The following paper comes from one of the dimensions that make up the Yard4All project, built under the Erasmus+ program. To reform conventional education, escape the traditional four walls and get in touch with reality, this document exposes the importance of working mathematical concepts in concrete, bringing this curricular area closer to children's daily lives. According to Feille (2021, 2013), the schoolyard is an essential pedagogical tool in the holistic development of any child, that helps them achieve several skills.

When students are able to touch their learning, experience it in real life, their understanding seems to emerge like snap peas peeking out of the fresh dirt. Their green tips poking above the nourished and moist earth. Nurtured with care and attention, they stretch and reach for fresh air and sun. (Feill, 2013, p.1)

The theoretical component presented here is linked to a research question: What practical activities, using mathematical concepts, are necessary to promote the global development of children, while exploiting the schoolyard?

Consequently, this project essentially defines three main objectives: (i) Develop and improve, in every child, cognitive, social and emotional skills, throughout non-formal learning and teaching environments, using outdoor activities in the schoolyard, that follow the principles of permaculture, while using mathematical concepts; (ii) Develop practical and useful activities that motivate all children to have a positive attitude towards Mathematics, where the entire school community is included and can actively participate; and (iii) Create a guide for teachers and other educational actors, specifying some activities, within the scope of Mathematics, for children with special educational needs and children without impairments, between six and twelve years old.

Firstly, it is important to define permaculture, since all the activities created are based on it. Permaculture is a form of agroecology and an alternative paradigm of production, based on ecological principles such as recycling waste, minimizing energy and water use, maximizing genetic diversity, regenerating soil, and promoting other beneficial biological synergies (Hathaway, 2016). Permaculture school gardens offer particularly valuable opportunities for a sustainable education, crucial for the XXI century learner. This practice is innovative in the school context and can provide children with practical experience of sustainable production means (Yard4All, 2022). But to work in a learning environment with these principles, children need to go outdoors and get to know nature, sense the biosphere, and explore their motor, cognitive, emotional, and social abilities. In fact, while discovering the schoolyard, children find opportunities to make decisions that encourage problem solving and creative thinking (Sá, 2016). Mathematics is often seen by children as a “bogeyman”, being considered not very humane and useful for everyday life. But Mathematics is in any day-to-day circumstances, and it is possible to relate it to various topics, formally and informally. The Yard4All (2022) project focuses on one of the most appropriate ways to work with Mathematics nowadays, using it with context. Mathematics in Context aims to use mathematical concepts in significant real contexts, moving from concrete and informal situations to the formal understanding of abstract concepts (Martins, Fernandes, & Guedes, 2020). This allows children to gain confidence and feel predisposed to learn Mathematics, in a place where they are curious, safe and, at the same time, have unpredictability (Feille, 2013) – the schoolyard. As a pedagogical tool, the schoolyard allows children to participate in the development of “their social and cognitive abilities, their sense of connection with other people, with nature and their natural environment” (Tsevreni & Bentenidi, 2013, p.39), including children with special needs. The schoolyard is a place where everyone can have their sense of belonging and participate in decision-making, characteristics of an inclusive education.

Within the European area, activities involving the use of mathematical concepts in the schoolyard were developed by four different countries: Portugal, Spain, Romania, and Hungary. In each school, the methodology was adapted according to the educational context, in specific, according to the characteristics of the space, the children (individually), and the work group (child-child and child-teacher relationship). The activities used in this project contained: concept development periods, that focused on revealing student’s prior knowledge of mathematics; moments for developing students' understanding of import mathematical ideas, linking concepts to their previous mathematical knowledge; episodes of problem solving, assessing, and developing students’ ability to apply the mathematical knowledge in real and significant learning contexts; and stages of reasoning development, in a flexible way for non-routine and unstructured problems, in the field of mathematics, using situations linked to the school’s garden. The activities were also designed for an average time of 90 minutes, but the teacher can evaluate and adapt these activities to the desired duration, with a minimum time of 45 /50 minutes. The methods used while applying the created math activities were various. One of them is called peer learning. Peer learning refers to “the use of teaching and learning strategies in which students learn with and from each other without the immediate intervention of a teacher” (Boud, Cohen & Sampson, 1999, pp. 413-414). The teacher was responsible for forming the groups, according to each activity purpose, so each group had between two and four children. The learning contexts incorporated children with special educational needs and children without impairments, from six to twelve years old and, because of that, teachers were able to do a pedagogical differentiation, based on observation in class and through reports prepared by Special Education teachers. In conclusion, the instruments for collecting information included direct observation, photographic records, written records by the children and the analysis of questionnaires given to the children, their caregivers/family, and their teachers.

In Yard4All (2022), a math guide was prepared, with enriching outdoor activities, namely in the school garden/ schoolyard. The pilots were carried out in the schools of the four countries stated and, the collected data provided final reports that reveal several findings: 1. The Mathematic guide from the project should be recommended to other schools and Mathematic teachers; 2. The guide will be improved so it can provide a greater variety of activities, including different approaches, innovative changes and new ways to work in and with the schoolyard; 3. Children showed enthusiasm and were motivated during the activities carried out within the framework of the project; 4. The existence of a permaculture garden in the schools was important, due to the different situations it provided for the school's service and because it was an inclusive environment. It also proved the following: “(…) schools and local communities have a symbiotic relationship. Permaculture offers an ethical system to reintegrate the care and edification of the next generation” (Raynolds, 2022, p.2); 5. Children said they learned and felt good when they were performing the tasks at the schoolyard; 6. Collaborative work and social skills were developed, which also demonstrates the benefit of a peer learning approach; 7. Children also liked to be in contact with vegetable gardens, comparing them with their owns at home, and they loved to take care of them and to be in contact with the plants and the soil; 8. It is a simple and unique way and opportunity to develop skills such as observation, planning, cooperation, communication, decision-making and the possibility of exploring their own interests; 9. The families, who took the pilot and responded to the survey, rated the project very highly. The comments that children made to their parents about the project were also very positive.

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