Mathematics is often perceived by students as abstract and disconnected from everyday life, contributing to anxiety and learning difficulties. This study presents an innovative educational experience that takes mathematics outside the classroom with a dual objective: on one hand, to reduce students' sense of hostility towards the subject by engaging them in a more stimulating and immersive environment; on the other, to develop problem-solving skills through real and concrete situations.

In recent years, there has been growing attention towards outdoor practices involving mathematics. Cultural itineraries have been created in cities and museums, many times in the form of a game, sometimes designed by teachers themselves also using apps like Map City Math. Our proposal adds to these existing initiatives by focusing on the possibility of creating curricular lessons outside the classroom, allowing students to work in a different environment and with alternative operational approaches compared to the traditional use of paper, pen, and standardized measuring tools. We design oudoor lessons for middle school students that do not involve the use of apps, as mobile phones are not allowed in Italian middle schools, and in many cases, no other devices are available for students.

Our project focuses on measuring the area and perimeter of non-standard shapes. Unlike traditional classroom problems, which are often simplified using familiar geometric figures, this experiment confronted students with authentic challenges, encouraging them to develop measurement strategies based on simple, readily available tools (such as ropes, strings, and improvised protractors).

To tackle these issues, we designed a learning pathway that allows students to concretely explore the difficulties of area calculation, considering both real physical spaces and scaled representations. The proposed activities included: measuring the perimeter and area of an irregular quadrilateral, created by stretching colored strings between four trees at a height of approximately 1.5 meters; measuring the perimeter and area of a leaf, with the goal of comparing different approximation and decomposition strategies.

During the experiment, students adopted non conventional approaches, such as decomposing the quadrilateral into triangles or using strings to measure the contour of the leaf. The difficulties in physically managing the problem in the real situation and in using mathematical tools have generated interesting discussions.
This study aims to analyze the strategies adopted by students, the challenges they faced, and the potential of an experiential, hands-on, and "de-schooled" approach to mathematics education.

The project was initially tested with a group of prospective teachers and later implemented in four middle school classes, involving a total of 90 students. In one school, a drone was also used to capture an aerial view of the quadrilateral, allowing for further discussion on scale representation.
At the end of the project, data was collected on student and teacher feedback regarding the effectiveness and engagement of the activities.

Keywords: Mathematics education, outdoor, active learning.