In this section, the researchers present the results of the study through the CRMT tool (Aguirre & del Rosario Zavala, 2013). They selected six dimensions of the CRMT tool which applied to themes analyzed from the data (language and social justice dimensions were not included in the data analysis). These dimensions included: intellectual support, depth of student knowledge and understanding, subject analysis, communication and discourse, student engagement, and the integration of the students’ funds of knowledge, cultures, and backgrounds. The researchers also discussed, within the dimensions of CRMT, the interaction between human (students) and nonhuman (technology/digital tools) actors in the AR and VR activities.
Intellectual Support
First, as a class, students discussed the differences between AR and VR technologies. Then, students explored and experimented with different coding, design, and digital reality materials and apps, such as the augmented tangible materials – the MERGE cube, the VR goggles, and AR books (i.e., premade technologies). Next, they created their own augmented reality in Cospaces Edu (i.e., scaffolded instruction from premade to creating their own AR). Additionally, students designed a character or visual robot to be simulated in an AR setting for the iRobot book and they controlled and manipulated (e.g., increased/decreased the scale) the characters (e.g., dinosaurs) in the AR setting while using the Jurassic World book. They also had to put into practice their problem solving and critical thinking skills to figure out how the technology worked and how to move the iRobot or dinosaur character to follow a linear path in a specific direction (see Figure 1).
Depth of Student Knowledge and Understanding
Many students used mathematical thinking when creating their digital animations. When designing the 3D objects in Cospaces Edu, students had to consider mathematical concepts, specifically of movements, measurements, and rates such as clockwise and counterclockwise rotations, angles, circumference, radius, distance, and speed when assembling or writing codes for animating characters. For example, one student coded the two characters (rooster and mouse) in their story to rotate in a circular motion to simulate a chase, one animated character running after another (see Figure 2). The student explained, “there’s a rooster and a mouse, running after each other and fighting” (P31, year 2). To code this animation, the student would have to understand that a repeated turn by 360° with a displacement of a radius of 1 meter per second per turn would create a navigation along a circular path (see Figure 2). The students demonstrated their understanding of circles, radii, and clockwise rotations and movements by writing code for the characters in their story to simulate the rooster chasing after the mouse (see Figure 2). The sequence of the code was a key factor in determining which character comes first and which one follows (i.e., the rooster was first and then the mouse second: the rooster was running after the mouse and not the other way around). Because AR and VR simulations are three-dimensional in nature, the students had to rotate the characters in the x, y, and z axes or planes. When creating a 3D model of the MERGE cube, there were some digital constraints related to the story illustration. The nature and magnitudes of the movements had to consider the dimensions, measurement, shape, surface area, and volume so that the animated characters fit within the dimensions/constraints of the cube. As such, students were speaking about the measurements they chose to ensure the characters did not run off the edges or lift off the surface of the plane of the cube.
Subject Analysis
As a class, students discussed the question: In what ways is video game designing related to mathematics constructions? Students specifically examined how different drawings, graphs on the x-y plane, and the patterns and rules for their relations – linear, circular, curved (e.g., exploring linear, quadratic, and exponential functions taught in the grades 8 to 11 mathematics curriculum) are used when writing the code for their animated characters, in order to be seen to move across the screen or a physical cube. Some students used several digital tools all at once, such as a hand-held connected device (i.e., iPhone or iPad) and a physical object (i.e., MERGE cube), with a potential for augmentation through a wireless connection using an app (i.e., Cospaces Edu). Some students created a simulation of characters within a story on a screen, while others created an augmented reality that they could interact with using the MERGE cube and handheld device.
