Editorial

摘要

This is the 5th edition of the Journal of Mathematical Modelling and Application. Among the six papers published, four present research reports on Modelling Education and two Mathematical Models about nature phenomena and may be used as examples to adapt in classrooms. It is interesting to observe that while modelling is an important method to solve the great variety of problems of different areas, and/or to improve or to create new medicines, products, technologies, as presented by the papers about mathematical models, the teaching through modelling in Basic Education is considered a way far being ‘traditional’ or ‘ordinary’. Even though in many countries the documents present math modelling and application as part of the math syllabus, it seems to not happen in ‘real life’. According to Frejd, author of one of the papers published in this edition, the teachers that contributed with his study did not seem “to give priority to integrate mathematical modelling into their everyday mathematics teaching”. Certainly there may be some reasons for that: the teachers did not learn to do modelling in their Teacher Education Course. As said by Lingerfj?rd, “there is so much content and information to cover in order to prepare prospective mathematics teacher for the upper secondary school level and usually rather few teaching hours in which we can teach it”. Kawasaki, Moriya, and Okabe suggest that teaching materials of mathematical modelling should be developed inside university education. Mathematical modelling for education has been defended for long time, official documents present indications of it, and when teachers listen to someone talking about it, they have an understanding, one possible conception or belief. As time passes, conceptions emerge, as Galbraith, in this Journal, captured two. Undeniably, each article published in this edition gives special contribution to the area. In what follows, we present a brief summary of the articles: - The paper Models of Modelling: Genres, Purposes or Perspectives, written by Peter Galbraith, from the University of Queensland, Australia, presents a study on “meanings, approaches, priorities, and intentions associated with the use of the term ‘mathematical modelling’ as it occurs in education”. He considered “two generic approaches to modelling within education: modelling that acts primarily as a ‘vehicle’ for the attainment of other curricular priorities, and modelling as ‘content’ that seeks first to nurture and enhance the ability of students to solve authentic real world or life-like problems”. The author discusses the approaches by subdividing them. For instance, the 1st approach ‘modelling as vehicle’, is explained in five topics: contextualized examples to motivate the study of mathematics; real problem situations as a preliminary basis for abstraction; emergent modelling; modelling as curve fitting; and word problems; the 2nd approach ‘characteristics of modelling as content’, is explained by two functions of modelling frameworks. The author’s intention in this piece of research was to recognize understandings on modelling in education and to collect data about two ably global approaches, “as fundamental archetypes stems from reasoning”. - Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school, written by Peter Frejd from Link?ping University, presents a study about teachers’ conceptions/beliefs about mathematical modelling in a group of 18 teachers. Data collected by means of interviews revealed that in general the teachers did not seem to prioritize the integration of mathematical modelling in their everyday mathematics teaching. “The teachers’ in this study have limited experiences about the notion of mathematical modelling in mathematics education. 50% of the teachers heard the notion just for one or two years when participated in Frejd and ?rleb?ck’s study”. This fact may explain the low level of integration of modelling activities in the math classes in the Swedish upper secondary context. - In the paper Learning Mathematics Through Mathematical Modelling, Thomas Lingerfj?rd, from the University of Gothenburg, Sweden, presents a research report about the data collected with students from a mathematics education course at the University of Gothenburg. He divided the students into two groups, the teacher group and the student group, with the objective of developing modelling tasks or modelling situations, explaining it to the classmate, and clarifying their “own thinking in order to give an explanation and must be prepared to have misconceptions confronted and corrected through discussion and listening”. In general, students learned much more when engaged in the teaching of a course. The author shows how this activity was carried out by two groups of students and what they thought they learned from it. He says: “the experiment with students constructing problems for others enables someone to study the learning outcome and thereby o