DSpace Collection:
http://hdl.handle.net/10773/5870
Thu, 18 Oct 2018 03:38:39 GMT2018-10-18T03:38:39ZExploring symmetry in professional development courses for mathematics teachers
http://hdl.handle.net/10773/24089
Title: Exploring symmetry in professional development courses for mathematics teachers
Author: Hall, Andreia
Abstract: In a way, mathematics can be generally described as a science that studies structure, relations,
order or patterns through its own language, in order to help us better understand the world we
live in. Structure, relations, order and patterns are also fundamental in art and therefore it is
not surprising that mathematics and art share a long historical relationship. Mathematics has
inspired several artists and art works are sometimes a good motivation for mathematical reasoning
or learning.
Combining artistic creativity and mathematical reasoning turns out to be a very appealing
way to explore several mathematical topics, in particular symmetry. Learning the mathematical
principles of symmetry by first looking at art works and exploring one's own creativity has proven
to be a very powerful and attractive strategy. During the last years I have explored symmetry
with mathematics teachers of all grades through several professional development courses. In
these courses teachers had the opportunity to create their own art works using different materials.
The topics explored in these courses covered all types of symmetry in the plane: rosettes, friezes
and wallpaper patterns.
In this paper we shall present some results of three of these courses, involving about 50
primary and secondary school teachers (grades 1 to 12). In all courses we studied symmetry
and the groups of symmetry of plane figures. We produced applications using two specific crafts
techniques: patchwork/quilting and ceramics.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10773/240892018-01-01T00:00:00ZVoronoi Diagrams: Didactical and Artistic Applications
http://hdl.handle.net/10773/24088
Title: Voronoi Diagrams: Didactical and Artistic Applications
Author: Hall, Andreia; Bento, Sandra; Ferreira, Helena
Abstract: Research on Voronoi Diagrams evolved a great deal from the original setting where a network of polygons marks the
separation of points by regions of influence. Multiple approaches have been taken to solve the elementary geometry
problems of bisecting segments and intersecting half-planes.The methods vary according to the type of point, the
distance used and the type of bisector. In this work we propose some didactical tasks based on creating Voronoi
diagrams. We also present some artistic quilt work, designed with the help of a Wolfram demonstrations project
applet, based on a convenient choice of the generating points of a Voronoi Diagram.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10773/240882018-01-01T00:00:00ZThe Mathematical Circus Project
http://hdl.handle.net/10773/24087
Title: The Mathematical Circus Project
Author: Hall, Andreia; Pais,Sonia
Abstract: Magic and mathematics appear hand in hand when it comes to promoting the interest and motivation for learning mathematics. Portugal, like other countries, has a high failure rate in school mathematics, which of course causes a negative attitude towards this subject in society. Mathematics is generally thought of as a difficult subject with little practical importance. Motivated by the need to fight this stigma, the Mathematical Circus Project emerged in 2012. Linking mathematics with the performing arts (theater and circus) is not as common as other connections such as with the visual arts. The Mathematical Circus team performs mathematical magic shows with a circus atmosphere in schools, science centers and other public spaces. In a traditional magic show, one often realizes that what causes the fantastic effects is the magician’s ability to manipulate objects combined with the art of controlling the perception of the spectators. The tricks performed in the Mathematical Circus are exclusively based on mathematical principles. In this paper we describe the Mathematical Circus project: its context, goals, contents and achievements.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10773/240872018-01-01T00:00:00ZMathematical magic in the classroom
http://hdl.handle.net/10773/24086
Title: Mathematical magic in the classroom
Author: Hall, Andreia; Pais, Sonia
Abstract: Mathematics, considered one of the basic areas of various formations, has been the subject of
concern for many authors and researchers due to its enormous academic and educational failure [1].
Its importance in day-to-day life and the formation of individuals is irrefutable [2]. One of the problems
identified in the failure of mathematics teaching is the lack of motivation that students feel towards the
discipline. According to [3], motivation is an essential factor in any learning since the quality of learning
is not only related to the capacity to learn, but also to the level of motivation that we have to carry out
this same learning. Considering that it is imperative to make the teaching and learning process of
mathematics more stimulating, taking into account modern society and student’s interests [4], the
authors have developed a qualitative case study to evaluate how "mathematical magic" can contribute
to increase students’ motivation for learning mathematics. In order to develop this experience, the
techniques of inquiry, direct observation and analysis of documents were applied and the following
instruments were used: questionnaires and respective analysis grids; production of a battery of tasks
of a diversified nature; field notes and interviews.
Although this project is still ongoing and therefore not yet completed, a previous analysis of the
collected data allows us to conclude that the use of mathematical magic tricks in the classroom, with
the purpose of motivating the students to learn mathematics, was revealed effective. Students were
curious about the new tricks and were positively surprised at the relative simplicity of their explanation,
as if saying to themselves, "How can such mathematical concepts bring so much surprise?" The
students showed that the topics gained more meaning after performing the tricks because they
witnessed real applications of the concepts, with an extremely attractive purpose. They often stated
that they were going to play the tricks on their friends / family outside the classroom context, which
meant that they were mastering the concepts involved.Thu, 01 Mar 2018 00:00:00 GMThttp://hdl.handle.net/10773/240862018-03-01T00:00:00ZOptimization conditions for some fractional problems
http://hdl.handle.net/10773/24049
Title: Optimization conditions for some fractional problems
Author: Almeida, Ricardo Miguel
Abstract: The purpose of this study is to present necessary
conditions for calculus of variations problems, where the Lagrange
function involves a Caputo fractional derivative with
nonconstant order. The fractional operator depends on another
function, and for particular choices of that function, we obtain
some well-known fractional derivatives. Several necessary
conditions of optimality are proven, namely the Euler–Lagrange
equationFri, 01 Jun 2018 00:00:00 GMThttp://hdl.handle.net/10773/240492018-06-01T00:00:00Z