When students were asked to reflect on their learning of mathematics, coding, technology, and other subject areas, they said the tools and process of animating and simulating inspired them to create and animate game-like characters, some of which they felt embodied them in the game as one of the characters. For example, one student said, “I am at the top right here and I am the king of the monkeys and dragons, and they are all dancing” (P28, year 2). Students used mathematical concepts when programming their animations, such as “rotation and geometry during creating in the Cospaces” (P26, year 2) and “angles” (P31, year 2). Students also had to consider the distance and relative position of the animated character from the cube so that it was easier to locate the virtual image on the iPhone or iPad screen (i.e., projection of their visual story on the MERGE cube). Other students created code that incorporated abstract concepts, such as the x, y, and z axes in which their characters would rotate three-dimensionally on top of the x-y axis and lift off in the x-y-z space or plane (see Figure 3). In Figure 3, the student coded one character, Raccoon 1 to rotate at a speed of 4.5 meters forward in a time-lapse of 1 second (4.5 meters per second) around the x, y, and z axes compared to the other character, Racoon 2, which took 2 seconds to rotate around the axes. In the sequence of code, the raccoons followed a linear path (4.5 meters forward in 1 second) and a non-linear path (turn 90° clockwise around the x, y, and z axes starting at the coordinate x = 90, y = 0 and z = 1). Students were able to use mathematical thinking and modelling to better understand abstract mathematical concepts when coding their animated characters in Cospaces Edu. In the STEAM camp, students learned about both coding and technology. One student said “I learned how to animate stuff in Cospaces. I could do my own MERGE cube in Cospaces [and] I felt good through the process” (P26, year 2). Similarly, another student expressed, “when I was creating an animation in Cospaces, I used coding to allow my characters to move around” (P39, year 3). Another student explained, “I learned how to add codes to move my character like how to make it speak and animate it to do moves” (P47, year 3). Some students made the connection between mathematics and coding “I learned that coding, math, animation, and 3D are all types of math that can lead to different activities like games and programming robots” (P38, year 3).
Communication and Discourse through Digital Storytelling
Beyond the curriculum content, digital storytelling appeared to be integrated into the design and animation of the 3D environment in Cospaces. For instance, in one design scenario, a student crafted a narrative focused on the rescue of baby animals (a baby pig and a baby sheep) who were being pursued by enigmatic creatures in a dense forest. To create a sense of urgency, the student coded these screen-based characters to cover 30 meters in 5 seconds, ensuring their swift movement in unison (toward safety in the scenario). The student had to consider mathematical concepts such as speed, direction, position on the coordinate plane, linear and non-linear movements, angle of rotation, and radius when animating the characters in this digital story world. Another student created a story around a common fantasy animal, a magical unicorn. In writing the code for this character, the student wove in verbal expressions which used slang terms and phrases, such as “cool,” “rudee” and “bro you have to know you are human and you can think,” “If you think you're so cool. What's the magical spell to turn the unicorn blue?” These slang terms and phrases were part of the narrative the student wrote for the animated characters (see Figure 4) in a story in the AR world.
One instructor noted that most “students seemed to interact with each other more during the AR and VR centres, they grouped with different students who they had not previously worked with throughout the [STEAM] camp and explored the tools together” (Instructor 1, year 2). Students who were more comfortable with the technology supported others who were less familiar with using the digital tools and software (e.g., coding in Cospaces Edu). One instructor explained, “some students, who figured out the features of the programs/apps/tools earlier aided their peers” (Instructor 2, year 2). For example, “during the Cospaces activity, one student had problems with how to move his 3D model, and his friend saw [him struggling] and showed him how to do it” (Observer 1, year 3). Another student explained to his peers how to add aesthetic features, such as music and sound effects to play in the background as the animated characters moved. Students were proud of their work and wanted to share it with others. One researcher noted that “each student was positive and confident in presenting all of their work to their parents . . . [Similarly, another] student showed his Cospaces work and his MERGE Cube work to all the instructors after he finished them” (Observer 1, year 3).
Student Engagement
Overall, the students appeared to be more engaged during the AR and VR integrated activities compared to earlier lessons which were solely screen-based and did not include either digital or physical tangibles. One student expressed, “I learned how to animate 3D stuff. It made me happy… I like doing Cospaces. Because it allows you to create virtual worlds and stuff” (P26, year 2). Similarly, another student said, “I was excited to try the AR/VR and excited to make a mini world” (P48, year 3). “I was excited [about] . . . Cospaces because I find it really fun and cool to create your own codes” (P47, year 2). One researcher reflected when he “compared to previous days [of the camp] they were more engaged in the activities. They completed multiple activities on the same day” (Observer 1, year 3). One instructor noted that the “students who engaged with the AR books, hologram projector, and MERGE Cubes were highly engaged, asking questions, and enjoyed the activities” (Instructor 4, year 3). Further, the researchers observed how the students became excited about creating and simulating their own augmented reality, AR, in Cospaces, and interacting with it using the MERGE cube. One instructor elaborated on why the students felt this way. The activities were “really . . . engaging, . . . very interactive and fun. And the kids seemed to really like it” (Instructor 3, years 2 and 3). Another instructor noted:
For the most part . . . they're very engaged, like, they're very interested in the stuff they were doing, especially when they knew that they got to go into the computer room and start building stuff just out of their imagination. Like, they were very excited about that (Instructor 4, year 3).
