Patterns, mathematics and culture : the search for symmetry in Azorean sidewalks and traditional crafts

In the hustle and bustle of daily life, how often do we stop to pay attention to the tiny details around us, some of them right beneath our feet? Such is the case of interesting decorative patterns that can be found in squares and sidewalks beautified by the traditional Portuguese pavement. Its most common colors are the black and the white of the basalt and the limestone used; the result is a large variety and richness in patterns. No doubt, it is worth devoting some of our time enjoying the lovely Portuguese pavement, a true worldwide attraction. The interesting patterns found on the Azorean handicrafts are as fascinating and substantial from the cultural point of view. Patterns existing in the sidewalks and crafts can be studied from the mathematical point of view, thus allowing a thorough and rigorous cataloguing of such heritage. The mathematical classification is based on the concept of symmetry, a unifying principle of geometry. Symmetry is a unique tool for helping us relate things that at first glance may appear to have no common ground at all. By interlacing different fields of endeavor, the mathematical approach to sidewalks and crafts is particularly interesting, and an excellent source of inspiration for the development of highly motivated recreational activities. This text is an invitation to visit the nine islands of the Azores and to identify a wide range of patterns, namely rosettes and friezes, by getting to know different arts and crafts and sidewalks.

Students' engagement in schools : differentiation and promotion

The objective of this work is to present elements of the project Student engagement in Schools (SES). The team consists of 10 researchers from six Universities. Student engagement in schools is a multidimensional construct that unites affective, behavioural, and cognitive dimensions of student adaptation in the school and has influence on students’outcomes. The team of researchers conceptualized two major studies, a differential study to analyze the relations between SES and contextual factors, personal factors, student’s outcomes, and a quasi-experimental study to analyze the effects on SES of a specific intervention programmes. In study 1, the sample size is around 600 students (150 6th graders, 150 7th graders, 150 9th graders, and 150 10th graders). We shall focus on years of school transition, with rural and urban populations, on different regions of the country, and on students with different family background. We shall conduct questionnaires with national and international scales. The study 2 will involve students in 7th and 9th grade, from four classes, two of the experimental group and two of the control group. Patterns of verbal communication between a teacher and students can influence the classroom environment and SES. This model of communication would result in more effective student management and more time on-task for learning.