ISMAT 14280

Didactics of Geometry

• ApresentaçãoPresentation

  The CU is approached in an integrated way, articulating theory and practice from a critical professionalization perspective. The CU combines a theoretical and hermeneutical dimension, substantiated in the reading and discussion of philosophical and epistemological currents, with a practical and heuristic aspect, centered on problem-solving and creation, on drawing in epure and on the conception of didactic materials, from a perspective of exploring geometric thinking and the possibilities created by the circulation between perception, construction, representation and conception. The use of expository, participatory and laboratory methodologies aims to promote the balanced development of skills. Graphic experimentation takes place in drawing and design workshops, while the creation of pedagogical instruments results from guided reflective practice. The evaluation integrates graphic, creative and instrumental components, aligned with professional teaching practice.  
• ProgramaProgramme

  1. Epistemological Foundations of Descriptive Geometry 1.1. Historical Legacy of Geometric Sciences and Theories of Representation 1.2. Philosophy of Knowledge Transmission in Geometry 1.3. Scenarios of School Evolution 2. Didactics and Pedagogy of Descriptive Geometry 2.1. Pedagogical Approaches and Teaching-Learning Methodologies 2.2. Views on Curriculum, Teaching, and Assessment 2.3. Didactic Transposition, Pedagogical Differentiation, and Visual Mediation 3. Concepts and Geometric Classification 3.1. Perceptual Universe of Geometry 3.2. Classes, Families, and Species of Geometric Figures 4. Dihedral System/Monge's Method 4.1. Study of the Point, Line, Plane, and their Relationships 4.2. Auxiliary Geometric Methods and Complex Projections 4.3. Essential Learnings: a framework subject to appropriation 5. Didactics of Problem Solving 5.1. Formulation of exercises, definition of evaluation criteria 5.2. Applied didactic-scientific illustration 5.3. Planning of activities and tests
• ObjectivosObjectives

  By the end of this course unit, students should be able to: 1. Understand the philosophical, epistemological, and didactic framework of Descriptive Geometry as a science of rational and empirical representation; 2. Master the fundamentals of the Dihedral System / Monge's Method, including point, line, plane, and auxiliary projections; 3. Identify, classify, and organize the main geometric concepts and figures, prioritizing their pedagogical value; 4. Formulate and solve geometric problems based on double orthogonal projection; 5. Design differentiated teaching strategies for teaching Descriptive Geometry, according to different contexts and student profiles; 6. Develop pedagogical tools such as exercises, assessments, and didactic-visual resources applicable to high school teaching.
• BibliografiaBibliography

  Aguilar, L. (1997). Alguns conceitos geométricos. SPA. Arnheim, R. (1997). Visual Thinking. Univ. California Press. Bensabat, F. (1995). Ensinar Geometria Descritiva. Abóboda. Cabezas, L., & Ortega, L. (2001). Análisis gráfico y representación geométrica. Ed. Universitat de Barcelona. Cosme, A., Lima, L., Ferreira, D., & Ferreira, N. (2021). Metodologias, Métodos e Situações de Aprendizagem. Porto Editora. Fonseca, V. (2014). Aprender a aprender: O papel da educabilidade cognitiva e da neuropsicopedagogia. (3ª edição). Âncora Editora. Izquierdo Asensi, F. (1993). Geometría descriptiva. Paraninfo. Izquierdo Asensi, F. (2002). Geometría descriptiva superior e aplicada. CLM. Machado, N. (2025). Epistemologia e Didática: As concepções de conhecimento e inteligência e a prática docente (7ª edição). Cortez Editora. Ricca, G. (2005). Geometria Descritiva: Método de Monge. FCG. Xavier, J. & Rebelo, J. (2001). Programa Geometria Descritiva A, 10.º-12.º anos. ME.  
• MetodologiaMethodology

  The course adopts a mixed and active methodological approach, combining lectures with practical workshops, critical reading sessions, and guided debates. Strategies such as collaborative problem-solving, didactic simulations, drafting in epure, and the construction of pedagogical tests are used. The alternation between student and teacher roles is promoted as a way to develop a critical awareness of teaching and learning processes and to reinforce the capacity for didactic planning. The pedagogical model values ¿¿the integration of theory, practice, and critical reflection.  
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não