The City as a Tool for STEAM Education: Problem-Posing in the Context of Math Trails

Abstract

This study presents an experience that combines problem-posing and Math Trails in the context of future teachers’ instruction. Pre-service teachers in the third year of their studies were faced with the design of tasks to be included in Math Trails for primary school students. The study analyzes, from a quantitative approach, 117 tasks contained in 11 Math Trails. The analysis was performed on the basis of classification variables (grade, mathematical content and object or real element involved in every task) and research variables which provide information about the nature of the tasks (procedural vs. problem-solving, level of cognitive demand, degree of contextualization, openness and creativity). Additionally, relationships between the different categories of analysis have been studied. The results reveal certain biases in the tasks in relation to the contents addressed (an abundance of tasks with a geometric component and a scarcity of tasks involving algebra or probability concepts). Most of the tasks are presented in a real context. However, a higher percentage of procedural tasks than problem-solving tasks is observed, with a predominance of low openness, creativity and cognitive demand. These results provide useful lines of work to address difficulties faced by future teachers in the STEAM field.

Development of a Mathematical Experience from a STEM and Sustainable Development Approach for Primary Education Pre-Service Teachers

“…Despite this, we believe that math trails are a great step in addressing the mathematical needs that future teachers will face [30]. Continuing with the design of the trails, we observe in our study that in line with previous research, students confirm that MathCityMap is a project with great potential and that it could be of great help to increase the problem-solving capacity of students when facing mathematical problems [7,10,44,45,56,58]. However, what most worries participants is the inclusion of tasks with a sustainable and interdisciplinary approach because creating mathematical tasks in the environment is not complicated; the really complex thing is to adapt them until they become STEM-SD tasks.…”

“…In this sense, we believe that it is essential to adequately prepare future primary school teachers and connect them with learning experiences in which outdoor STEM education is used as a facilitating resource for the teaching-learning of mathematics [44,56]. It is essential that in their professional futures, they know how to look for possible alternatives to traditional teaching that help enhance students' mathematical skills and ability to solve problems [57].…”

“…On the other hand, in the execution phase, future teachers and current university students perceived that the mathematical knowledge that was presupposed to carry out the proposed trails was greater than what they expected, so we conclude that it is necessary to delve deeper into the approach of the trail and test it properly before putting it into practice. As has been demonstrated in other intervention studies on STEM trails in primary education, it is important to design the trails taking into account the mathematical content, resolution procedure, level of cognitive demand, degree of contextualization, and creativity of the tasks included in the trail [44,56].…”

“…We have also been very struck by the tendency of future primary school teachers, and even active teachers, who have participated in the experience to think that math trails would be better applied in the last years of primary education. However, this is something that tends to predominate in the studies that have been analyzed; for example, in the study by [56], 55% of the STEM trails that were analyzed corresponded to the sixth grade, and those carried out in [44] were designed for children between 10 and 12 years old. Here, again, we think that this is due to the insecurity that many teachers claim to have due to not having sufficient training in mathematical educational innovation [63].…”

Investigating problem-posing during math walks in informal learning spaces

“…This study tested and established the possibility of implementing a purely online math walks program. In prior studies, math walks were mostly implemented through in-person programs where children and youth meet with their facilitators at the learning sites (Lancaster, 2021 ; Wang et al, 2021 ; Martínez-Jiménez et al, 2022 ). This study provided future researchers with some insights about implementing a completely virtual math walks program.…”