P. Catarino, C. Costa

Universidad de Trás-os-Montes e Alto Douro (PORTUGAL)
In this study we intend to recover some of the mathematical themes that were formerly part of the training of students of agricultural education courses in Portugal and, mainly, the way that they were approached. The main source used it was the Portuguese textbook of Rural Mathematics of the early 60's, of 20th century (Almeida, 1966). We have analysed this textbook focusing only on the mathematical contents and the way of presenting them. We have partially implemented the analysis proposed by (Sierra, González & López, 2003), namely with regard to conceptual analysis, didactic-cognitive aspects and to phenomenological elements. We have observed this information having in mind the most recent studies in mathematical education (NCTM, 2000) and in ethnomathematics (D’ Ambrósio, 2016) in order to assess the modernity of the methodologies used in this textbook. The purpose of this work is to reflect on the potential of this textbook (or part of it) to be recovered for the teaching of certain courses, possibly of a professional nature.

The mathematical themes in Almeida (1966) are: Counts and measurements, numbers; Metric systems; Complex numbers; Algebraic numbers; Squares and cubes, square root; Proportionality and its applications; Brief notions of agricultural accounting; Geometry.
Regarding the way of approaching the content, it is notorious and common the cultural/professional contextualization, with real examples of applications to diversified activities related to the rural environment, such as accounting, measurement conversion tables, tables of squares and cubes, interest rates tables, etc.

Comments with detailed explanations are often sought to highlight which is more important to retain from previously presented content.
The emphasis is given to the exercises and problems, being once again these contextualized, what is explicitly stated in the Previous Note, where the author states that:

“The problems of rural environments vary greatly from region to region,(…). They arise in daily occurrences, in school life and in agricultural life. For this reason, the exercises and problems proposed at the end of each chapter of this textbook are only suggestions and paradigms for many others that surely the worthy teachers of the General Instruction of the Complementary Courses of Agricultural Learning will put to the consideration of their students. This Mathematics, in order to be truly useful to the intended audience should be essentially practical in order to provide problem-solving techniques as complete as possible.” (Almeida,1966,p.5, authors’ translation). In this work we intend to focus on the contents related to the rural teaching of mathematics based on the referred textbook, presenting and discussing the methodology used, the didactic resources, the problems (proving the last statement of the author that we transcribed above, among others) and that allowed the students to acquire competences which made their life easier.

[1] ALMEIDA, J.M. 1966. Matemática rural (3ªed). Lisboa: INOVA
[2] D’ AMBRÓSIO, U. 2016. Etnomatemática: elo entre a tradição e a modernidade. Belo Horizonte: Autêntica Editora
[3] NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM). 2000. Princípios e Normas para a Matemática Escolar. Reston: NCTM
[4] SIERRA-VÁSQUEZ, M., GONZÁLEZ-ASTUDILLO, M.T., & LÓPEZ-ESTEBAN, C. 2003. El concepto de continuidad en los manuales españoles de enseñanza secundaria de la segunda mitad del siglo XX. Educación Matematica, 15( 1):21-49E