Center for Research and Development in Mathematics and Applications

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Publications

Publication . Hall, A.; Almeida, P.; Vettori, P.; Pais, S.

The Mathematical Circus project was created in 2011 by the LUDUS association with the main goal of promoting the interest and motivation for learning mathematics. The Mathematical Circus team performs mathematical magic shows where complementary skills are merged to produce a high intervention capacity within a wide geographical range in Portugal. Some tricks are performed by a mathematical clown, a unique character in the circus world, who brings together the usual foolish characteristics of a clown and the rigorous mathematical knowledge. In this paper we will describe and explain some of the tricks of the Mathematical Circus repertoire involving the clown.

2019Conference object

Open access

Mathematical magic in undergraduate mathematical classes for pre-service teachers

Publication . Hall, Andreia; Pais, Sónia

Nowadays we live in an ever-changing society. The educational context is no exception, and requires a renewal of paradigms. Profound changes to the role and function of the teacher and the students are particularly vital [1], [2], [3]. The current University students have different motivations, different attitudes towards the teaching and learning process, and different responses to specific classroom environments and instructional practices [4]. The challenge that teachers face today is to motivate students to learn, get them to commit to and have an active role in their learning [5]. 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 [6], the authors have developed several strategies to increase the interest and improve the success of students in mathematics. Thus, they decided to use mathematical magic tricks in their classes to raise the motivation of the students, captivating them and stimulating their interest in mathematics. In this work, a case study to evaluate how mathematical magic can contribute to increase students' motivation for learning mathematics is presented. The paper describes how it is conceived as well as the main results.

2019Conference object

Open access

A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus

Publication . Ferreira, M.; Rodrigues, M. M.; Vieira, N.

In this paper, we develop a time-fractional operator calculus in fractional Clifford analysis. Initially, we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogs of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems.

2018-12-24Journal article

Open access

Using mathematical magic to improve student’s motivation in mathematics classes

Publication . Pais, Sónia; Hall, Andreia

One of the problems identified in the failure of mathematics teaching is the lack of motivation that students feel towards the discipline. Considering that it is imperative to make the teaching and learning processses of mathematics more stimulating, taking into account modern society and student’s interests, the authors have developed several strategies to increase the interest and improve the success of students in mathematics. Thus, they decided to use mathematical magic tricks in their classes to raise the motivation of the students, captivating them and stimulating their interest in mathematics. In this work, a case study to evaluate how mathematical magic can contribute to increase students’ motivation for learning mathematics is presented. 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 and field notes. The 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, revealed to be effective.

2019Journal article

Open access

Interlacing mathematics and art: hands-on non-Euclidean geometry

Publication . Hall, Andreia; Brás, Isabel; Pais, Sónia

Elliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning. This is true for any subject, including mathematics. Geometry related topics make a perfect setting for a deeper contribution of art to education. One such topic is the study of non-Euclidean geometry. In this paper, we present some results of a professional development course for mathematics teachers where the participants studied non-Euclidean geometry concepts. The participants created ceramic pieces using the Poincaré disk and styrofoam balls covered with fabrics using spherical geometry.

2019Conference object

Open access