Recommended Prior Knowledge

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Objectives

- Deepen scientific knowledge of maths topics;- Understand and use mathematical topics to interpret, represent and explore problems of diverse origin;- Represent and explore problems using different strategies and representations;- Understand what it means to reason mathematically;- Understand and mobilise different types and processes of mathematical reasoning;- Produce and evaluate mathematical arguments related to different mathematical topics, using different types and processes of reasoning;- Mobilise knowledge of mathematical reasoning and problem solving to critically reflect on the development of these mathematical skills in the early years.

Teaching Methods

The work to be carried out within this course adopts an active learning approach, with students-either individually or in groups-engaged in situations designed to deepen their knowledge of the specified topics and to develop their critical thinking, creativity, and innovation.

Sessions include the presentation and analysis of course content within a context of problem-solving and research tasks, prioritizing approaches based on the development of challenging tasks (Task-Based Learning) and complex problems (Problem-Based Learning). The work processes include solving proposed tasks and preparing reports; writing and presenting written assignments; and reading, discussing, and analyzing scientific articles on the course topics. They also include the use of information and communication technologies (ICT), specifically digital educational resources (DER), such as interactive platforms or tools that enable collaborative work, notably Padlet and Jamboard.

Tutorial support will consist of guidance and organization of study on the various topics, as well as the clarification of questions arising from the study.

Internship(s)

Não

Syllabus

Problem solving in math-What is a problem-Types of problems-Stages of problem solving - Polya's model-Problem-solving strategies - heuristics-Formulating mathematical problems from different contexts-Problem solving in early years math learning Mathematical reasoning-Characterising mathematical reasoning-Types of mathematical reasoning-Mathematical reasoning processes-Tasks that promote mathematical reasoning-Mathematical reasoning in early years math learning Problem-solving and the development of mathematical reasoning in the context of different mathematical themes: Numbers, Geometry and Measurement, Algebra and Data. Problem solving and mathematical reasoning in curriculum documents related to the early years.

Content Explanation

Two of the transversal mathematical skills present in current official curriculum documents, such as the Curriculum Guidelines for Pre School Education and the Core Maths Learning for Basic Education, are problem-solving and mathematical reasoning. Furthermore, one of the areas of competence identified in the "Profile of Students Leaving Compulsory Schooling" (Martins et al., 2017) is precisely "Reasoning and problem solving". It is, therefore, important that future Kindergarten and elementary teachers acquire a solid scientific knowledge of problem solving and mathematical reasoning and how to promote these in the context of early years math.

Methodology Explanation

At the end of the course, students are expected to: (a) deepen their scientific knowledge of mathematical topics and use it to interpret, represent and explore problems of different origins; (b) use different strategies and representations to solve problems; (c) understand what mathematical reasoning consists of and mobilise different types and processes of mathematical reasoning; (d) produce and evaluate mathematical arguments related to different mathematical topics, using different types and processes of reasoning; and (e) mobilise knowledge about mathematical reasoning and problem solving to critically reflect on the development of these mathematical skills in the early years. To achieve the objectives of the course, students will be involved in a variety of activities, individually or in groups, in face-to-face or distance sessions, such as solving problems about different mathematical topics and producing reports, as well as preparing and presenting work related to mathematical reasoning processes. Making, presenting and discussing assignments in class will be important activities for students to develop the ability to communicate mathematically (using different representations and producing mathematically valid arguments), a transversal ability associated with both problem-solving and the development of mathematical reasoning. We also envisage a pedagogical isomorphism between the teaching-learning process adopted in this course and the teaching practices that students will develop both in their internship and in their professional context, in order to promote the development of problem-solving and mathematical reasoning in the early years.

Responsible Lecturer(s)

Maria de Fátima Pista Calado Mendes - 1.º Semester

Bibliography

Boavida, A., Paiva, A., Cebola, G., Vale, I., & Pimentel, T. (2008). A experiência matemática no ensino básico. DGIDC. ME. Delgado, C., Brocardo, J., & Mendes, F. (Orgs.). (2022). Desenvolver o Raciocínio Matemático dos Alunos: Práticas e Desafios. Instituto Politécnico de Setúbal. http://hdl.handle.net/10400.26/39881 Delgado, C., Mendes, F., & Mata-Pereira, J. (Orgs.). (2022). Raciocínio matemático nos 1.º e 2.º ciclos. Números. Brochuras Reason. http://reason.ie.ulisboa.pt/wp-content/uploads/2023/01/EBOOK_BROCHURA_NUM12.pdf Mendes, F., Delgado, C., & Mata-Pereira, J. (Orgs.). (2022). Raciocínio matemático nos 1.º e 2.º ciclos. Geometria. Brochuras Reason. http://reason.ie.ulisboa.pt/wp-content/uploads/2023/01/EBOOK_BROCHURAS_GEOM_12S.pdf NCTM (2017). Princípios para a Ação. Assegurar a todos o sucesso em Matemática. APM. Vale, I., Pimentel, T., & Barbosa, A. (2015). Ensinar matemática com resolução de problemas. Quadrante, 24(2), 39–60. https://doi.org/10.48489/quadrante.22923