Math pathways emerging from Design Thinking methodology

Abstract

Access to knowledge is no longer in the restricted domain of schools and becomes accessible through the most diverse digital supports. The pandemic disruption has taught us all, in a long experience of several months, that the adaptation of teaching and learning processes, without the physical presence of the teacher and in an interaction, at a distance, with their students, is not only possible but faster than initially thought to be. During this period things changed at breakneck speed, continuing to roll at a no less breakneck speed, in a way that teachers and students have to adapt. There are still many aspects that remain the same old way. Creativity is a demanding need for future success, including dealing with permanent change. Motivation takes many forms, but it's still the force that keeps many of us moving. Another characteristic that contributes not only to this purpose but also to the well-being of all of us is empathy, which we must make a point of promoting. Instead of continuing to discuss in collegiate colloquiums or in the teachers' room, the option, in this work, was to take the risk of doing. Giving up on the persistent questions of balance between the formal and classic forms of face-to-face teaching and non-formal approaches. Looking for the transposition of mathematical concepts to common aspects present outdoors, in the streets and parks, it seemed a good idea to engage students in the discussion and construction of the possible strategies to reach a such challenge. The math pathways are a possibility to do this transposition. This study involved a math pathway conceived under the Design Thinking framework, having in mind the promotion of mathematical learning for students attending the third cycle of Portuguese basic education. To achieve this objective, the following research questions were outlined: - How does the Design Thinking methodology contribute to the design of a math pathway as a teaching strategy? - What are the problem-solving strategies used by students associated with the math challenges of the conceived math pathway? Adopting a mixed approach where data were collected through an individual questionnaire, focusing on approaches that they considered more promising to their math learning of mathematics, applied to 271 students, attending 7th and 9th grades,12 to 14 years old, of a Portuguese school; and the 19 written productions of the students, who performed the math pathway. The results obtained suggest that the Design Thinking approach proved to be an adequate methodology for designing the math pathway adapted to the interests expressed by the students, namely, learning outside the classroom; use of digital resources; collaborative work, and interdisciplinarity between different subjects. Students were most confident in data collection and organization, and in presenting their solutions, following distinct paths of reasoning. About their strategies, the following were identified: direct measurements with standard and non-standard measurement instruments, to calculate, for example, the diameter of a sphere (city monument), and inaccessible heights; technological resources were also used, highlighting the use of GeoGebra for modelling.