Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1907.02099

GeoGebra e situações que envolvem modelação numa abordagem STEAM

J. M. D. S. Dos Santos·A. P. Silveira·A. E. S. Trocado
View original source ↗Read source document ↗Export metadata ↓

Abstract

In order to implement a STEAM approach including the use of technology, namely the use of interactive mathematics software GeoGebra, in mathematics classes, in the lusophone space, the materials presented here were conceived, to be implemented in a first phase among teachers. Later, with the necessary adaptations, these tasks will be applied to the students. The tasks deal with modeling situations, in two- and three-dimensional geometric problems, in order to apply GeoGebra software in its analysis to illustrate its capabilities. The different windows of this software are used, namely the 2D and 3D windows, CAS window, spreadsheet and extra two dimensional windows in order to study cutting planes in solids and some surfaces. The tasks are presented so that any user, regardless of the degree of knowledge they have of the software, can follow them, being supported in scripts with some indications of the tools and commands to use. Designed for the teaching and learning of Mathematics, from a STEAM approach, these tasks allow connections with other Sciences and the Arts, and allow the development of projects using and consolidating relevant mathematical contents. These tasks are part of the proposals of activities of the participants of the Training Courses for Trainers in GeoGebra for Portuguese Speaking Countries, which from 2019 have an impact on the STEAM approach. These courses are carried out with the high sponsorship of the Organization of Ibero-American States for Education, Science and Culture (OEI). Given the interest that the tasks have for the users of the Iberian space, as well as their dissemination at a global level, the materials initially developed in Portuguese language will be adapted for Spanish and English speakers.

Explore related subjects

math.HOcs.CY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. M. D. S. Dos Santos, A. P. Silveira, A. E. S. Trocado. 2019-07-03. GeoGebra e situações que envolvem modelação numa abordagem STEAM. https://arxiv.org/abs/1907.02099

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the Reconstruction of SAS from Other Triangle Congruence Criteria, Part II: Eliminating the Pons Asinorum

In the first part of this work we showed that, within a Hilbert plane deprived of the Side-Angle-Side axiom, the Side-Angle-Angle criterion, together with a ray correspondence principle [\textbf{RCT}], the existence of angle bisectors [\textbf{AB}], the congruence of supplements of congruent angles [\textbf{SA}], and the Pons Asinorum [\textbf{PA}], suffices to reconstruct SAS. We left open the question of whether [\textbf{PA}] is genuinely required alongside the other three principles, noting only a qualitative asymmetry in the nature of the principles involved. In this second part we answer this question: we show that \begin{equation*} \textrm{SAA},\ [\textbf{RCT}],\ [\textbf{AB}] \;\vdash\; [\textbf{PA}], \end{equation*} so that [\textbf{PA}] is redundant among the hypotheses of our main theorem, which improves to \begin{equation*} \textrm{SAA},\ [\textbf{RCT}],\ [\textbf{AB}],\ [\textbf{SA}] \;\vdash\; \textrm{SAS}. \end{equation*} The proof adapts an argument recently given by Donnelly, who reconstructs SAS from SAA together with an angle addition axiom and the existence of angle bisectors.

math.HO↗
arXiv2026

Chebyshev and garment cutting. Debunking some myths

In {\tt 1878}, Pafnuty Chebyshev presented to the {\it Association fran\c caise pour l'avan\-cement des sciences} {\it [French Association for the Advancement of the Sciences]} an article \cite{Chebyshev1878} dealing with garment cutting. According to Chebyshev himself, his interest was sparked by a lecture given by Édouard Lucas that he had attended in {\tt 1876} \cite{Lucas1876}. There is a second story on the origin of Chebyshev's interest in garment cutting according to which in the 1850s, being short of money, Chebyshev got himself a job as a consultant to a clothing factory. At the time of the Crimean War (1853-1856), there was a great demand for uniforms. Chebyshev was allegedly asked to optimize the use of fabric, and it was there that his interest in garment cutting was born. This second story appears to have its origin in a post by Clive J. Grant to MacTutor in 1996 \cite{Grant1996}. However, this contribution contains no references, and no other source of information that I have found offers any first-hand documentation to support this story. Our conclusion is that this second story is a fabrication, invented out of whole cloth.

math.HO↗
arXiv2026

Mathematics Graduate Training in the Age of AI

Generative AI changes the conditions under which graduate mathematics is learned, assessed, written, and defended. The central claim of this paper is that mathematics graduate programs should respond to the moment by clarifying what graduate mathematics education is trying to teach and assess. In most ways, the goals of mathematics education have not changed. Rather, with changing tools it has become more essential than ever to make clear the goals of mathematical training. We use the term mathematical judgment to refer to the capacity to evaluate mathematics (e.g., claims, definitions, examples, proofs, analogies, computations, uses of tools, research directions) as mathematically sound, useful, well-posed, and appropriately justified. The recommendation is to center training on mathematical judgment, and we examine possible policies for graduate programs in Mathematics to this end.

math.HO↗