comments about not wanting to participate or go out in any of the sessions, or about the exam or being nervous about not knowing how to do something. Anxiety was only rarely expressed when they did not have time to finish building the geometric bodies. There was no penalty for an incompletion, only their desire to finish building it.)  
E.4. Satisfaction  Not applicable  Comments from students of satisfaction at the end of the course by the students: “I am happy with my work on this topic.” “I’ve managed to do everything you sent me. It’s been a long time since I’ve done that in maths.”  Results Table 8. Results in Kahoot! Results Table 9 (E).  
E.5. Group success  Not applicable  Inaccessible heights calculated in the courtyard, Pythagorean puzzles, Gymkhana  All sessions were cooperative and groupbased, including the Breakout EDU final assessment.  
Variables Associated with CG  Point 0 Traditional  Cycle 1 Approximate Model to a Gamified Approach to STEM  Cycle 2 Complete Gamified STEM Model  
CG.1. Unity, sense of belonging  Not applicable  Individual or collaborative work.  Cooperation when playing Kahoot! Cooperative learning work, Classcraft group membership with coats of arms and design of corporate identity.  
CG.2. Social skills  Not applicable  Some in the Gymkhana or measured inaccessible heights courtyard.  Twitter, Classscraft, in class exercising with their cooperative learning roles.  
CG.3. Contribution of all members  Individual work  Only in some sessions.  All sessions.  
CG.4. Altruism, cooperation, enrichment of approach  Not applicable  Only in Gymkhana.  All sessions.  
CG.5. Interaction and communication with ICT  Not applicable  Edmodo, interactive maps, QR codes with smartphones.  Classcraft, Twitter, AR, VR, QR codes, quiz video games apps, Kahoot! 
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MoralSánchez, S.N.; SánchezCompaña, M.ª.T.; Romero, I. Geometry with a STEM and Gamification Approach: A Didactic Experience in Secondary Education. Mathematics 2022, 10, 3252. https://doi.org/10.3390/math10183252
MoralSánchez SN, SánchezCompaña MªT, Romero I. Geometry with a STEM and Gamification Approach: A Didactic Experience in Secondary Education. Mathematics. 2022; 10(18):3252. https://doi.org/10.3390/math10183252
Chicago/Turabian StyleMoralSánchez, Silvia Natividad, M.ª Teresa SánchezCompaña, and Isabel Romero. 2022. "Geometry with a STEM and Gamification Approach: A Didactic Experience in Secondary Education" Mathematics 10, no. 18: 3252. https://doi.org/10.3390/math10183252