The students also used their senses (sight, sound, and touch) to query and interact with the AR and VR tools. Using the Cospaces Edu app on handheld devices (iPhone or iPad) the students were able to interact with the digital animation that was projected on the MERGE cube (see Figure 5) and VR goggles (see Table 1). Students were able to physically rotate the MERGE cube in their hand and look at their animated characters from different perspectives (i.e., top, front, and side views), and to increase or decrease the scale of the 3D objects projected on the MERGE cube, depending on how close or far away the MERGE cube was from the handheld device (iPhone or iPad). Several students decided to add sound (i.e., music or sound effects) and gestures when writing code for animating their characters to speak, and actions when writing code for animating their characters to dance, jump, and run following a geometrical path such as a circle. For example, one student programmed the MERGE cube to play cricket noises in the background of the 3D campfire scene they had created. The students were able to engage with AR and VR technologies through visual, movement, auditory, and kinesthetic interactions.
Students’ Funds of Knowledge, Cultures, Backgrounds, and Interests
In some instances, students appeared to make a connection between their culture and the mathematics taught in the lessons/activities:
When you think about math, and how it relates to art, like some of the artwork, or some of the architecture was in mosques, a lot of the students were able to kind of see that and relate because they go to their mosques every week. And so, they're able to recognize that there is math within our world. . . [and making] those connections . . . being able to believe that math can be intertwined with their culture, and like they're not two completely separate things (Instructor 4, year 3).
The instructors reflected on how the students were able to make other connections to their culture and explore their own identity. One instructor expressed, “they were able to think about culture and other people's cultures and recognize that culture does play a really big part in people's lives. And stories reflect people's cultures . . . and how it [culture] kind of forms their own personal identity” (Instructor 4, year 3). Similarly, another instructor noted: “The students were able to . . . reflect on their culture, and their identity and their likes and their dislikes, and how they saw themselves . . . bringing in like different symbols that were representative of their” culture (Instructor 3, years 2 and 3).
Specifically, in the AR and VR activities, students incorporated images, symbols, and cultural monuments from their family's culture and background as well as historical buildings and places of interest into their designs. A student commented: "I saw a mosque which really reminded me of my culture [beliefs] because I am Muslim and Muslims pray in the mosque" (P22, year 2) and "[I chose] Dubai because it is my culture [country of origin]" (P36, year 3). Others wanted to explore historical and religious monuments and places of interest, such as "castles in Portugal, and mosques in India" (P44, year 3). Additionally, another student expressed that she wanted “to explore [new countries, traditions and cultures] something that [her] family is not connected to at all, China" (P37, year 3). The students appeared to realize what they envisioned as they created and animated their MERGE cube in Cospaces. To do that, they had to integrate some mathematical aspects, such as lines, measurements, symmetry, area and volume into the design of the monuments and manipulate the 3-D objects by increasing/decreasing the scale and rotating it three dimensionally, among other transformations.
The students appeared to seamlessly incorporate the mathematics and cultural aspects of their digital creations as they shared their projects with the instructors/researchers. For example, one student described her creation in Cospaces and the mathematical concepts represented in her digital creation, “the plane takes a full spin around the earth. It stops at different places such as New York, Rome, and Dubai. The angle is 360 because it takes a full circle [to rotate around the MERGE cube]. The low number [i.e., radius] makes it faster. For example, if it’s 1, the plane moves super-fast,” as seen in Figure 6 (P54, year 3).
The instructors found that “some students [succeeded in incorporating their culture and background into their digital designs while others] struggled to make those connections . . . so then some of them would like, struggle to go more in-depth” during the cultural component of the activity (Instructor 3, years 2 and 3). This made it difficult for timing because “some students would put so much time and effort into it, and then others maybe, like finished more quickly” (Instructor 3, years 2 and 3). The instructors had to anticipate and provide extension activities for those students who finished earlier (e.g., students were able to create multiple digital worlds in Cospaces and explore them using the iPhone, iPad, and/or VR goggles).