GeoGebra e situa\c{c}\~oes que envolvem modela\c{c}\~ao numa abordagem STEAM

A. E. S. Trocado; A. P. Silveira; J. M. D. S. Dos Santos

arxiv: 1907.02099 · v1 · pith:IUFHNKIKnew · submitted 2019-07-03 · 🧮 math.HO · cs.CY

GeoGebra e situac{c}\~oes que envolvem modelac{c}\~ao numa abordagem STEAM

J. M. D. S. Dos Santos , A. P. Silveira , A. E. S. Trocado This is my paper

Pith reviewed 2026-05-25 09:12 UTC · model grok-4.3

classification 🧮 math.HO cs.CY

keywords GeoGebraSTEAMmathematical modelinggeometric problemsteacher traininginterdisciplinary connectionslusophone education

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The pith

GeoGebra modeling tasks connect mathematics to sciences and arts in a STEAM approach for teacher training and student projects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a collection of guided tasks that apply GeoGebra to modeling problems in two- and three-dimensional geometry as part of a STEAM framework aimed at mathematics classes in Portuguese-speaking countries. The materials are created first for teachers through training courses, with later adaptations for students, and rely on the software's 2D, 3D, CAS, and spreadsheet windows to examine solids, surfaces, and cutting planes. Scripts guide users of any experience level through the commands needed to complete the tasks. The authors state that these activities foster links across disciplines and support project work that reinforces core mathematical ideas.

Core claim

The tasks use GeoGebra to model geometric situations in 2D and 3D, employing its various windows and guided scripts so that teachers and later students can explore the software's capabilities, make connections with other sciences and the arts, and carry out projects that consolidate relevant mathematical contents as part of a STEAM approach.

What carries the argument

Guided modeling tasks in GeoGebra that combine its 2D, 3D, CAS, and spreadsheet windows with scripts to analyze cutting planes in solids and surfaces.

If this is right

Teachers can introduce the tasks in mathematics classes to combine technology use with STEAM elements.
Students gain opportunities to build projects that reinforce mathematical contents while drawing links to sciences and arts.
The same materials can be adapted for Spanish- and English-speaking users to widen their reach.
The tasks form part of ongoing GeoGebra trainer courses that began in 2019 under OEI sponsorship.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Task structures like these could be recreated with other dynamic geometry tools to test whether the STEAM connections hold across platforms.
Follow-up classroom data on student project quality could reveal whether the modeling activities produce the claimed consolidation of contents.
Wider translation and local adaptation might allow similar modeling sequences to support STEAM efforts in additional language communities.

Load-bearing premise

That teachers and students following the provided scripts and tasks will achieve the described interdisciplinary connections and mathematical consolidation without further evidence of learning results.

What would settle it

A classroom trial in which students complete the tasks yet show no measurable increase in ability to link geometry to other subjects or to apply the targeted mathematical concepts in projects.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a descriptive write-up of scripted GeoGebra tasks for STEAM geometry aimed at Portuguese-speaking teachers, with no data or new techniques.

read the letter

This paper is a descriptive write-up of scripted GeoGebra tasks for STEAM geometry aimed at Portuguese-speaking teachers, with no data or new techniques. It lays out step-by-step activities that use the 2D, 3D, CAS, and spreadsheet windows to model solids, cutting planes, and surfaces. The scripts are written to be usable by people with different levels of software experience, and they are framed as starting points for teachers before later student use. The link to OEI-sponsored training courses and the note about future Spanish and English versions shows some attention to reach within the lusophone space and beyond. That practical focus is the main thing the paper contributes. The limitation is straightforward: the central statements about allowing cross-disciplinary connections and consolidating math content are presented only as what the tasks are intended to do. There is no classroom data, teacher feedback, or outcome measure of any kind. The paper does not claim to have tested these effects, so the absence of evidence is not an internal contradiction, but it does mean the work stays at the level of material design rather than evaluation. This is aimed at educators and trainers who need concrete Portuguese-language examples they can adapt. Readers looking for measured learning results or original geometric methods will not find them. The organization of the tasks is clear and the scripts appear usable on their own terms. I would not bring this to a research-focused reading group. I would not cite it. It does not need peer review in a standard research journal.

Referee Report

1 major / 2 minor

Summary. The manuscript describes the design of GeoGebra modeling tasks for 2D and 3D geometric problems, created for initial use in teacher-training courses for Portuguese-speaking countries under OEI sponsorship. The tasks employ the 2D, 3D, CAS, and spreadsheet windows together with provided scripts; the authors state that the materials illustrate GeoGebra capabilities, enable connections with other sciences and the arts, and support project-based consolidation of mathematical content, with future adaptation to Spanish and English.

Significance. If the tasks function as intended, the work supplies concrete, scripted resources that could support technology-enhanced STEAM implementation in mathematics classrooms across the lusophone and Iberian regions.

major comments (1)

[Abstract] Abstract: the central claim that the tasks 'allow connections with other Sciences and the Arts, and allow the development of projects using and consolidating relevant mathematical contents' is asserted on the basis of design intent alone; the manuscript supplies neither explicit mappings of the described tasks to other disciplines nor any student or teacher outcome data that would substantiate the claim.

minor comments (2)

The manuscript is written entirely in Portuguese; an English abstract (or bilingual presentation) would improve accessibility given the stated plan to adapt the materials for Spanish and English speakers.
No section headings, numbered tasks, or explicit list of the modeling situations are referenced in the provided text, making it difficult for readers to locate or replicate specific activities.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful review and the constructive comment on the abstract. We respond point by point below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the tasks 'allow connections with other Sciences and the Arts, and allow the development of projects using and consolidating relevant mathematical contents' is asserted on the basis of design intent alone; the manuscript supplies neither explicit mappings of the described tasks to other disciplines nor any student or teacher outcome data that would substantiate the claim.

Authors: We agree that the claims rest on the design of the tasks rather than on collected outcome data or explicit mappings provided in the manuscript. The paper describes tasks created for initial use in OEI-sponsored teacher-training courses in Portuguese-speaking countries, with the multi-window GeoGebra approach (2D, 3D, CAS, spreadsheet) intended to support modeling that can connect to other fields. To address the concern we will revise the abstract to state that the tasks are designed to enable such connections and project work. We will also add short explicit examples in the main text illustrating links (for instance, cutting planes to physics and engineering, geometric visualization to visual arts and design). We cannot supply outcome data because the tasks are prepared for future implementation in the training courses and have not yet been applied or evaluated with participants. revision: partial

standing simulated objections not resolved

Empirical student or teacher outcome data, as the tasks are at the design stage for upcoming training courses and have not been implemented or assessed.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript is a purely descriptive account of educational task designs and scripts for using GeoGebra in STEAM modeling activities. It contains no equations, derivations, fitted parameters, predictions, or uniqueness theorems. The central statements concern intended affordances of the created materials (e.g., that the tasks 'allow connections with other Sciences and the Arts') rather than any claim that reduces to its own inputs by construction. No self-citations function as load-bearing premises. The document is therefore self-contained with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical claims, derivations, or empirical measurements are present. The document is a description of created teaching materials rather than a research contribution with free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5863 in / 1041 out tokens · 18511 ms · 2026-05-25T09:12:46.511215+00:00 · methodology