Exploring New PLTL Modalities, Forging New Alliances

This essay focuses on rethinking and reimagining elements of a PLTL program, and on the new modalities to meet challenges of online undergraduate mathematics courses and rising demands for flexible student support. It examines advantages and challenges as found in the Integrated PLTL and Virtual Peer-Led Mathematics Study Groups, including issues such as meeting protocols, and the selection and training of peer leaders. Finally, it discusses an alliance with the college’s mathematics education program, which allows the PLTL program to draw on senior prospective teachers to co-organize and facilitate virtual study groups supporting undergraduate mathematics courses.

A filosofia nos cursos de licenciatura em matemática do IFMG

Neste artigo, pretendemos investigar como a temática filosófica é tratada nos cursos de Licenciatura em Matemática do Instituto Federal de Minas Gerais (IFMG), presentes nos campi de Formiga e São João Evangelista. Metodologicamente, realizamos uma pesquisa de natureza qualitativa e caráter exploratório, subsidiada pela análise documental a partir de consultas aos Projetos Pedagógicos dos Cursos. Em ambos, observamos a falta de uma abordagem mais abrangente do tema, o que nos levou a propor a inclusão de uma disciplina voltada para a Filosofia da Matemática na grade curricular. Essa disciplina consideraria aspectos históricos, socioculturais e científicos da construção da Matemática enquanto Ciência e daria ênfase às contribuições dos principais filósofos para o seu desenvolvimento, destacando o pioneirismo de Tales de Mileto e Pitágoras, nas demonstrações geométricas, e o protagonismo de Platão, Aristóteles, René Descartes e Immanuel Kant. Além disso, ela discutiria acerca de três correntes filosóficas - Logicismo, Intuicionismo e Formalismo – e o modo com que elas trazem para si uma discussão sobre o pensar a Matemática. Esperamos que este artigo promova um debate entre os professores e gestores dos cursos, considerando que a Matemática, que hoje conhecemos, é fruto de todo um processo filosófico de elaboração e reelaboração de si mesma. Palavras-chave: Filosofia. Filosofia da matemática. Educação matemática. Philosophy in undergraduate mathematics ifmg courses: analysis, reflections and a teaching proposal Abstract In this paper, we initially intend to investigate how the philosophical theme is treated in the Mathematics Graduation courses from the Federal Institute of Minas Gerais (IFMG), in Formiga and São João Evangelista campi. The methodological procedure adopted was the exploratory research, through a documentary analysis carried out in the courses Pedagogical Projects. In both, we noted that the theme approach was deficient, which led us to propose the inclusion, in the curriculum, of a discipline focused on Mathematics Philosophy. This discipline will consider historical, sociocultural and scientific aspects of Mathematics construction as a science, and it will emphasize the contributions of leading philosophers to their development, highlighting the pioneering spirit of Tales of Miletus and Pythagoras in geometric demonstrations, and in the role of Plato, Aristotle, René Descartes and Immanuel Kant. In addition, it is intended to discuss about three philosophical currents – Logicism, Intuitionism and Formalism –, and the way in which they promote a discussion about Mathematics thought. It is hoped that this paper will promote a debate between teachers and course managers, considering that the Mathematics, that we know today, is the result of a whole philosophical process of itself elaboration and re-elaboration. Keywords: Philosophy. Mathematics philosophy. Mathematical education.

Investigating insight and rigour as separate constructs in mathematical proof

In this paper we investigate undergraduate mathematics students' conceptions of rigour and insight. We conducted comparative judgement experiments in which students were asked to judge different proofs of the same theorem with five separate criteria: rigour, insight, understanding, simplicity and assessment marks. We predicted, and our experiment found, that rigour is a reliable construct. We predicted that insight is also a reliable construct but asking students to judge on the basis of ``which proof gives you more insight into why a theorem is true'' did not result in a reliable judging scale. Our analysis suggests two distinct dimensions: rigour and marks contribute to one factor whereas simplicity and personal understanding relate to a second factor. We suggest three reasons why insight was related almost equally to both factors. First, while comparative judgement was suitable for assessing some aesthetic criteria it may not be suited to investigating students conceptions of insight. Second, students may not have developed an aesthetic sense in which they appreciate insight in ways which are regularly discussed by mathematics educators. Lastly, insight may not be a coherent and well-defined construct after all.