Interdisciplinary Approaches to Geometry

Code:

MEAV04

Acronym:

DIG

Keywords
Classification	Keyword
OFICIAL	Visual Arts

Instance: 2025/2026 - 1S

Active?	Yes
Responsible unit:	Education Sciences
Course/CS Responsible:	Master in Teaching of Visual Arts for Teachers of the 3rd cycle of Basic Education and of Secondary Education

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MEAV	9	Plano de Estudos 2025	1	-	6	45	162
		Plano de Estudos 2025 - Transição	1	-	6	45	162

Teaching language

Suitable for English-speaking students

Objectives

“Interdisciplinary Approaches to Geometry” aims at contributing to the formation of responsible, active, critical and solution-oriented free citizens, prepared for constant learning.

It will be an open laboratory to all who might be interested. The course will be shaped according to its students’ academic and personal profiles. Thus, it is open not only to all graduated students, but also to teachers, trainers and professionals.

There are three general structuring aims indicated as necessary for the acquisition of skills and knowledge under “Interdisciplinary Approaches to Geometry”:

 - to recognize the Drawing and Mathematics approaches to Geometry;

- to problematize the common denominators in the different approaches to Geometry, either from a fundamental science’s point of view or from problems of applied sciences;

- to delineate common strategies of problem solving possible to be evoked by the Geometric Model from Drawing and Mathematics perspectives.

Learning outcomes and competences

Students will be able to achieve four specific skills and learning outcomes:

- to know and value different disciplinary approaches to Geometry;

- to enunciate interdisciplinary research proposals, attending and involving those to whom it might be addressed; 

-to identify permanent and participated means of future research development and evaluation;

- to communicate, to disseminate, to transmit and to share research products and effects.

Working method

Presencial

Program

- Approaches to creation of form: Drawing and Mathematics approaches to Synthetic Geometry and to Analytic Geometry - polygons, tilings, polyhedra, tessellations;

- Approaches to transformations of form: Drawing and Mathematics approaches to Geometric Transformations - Boolean operations, isometries, homotheties;

- Approaches to representations of form: Drawing and Mathematics approaches to Projective Geometry - projective geometry, systems of representation.

Mandatory literature

Cardoso, V. & Mena-Matos, H. ; Drawing and Mathematics in Art Education and Design: Interdisciplinary Approaches to Geometry, Tessellations Publishing, Phoenix, USA, 2025. ISBN: 978-1-938664-51-9 / 1099-6702 (in Verhoeff, T. et.al. (Eds). Proceedings of Bridges 2025: Mathematics and the Arts [https://repositorio-aberto.up.pt/handle/10216/167718])
CUCKER, Felipe; Manifold Mirrors: The Crossing Paths of the Arts and Mathematics, Cambridge University Press, 2013. ISBN: ISBN 978-0-521-42963-4
IVINS Jr., William M. ; Art and Geometry: A Study in Space Intuitions (1.ª Ed. 1964), Dover Books, 2011. ISBN: ISBN: 486-20941-5
RICCA, Guilherme; Geometria Descritiva, Fundação Calouste Gulbenkian, 1992. ISBN: ISBN: 972-31-0547-0

Complementary Bibliography

ANDERSEN, Kirsty; The Geometry of an Art - The History of the Mathematical Theory of Perspective from Alberti to Monge, Springer, 2007. ISBN: ISBN: 978-0-387-25961-1
FRANTZ, Marc, CRANNELL, Annalisa; Viewpoints: Mathematical Perspective and Fractal Geometry in Art, Princeton University Press, 2011. ISBN: ISBN: 978-0-691-12592-3
GAMWELL, Lynn; Mathematics and Art: A Cultural History, Princeton University Press, 2016. ISBN: ISBN: 978-0-691-116528-8
KAPPRAFF, Jay; Connections: The Geometric Bridge Between Art and Science (1.ª Ed. 1990), World Scientific, 2001. ISBN: ISBN: 981-02-4585-8

Teaching methods and learning activities

The adopted methodology is based on research practices, once it can stimulate active pedagogies which enable the follow up of the defined training process.
Research will be developed based in partnerships, either with peers, individuals or institutions, such as schools, or companies. The promotion of field trips, debates and readings will also be of major importance. These moments will find theoretical support in the recommended bibliography, reinforcing its role in learning.
In order to complete the adopted methodological profile, it is important to underline the relevant role of a permanent, responsible, critical and evaluative debate, which will be fundamental in the assessment and reorientation of activities.
Based on these principles, it is proposed the following distribution of activities, between Contact Hours and Autonomous Work Hours.

