There are many students who dislike mathematics, or don’t understand the purpose of studying it, because they never had the chance to feel mathematics and enjoy it or maybe they had not opportunity to be exposed to an adequate teaching. Even if students aim to understand mathematics, very often and for many reasons, they can’t make connections among several subjects and make use of different tools to approach the same problem. According Kenderov et al. (2009) the classroom is only one of the ‘‘homes’’ of education. The process of acquiring information and develop students knowledge takes place of many forms and in many places. Using the outdoors as a classroom environment can promote positive attitudes and a deep appreciation towards the study of mathematics, perceiving the real-life application of mathematics. A Mathematical Trail “consists of a sequence of stops along a pre-planned route on which students examine mathematics in the environment” (Cross, 1997, p. 38) and offers concrete learning experiences for any of the mathematics concepts taught in the school curriculum. It also offers enormous potential for learning experiences at all ages. This activity, among other features, creates a space for informal meeting on the learning of mathematics simultaneously accomplish the approach to problem solving, making connections, communicating, and applying skills in a meaningful context (Richardson, 2004). A bounty of opportunities exist to utilize the outdoors in orchestrating learning experiences, not only in mathematics, but also through the integration of knowledge with outcomes stated in other curricular and not curricular learning areas. Because it takes place outside the classroom, a math trail creates an atmosphere of adventure and exploration and, at the same time, gives students an opportunity to solve and pose problems. By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding, having also opportunities to develop their creative thinking. Teachers are the main vehicle for doing this because they have the power to unlock the creative, innovative and critical potential of young students. If we believe that learning mathematics is strongly dependent on the teacher and creativity is connected with problem solving and problem posing, it is necessary, thus, to offer pre-service teachers diverse experiences, in order to develop their problem solving skills.

Teacher education should promote a new vision about mathematics knowledge and teaching, allowing future teachers experiencing the same tasks that we expected they will use with their own pupils.

In recent decades, problem solving has played an important role a bit around the world as an organizing axis of the mathematics curriculum. Students’ mathematic learning should include more than routine tasks, it should be enriched with challenging tasks, such as problem solving. This is of great importance, not only for students but also for teachers, especially if these tasks lead to structural understanding of mathematical concepts and encourage fluency, flexibility and originality as essential components of creative thinking. Teaching that does not provide moments in which students are creative denies them any opportunity to develop their skills in mathematics, but also to appreciate this subject.

To overcome some of the referred shortcomings, we developed a project named Mathematical Trails outside the classroom. With this project, we intended to promote the contact with a contextualized mathematics, starting from the daily life features, walking through and analyzing the city where we live in, connecting some of its details with exploration and investigation tasks in school mathematics. Its aim is to promote a new attitude to mathematics through the observation and exploration of the urban environment, while designing mathematics curriculum for elementary education. 

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