Art and Geometry of Plants: Experience in Mathematical Modelling through Projects

Fabio Grajales
2017 Eurasia Journal of Mathematics, Science and Technology Education  
This article presents some results of a qualitative-case study carried out with students in last year of secondary education (15 -17 years) into an official educational institution. The research looked at learning outcomes through the development of mathematical modelling projects related to studying the distribution of the leaves and the growth of some plants. According to the results, when modelling projects grounded in studying the form and geometric magnitudes are carried out, students are
more » ... out, students are able to find out the meaning of certain mathematical concepts and participate in activities to reach other processes such as exploration, representation, formal construction, and validation of mathematical results. Some implications for teaching and learning in classroom derive from this study, particularly, the need for students to face the project development articulating research and mathematical modelling. In Colombia, as in other countries, it has been raising the need to articulate five transversal processes in mathematics education for levels of elementary/secondary education; mathematical modelling is one of these processes. It makes sense in mathematics study and, among them, issues and ideas related to spatial thinking. Through modelling, space's mathematical models can be built and a predominantly geometric reality can be interpreted. In this regard, the Ministry of National Education from Colombia (MEN, 1998) expresses: Geometry, by its nature as a tool to interpret, understand and appreciate a world predominantly geometric, becomes an important modelling source and field for excellence to develop spatial thinking and high-level processes and, in particular, different ways of arguing. (p. 33) An interpretation of MEN considerations allows to have a conception about geometry, and perhaps, about mathematics in general, as a set of models (theories) historically constituted as an abstraction of the human experience with the nature. In that sense, mathematical theories, or part of them, are considered as models resulting from a process to mathematising of real it (Israel, 1996) . In this sense, the process of mathematical modelling plays an important role to study school geometry since, by its practical nature, it should allow students be closer to the study of their own reality and to the constitution of their own models and interpretations of that reality. The interrelationships between the "real world" and mathematics have special meaning in works of mathematical modelling because these are where descriptions of what is mathematical modelling commonly are Contribution of this paper to the literature • This paper offers one way of tackling school geometry teaching by means of math modelling by using projects where students solve situations or phenomena of their daily lives. This is shown with an example, ways to study geometric objects, in one hand by studying the shapes and on the other hand by studying the magnitude. In the examples, the technology role is shown for each case. Besides, it helps to understand math modelling in geometry, what proposes two ways to act, as a part of mathematics where both intra and extra math situations can be given. • The questions about the nature of geometric models, the contexts and situations which are modeled in geometry and their relation to other math areas and the other sciences, takes special sense for research in math education.
doi:10.12973/ejmste/76958 fatcat:i4xczftu6jfztkilncjku2vbda