The Contact Hours will be devoted to theoretical and practical classes, oriented towards the ongoing students’ researches. Nevertheless, the study leading to assure the transmission of the gained knowledge will also be attended. The remaining moments will be occupied with the following activities:

- presentations addressed by invited researchers, discussing experiences considered to be relevant;

- field trips, either to homologous research centres or to partner educational entities, as well as to research primary sources;

- periodical evaluative debate, keeping students, and teachers always aware of the teaching-learning process evolution, as well as of the overall grade of satisfaction among all involved. Therefore, necessary consolidations or reorientations will be able to take place whenever considered. 

The Autonomous Work Hours will be reserved to:

- develop and consolidate individually and in group, the acquired knowledge;

- construct a research project based on partnerships and debate, and under teacher orientation when required by the student.

keywords

Humanities > Arts > Fine arts > Drawing
Physical sciences > Mathematics > Geometry

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Trabalho prático ou de projeto	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Elaboração de projeto	38,00
Estudo autónomo	38,00
Frequência das aulas	45,00
Trabalho de investigação	38,00
Apresentação/discussão de um trabalho científico	3,00
Total:	162,00

Eligibility for exams

The evaluation will be distributed and will focus 100% on the research projects conducted by the students.

The student's attendance (75%) is an essentially prerequisite to enable ongoing evaluation inherent to the nature of this theoretical-practical course.

Considering the students' individual curricula, teachers will be able to better establish the assessment profile orientation. On the other hand, and subsequently, students will be involved in the definition of a generic body of evaluation parameters, given the challenges that the curricular unit will present to them. It is important to mention the parameters’ flexibility with respect to the developed work over time, and after discussion. However, that feature must be constrained by a strict quality criterion regarding the knowledge to be produced.

At the end of the academic semester there will be a time for all students to reflect critically, individually and in a class group, on the production of knowledge achieved, according to the established assessments parameters.

Calculation formula of final grade

The follow-up of the investigative work and participation in the classes will reveal the investment each student made, and how he did it. It will also reveal students’ gains from classes, bibliography and critical group-class sessions. On the other hand, the students´ performances overview will allow them to become aware of their learning progress and directions to try and/or consolidate. This monitoring will correspond to 40% of the final classification.

The final result obtained from the research work will represent 60% of each student’s final classification.

Internship work/project

There will be two essential tasks to be accomplished by the students, so that they can achieve the proposed skills and knowledge. By doing so, the students will fulfil the course’s goals:

- To formalize research proposals on possible integrated approaches to Geometry as a response to a problem;

- To establish communication strategies to assure transmission and application of the research, for example in future teaching/learning contexts.

Special assessment (TE, DA, ...)

Students with special status or condition must establish with the teachers a Distributed Assessment plan for the component of study and work related to the Contact Hours, in a way equivalent to that of the other UC’s students, but in accordance with their conveniences. The plan must be established in the first two weeks.

Classification improvement

It is settled the improvement of classification in this UC can be achieved by frequency in the following edition of the UC in the course.

Observations

In “Interdisciplinary Approaches to Geometry”, the student will belong to a research group. Therefore, we expect him to be autonomous as well as able to work in a group. Thus, the student will exercise his decision-making power over his knowledge development.

The proposed teaching method will be based on individual and collective research, such as if “Interdisciplinary Approaches to Geometry” was a laboratory. The assessment system will be of an integrated perspective, regarding the entire process and involving a common and responsible participation, both in the definition of the criteria and in its application - under the teachers’ guidance. With these two supports, we can build a process of active and participated knowledge.

Investigative work was chosen to foster a harmonious and synchronized development, both individually and as a group. Thus, and aware of partnerships and networks of knowledge, it will be possible to achieve specific knowledge and skills which were outlined as a cohesive and meaningful body.

On the other side, the followed assessment method will promote individual and collective responsibility reinforcing transversal knowledge and at different times. Therefore, it will be adequate to the development of the mentioned body of knowledge and skills.