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Utilizing the theories of connectivism and social constructivism, this study examines the role of AR tools and overlays in facilitating mathematical thinking. I use these two lenses to work to understand how AR technology facilitates learners’ mathematical thinking and connects learners to each other to develop mathematical thinking skills.
First introduced by Siemens (2005), Connectivism places student learning in the context of the connected nodes that digital technology brings learners in contact with. Connectivism emphasizes the role of informal learning. This emphasis is especially appropriate in the context of the MathExplorer project, which takes place in informal learning spaces in students’ communities. Furthermore, the role of technology as a facilitator of a non-linear learning process, rather than a delivery mechanism, is emphasized. As such, not all students are working towards the same content goal but are following their own paths and have different ways of expressing their understanding. Students in the MathExplorer project come from a variety of learning environments. The artifacts they produce, in the form of their own math questions reflect not a predetermined outcome, but their own personal mathematical thinking.
Connectivism also understands that not only do we as humans create technology, but that technology shapes our brains. True to its name, it emphasizes the ability of learners to connect “fields, ideas, and concepts” as a “core skill” (Siemens, 2005, p. 6). This aspect of connectivism is especially relevant in the context of the MathExplorer project as the goal is to explore and advance ways in which a place-based technology can connect students to everyday objects in their communities to advance their mathematical thinking.
While connectivism focuses on the interaction of student and technology, technology-facilitated student learning takes place within a context of social interaction, and that must be considered (Bell, 2011). Thus, my analysis also conceptualizes student learning through the lens of social constructivism, which views learner construction of knowledge as a “product of social interaction” (Adams, 2006, p. 245). While AR tools and overlays are technologies that act as conduits for knowledge construction, they are also facilitators of social interactions, particularly given some of the unique ways that these tools are implemented in our app. The framework of social constructivism adds depth to the analysis of digital learning by recognizing the centering the learner as a social being (Constatinos & Rybska, 2024). Following this precedent, I examine how the social interactions resulting from the use of these technologies contribute to the development of student mathematical thinking.
This study is part of the larger MathExplorer project, a multiyear project carried out at several community-based locations in a large urban area. The project partners university-based researchers, a local STEM nonprofit, and community-based partners to develop the MathExplorer app. This location-based mobile app is used in conjunction with math walks in students’ local communities. During math walks, students ask mathematical questions about everyday objects in their environment, which are entered into the app and shared among students.
During year 3 of the larger project, the focus of this study, the use of AR tools was introduced into the app. This study examines data collected from 20 participants who attended a three-day Thanksgiving week camp at a local zoo. Part of a larger group, these participants used AR overlays specific to three different location-specific walk stops, one on each day of the camp. For example, in the Zoo’s Hippo Hut, the students used an AR overlay that showed, through their camera feed, a hippo growing from a baby to an adult, and tracked its length and weight in a table. They could view the virtual hippo and capture its photo while still viewing their surroundings live through the camera feed. They also had access to general AR tools they could use for measuring lengths, angles, and area, and for counting. These tools functioned by having students click on different positions and real-world objects in their live camera feed on their device.
The data collected over the course of the camp included camcorder recordings of participants as they engaged in math walks, screen recordings of their interactions with the app on their iPads, student-created “walk-stops,” in which students write their own mathematical questions and answers about objects in their environment coupled with annotated photos, and camcorder recordings of semi-structured focus group interviews as well as demographic information and pre- and post- surveys on attitudes towards math based on a Likert scale. Graduate and undergraduate students worked to create transcripts of all camcorder recordings and content logs of the screen recordings.
I will complete a content analysis of the transcripts of the video recordings of students, content logs of student screen recording, and student-created walk stops in order to understand the development of mathematical thinking during the AR activities and the reflection of mathematical thinking in products produced using the AR tools and overlays.
I am currently engaged in this process. My process is iterative and informed by the data analysis spiral (Creswell & Poth, 2018). I am currently reading, viewing, and memoing data, and expect to categorize and recategorize my codes before finalizing a coding schema (Saldana, 2021).
The analysis is partially completed. The expected finding of this analysis, based on the researcher's own anecdotal interactions with students during data collection and the preliminary analysis of transcripts and content logs is that the use of AR tools and overlays helped students think mathematically about objects in their environment, facilitated math discussions between participants, and led to the creation of questions which reflect mathematical thinking. However, there was variance in the degree to which different AR implementations were effective.
The results will look closer at the processes that took place, identifying and categorizing the ways in which the AR tools and overlays facilitated mathematical thinking on their own and by leading to student interactions. Furthermore, the content analysis will identify the types of mathematical thinking students engaged in. These findings will help educational technology designers, administrators, and educators the most effective ways to leverage AR technology to achieve the student outcomes they desire.
While this study takes place in an informal setting, in the context of current digital technology, the lines between formal and informal learning have been blurred significantly (Sangra & Wheeler, 2013). This study will help the conference audience understand the role of AR in facilitating mathematical thinking in all learners, furthering their engagement in math. With so many options for technology-enhanced learning available, this research informs effective decision-making when choosing which types and uses of technology to utilize to make an impact.
References
Adams, P. (2006). Exploring social constructivism: Theories and practicalities. Education 3-13, 34(3), 243–257. https://doi.org/10.1080/03004270600898893
Bell, F. (2011). Connectivism: Its place in theory-informed research and innovation in technology-enabled learning. International Review of Research in Open and Distance Learning, 12(3), 98–118. https://doi.org/10.19173/irrodl.v12i3.902
Chang, H., Binali, T., Liang, J., Chiou, G., Cheng, K., Lee, S. W., & Tsai, C. (2022). Ten years of augmented reality in education: A meta-analysis of (quasi-) experimental studies to investigate the impact. Computers and Education, 191, 104641. https://doi.org/10.1016/j.compedu.2022.104641
Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design (Fourth edition, international student edition ed.). SAGE.
Garzón, J., & Acevedo, J. (2019). Meta-analysis of the impact of augmented reality on students’ learning gains. Educational Research Review, 27, 244–260. https://doi.org/10.1016/j.edurev.2019.04.001
Garzón, J., Pavón, J., & Baldiris, S. (2019). Systematic review and meta-analysis of augmented reality in educational settings. Virtual Reality : The Journal of the Virtual Reality Society, 23(4), 447–459. https://doi.org/10.1007/s10055-019-00379-9
Pratiwi, H., & Nugraheni, N. (2024). How does an augmented reality-based pocket book enhance students' critical thinking skills? Al-Jabar, 15(1), 241–250. https://doi.org/10.24042/ajpm.v15i1.21650
Saldaña, J. (2021). The coding manual for qualitative researchers (4E ed.). SAGE.
Sangrà, A., & Wheeler, S. (2013). New informal ways of learning: Or are we formalising the informal? International Journal of Educational Technology in Higher Education, 10(1), 286–293. https://doi.org/10.7238/rusc.v10i1.1689
Siemens, G. Connectivism: A learning theory for the digital age. (2005). International Journal of Instructional Technology & Distance Learning, 2(1), 1–9.
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