Introduction to the Didactics of Mathematics
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Recommended Prior Knowledge
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Objectives
Demonstrate knowledge and understanding of fundamental mathematical topics and their learning in the early years, articulating with
mathematical processes, in accordance with research results and current curricular guidelines;
Discuss the main challenges of teaching Mathematics in the first years in light of theoretical and pedagogical assumptions and foundations
of educational processes in Mathematics;
Analyse and discuss the educational potential of different resources and reflect on their use;
Design powerful Mathematics learning experiences by mobilizing and integrating knowledge about teaching Mathematics in the early years,
resources, concepts, processes and mathematical procedures;
Reveal autonomy in identifying and solving pedagogical problems, considering the risks and benefits when making decisions;
Demonstrate an attitude of self-confidence towards Mathematics;
Communicate clearly, coherently and rigorously. -
Teaching Methods
The work to be carried out within the scope of this course favors an active learning perspective, with the students involved, individually or in
groups, in situations that seek to deepen knowledge related to the indicated topics and the development of their critical thinking, creativity
and innovation.
The sessions include the presentation and analysis of the syllabus in a context of problem-solving and exploration of research tasks,
favoring an approach to Project Based Learning, Task Based Learning, Problem Based Learning, Game Based Learning or Inquiry Based
Learning. The work processes include solving proposed tasks and preparing reports; carrying out and presenting written work; reading,
discussing and analysing scientific articles on the themes of the course. They also resort to Information and Communication Technologies
(ICT), namely digital educational resources, as platforms and interactive tools.
Some of the sessions are held in distance learning mode (E@D), both synchronously and asynchronously. Some of the synchronous E@D
sessions have the purpose of discussing a particular topic or solving challenging tasks proposed by the teacher, in small groups (in
simultaneous rooms or breakrooms). Later, in these sessions, the students from the various groups present their conclusions or their
solutions to the class. Also, in the E@D modality, in synchronous sessions, online quiz tools are used (from the Moodle platform and/or
other tools such Kahoot, Mentimeter, Slido, Plickers, Socrative) to do real time questions and answers (Q&A) allowing to assess students'
knowledge of the topics under study and providing immediate and meaningful feedback. There will also be used tools that allow
collaborative work such as Paddlet, Miro, Stormboard, Jamboard.
Asynchronous E@D sessions favour the flipped classroom model and are held alternately with synchronous sessions. In some of these
sessions students will use some of the collaborative tools already referred, as well as shared editable, so the students can collaborate in
solving tasks as a group. Another type of E@D session, in asynchronous mode, is aimed at viewing video-recorded lessons in which the
teacher explains key concepts and gives examples. These can be accessed by the student according to their learning pace, space and
time.
Tutorial support consists of guiding and organising the study of the various topics and clarifying any doubts arising from the study and is
done at a distance in synchronous sessions. -
Internship(s)
Não
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Syllabus
The contents of this course are organised around four main themes:
Numbers and Operations in the early years
- Development of number sense: meaning and perspectives.
- Didactic perspectives associated with the development of number sense.
Geometry in the early years
- Development of spatial sense: meaning and perspectives.
- Didactic perspectives associated with the development of spatial sense.
Quantities and measures in the early years
- Quantities and measurement: differentiating meanings.
- Didactic perspectives associated with the construction of the concepts of quantity and the process of measurement.
The mathematical activity
- essential mathematical processes: problem solving and mathematical reasoning.
- mathematical tasks and other resources to support teaching and learning. -
Content Explanation
The choice of the syllabus stems from the importance of future kindergarten teachers and/or primary school teachers understand how
children of pre-school education and of the first six years of schooling evolve in learning mathematics and how they can support their
progress concerning this evolution. From this arises the option to center the course on didactical perspectives associated with learning
some of the key mathematical themes: Numbers and Operations, Geometry and Quantities and Measurements. Because learning, with
understanding, is inseparable from the learner's involvement in a mathematical activity in which problem-solving and reasoning are at the
forefront, it was also decided to articulate the themes with these two mathematical processes. Through these pathways, we hope to
contribute to the scientific and pedagogical growth of future professionals responsible for learning Mathematics in the early years. -
Methodology Explanation
This course is included in Didactics and is the first in mathematics education that students attend. It is intended to provide them with
resources they can mobilize in the future profession of childhood educators or primary and upper-primary teachers. The option of a
problem-solving pedagogy stems from the fact that these professionals, in their actions, face, constantly, different types of problematic
situations, which can only be successfully addressed if they know and are able to use theoretical and practical knowledge that enable.
Them to understand the origin and nature of the problems and devise ways of acting that lead to satisfactory solutions.
The professional knowledge necessary to teach mathematics is multifaceted. It includes mathematical knowledge and pedagogical content
knowledge of mathematics, which underlies the importance of the exploration and discussion of mathematical tasks and their educational
potentialities. It also includes the knowledge of the students and their reasoning processes, which is reflected in the decision to analyze and
discuss students' productions.
That knowledge has a practical dimension and a theoretical dimension. Hence the need to analyze documents that have a theoretical and
practical character focused on the teaching and learning of mathematics in conjunction with classroom episodes that allow an
understanding of how theoretical ideas are reflected in teaching practices.
Preparing an essay with supervision promotes the integration of these various types of knowledge and directs students to their integration in
educational contexts. The oriented bibliographic search tutorial guidance is essential both to support students’ study and to the preparation
of the essay. -
Responsible Lecturer(s)
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Bibliography
Boavida, A., Paiva, A., Cebola, G., Vale, I., & Pimentel, T. (2008). A experiência matemática no ensino básico. ME/DGIDC.
Breda, A., Serrazina, L., Menezes, L., Oliveira, P., & Sousa, H. (2011). Geometria e medida no ensino básico. ME/DGIDC.
Brocardo, J., Serrazina, L., & Rocha, I. (Orgs.) (2008). O sentido do número – reflexões que entrecruzam teoria e prática
(pp. 3-28). Escolar Editora.
Castro, J. P. e Rodrigues, M. (2008). Sentido de número e organização de dados, Textos de apoio para Educadores de Infância.
ME/DGIDC.
Lannin, J., Ellis, A., & Elliot, R. (2011). Developing essential understanding of mathematical reasoning, Pre-K-grade 8. NCTM.
Mendes, F., & Delgado, C. (2008). Geometria, Textos de apoio para Educadores de Infância. Lisboa: ME-DGIDC.
NCTM (2017). Princípios para a ação: Assegurar a todos o sucesso em matemática. APM.
Ponte, J. e Serrazina, L. (2000). Didáctica da matemática do 1.º ciclo. Universidade Aberta.
Course details
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Code
01103716
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Teaching Mode
PRESENCIAL
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ECTS
4.0
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Duration
Semestrial
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Hours
12h Orientação Tutorial
6h Seminário
30h Teórico-Práticas
Conteúdo atualizado em 09/03/2025 23:14
CONTACTS
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