Several studies (e.g., Barbosa & Vale, 2016; Vale et al., 2019) have emphasized the importance of working with mathematics outside the classroom as a complement to the formal teaching and learning context. These studies highlight its potential in promoting positive attitudes and increased student engagement. In this context, mathematical trails stand out as a strategy that reveals the connections between mathematics and reality, particularly with the surrounding environment. The evolution of technology, especially mobile devices and their applications, has influenced the way students access information and even how they solve problems. These digital resources are seen as facilitators for developing 21st-century skills. The MathCityMap (MCM) app was designed with this purpose in mind, allowing users to create and solve tasks organized within a math trail that integrates real-world contexts with a digital environment.

Believing that these approaches are relevant for mathematics education and for developing key competencies, we introduced this technological resource to future elementary school teachers (ages 6-12). Our goal was to understand their perspectives on using mobile devices for learning mathematics outside the classroom. Based on this problem, we stated the following research questions: (1) What potential and limitations do participants recognize in MCM?; (2) How can we characterize participants' reactions to a math trail conducted with MCM?

School mathematics should be guided by a set of principles (NCTM, 2014), particularly seeking to provide students with meaningful and authentic learning experiences that help them attribute significance to mathematical ideas and concepts. The lack of adequate teaching and experiences that allow students to truly appreciate the essence of mathematics can lead to a negative perception of the subject (Kenderov et al., 2009). In this regard, non-formal learning contexts, such as the surrounding environment, can complement classroom work, adding meaning and applicability. Although mathematics teaching and learning mainly take place in the classroom, we believe in the importance of diversifying learning contexts and experiences. Among these, math trails are a valuable approach, which are defined as sequences of tasks along pre-planned routes (with a beginning and end), consisting of stops where students solve mathematical tasks in the environment (Vale et al., 2019). Participants are challenged to solve authentic and stimulating mathematical problems, applying acquired knowledge to real-world situations while developing problem-solving, communication, and connection-making skills (Richardson, 2004).

Digital technology, particularly mobile devices, is fully integrated into students' daily lives. This reality implies that teachers should be aware of technological trends and incorporate these resources into their practices when relevant. Moreover, mobile devices are becoming powerful tools not only in the classroom but also outdoors, fostering more meaningful learning experiences (Shuler, 2009). This type of technology is no longer merely a functional accessory; it allows students to move freely, collect and process data anytime and anywhere, improving social interactions and enabling a more personalized learning experience (Shuler, 2009). An app that combines mathematics outside the classroom with mobile learning has been developed: MathCityMap (https://mathcitymap.eu/pt/). Designed for mobile devices, this application enables users to complete mathematical trails created through an online portal where tasks are submitted and linked to GPS coordinates. Users access the trail and the associated tasks using GPS navigation, input their solutions via mobile devices, and receive immediate feedback on their validity. Additionally, MCM offers up to three hints to guide users toward a solution when they encounter difficulties. These hints are intended to assist rather than provide direct answers. This mobile app has proven useful for exploring mathematics outside the classroom through problem-solving. It supports both teachers and students in the teaching and learning process, including motivational and affective aspects (Barbosa et al., 2022; Cahyono & Ludwig, 2019).

This study follows a qualitative and interpretative approach (Erickson, 1986) and involved the participation of 48 future elementary school teachers (ages 6-12), most of whom had little or no experience with mathematics learning outside the classroom. Therefore, an initial questionnaire was administered to understand these pre-service teachers' prior ideas regarding teaching and learning mathematics outdoors, as well as the potential use of mobile technology in this context. In a second phase, participants were divided into groups of 3 or 4 members and completed a math trail organized by the researchers in the historic city center, using the MCM application. The trail included tasks covering diverse content areas and varying levels of cognitive demand. During the activity, each group had access to a mobile phone to access tasks and submit responses, a folding ruler, and a calculator, sharing responsibilities among members. Following this experience, a second questionnaire was administered to analyze changes in participants' perspectives and gather their opinions on using MCM. Data collection methods included observation, two online questionnaires, and photographic records. The questionnaires mainly consisted of open-ended questions designed to obtain detailed responses regarding participants' understandings, interpretations, and reactions. Data analysis followed an inductive approach, using content analysis (Miles & Huberman, 1994). The data were reduced to establish a categorical system for organizing insights into the potentialities and limitations of MathCityMap, as well as participants' reactions to completing the mathematical trail, which were considered key categories of analysis.

The first questionnaire revealed that most participants (91%) believed mathematics could be taught and learned outside the classroom, citing examples such as daily life situations, counting activities, games, clubs, field trips, architecture, nature, and math trails. However, 87% reported never having experienced mathematics learning outdoors. Additionally, 60% were unfamiliar with digital resources for exploring mathematics outside the classroom, while the others mentioned digital games, applications, and robots, though none specifically met the intended purpose. During the math trail using MCM, groups demonstrated autonomy in solving the tasks, finding the app easy to use. At each stop, they accessed the task, observed relevant objects, and collected necessary data (e.g., measurements, counting). The app’s gamification feature, which awards points based on answer accuracy, was motivating and encouraged careful answer submission. Participants also valued the hint system, which supported autonomous problem-solving. The MCM-based math trail fostered collaboration within and between groups, as they worked collectively to complete tasks. Participants remained engaged throughout the activity, though some tasks requiring lengthy calculations were perceived as more demanding. The immediate feedback from MCM encouraged motivation and active participation. The second questionnaire confirmed that all participants recognized the value of this non-formal learning context in complementing traditional mathematics instruction. They appreciated the challenge and the integration of historical and cultural elements but found extensive calculations less engaging. Key strengths of MCM included its intuitive interface, potential for interdisciplinarity, immediate feedback, and ability to diversify educational contexts. However, limitations such as limited Wi-Fi access and the lack of mobile devices for younger students were noted. In conclusion, the combination of math trails and MCM’s interactive features enhanced engagement and learning. Pre-service teachers acknowledged the importance of technological advancements and expressed interest in integrating MCM and math trails into their future teaching practices, emphasizing the value of this experience.

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