Didactics of Mathematics in the 2nd Cycle

Scholar Year: 2023/2024 - A

Courses

Head Teacher Responsability Maria de Fátima Pista Calado Mendes Head

Weekly workload Hours/week T TP P PL L TC E OT OT/PL TPL O S Type of classes Lectures Type Teacher Classes Hours Contact hours Totals 1 2,40 Catarina Delgado   0,53 Maria de Fátima Mendes   0,67

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

• To know fundamental conceptual instruments of Mathematics didactics in the 2nd cycle of basic education, with a view to the teaching and learning process in this cycle of education;
• To develop the ability to analyze the professional practice of teachers and to promote reflection around issues inherent to this practice, particularly about teaching and learning situations of Mathematics in the 2nd cycle of basic education;
• To develop autonomy and the ability to work in cooperation and encouraging future teachers to assume, in their future professional practice, a perspective of continuous professional development.

Syllabus

Numerical, algebraic, geometric and data organization and processing learning in the 2nd cycle, in particular, operations with rational numbers in the different representations, properties of plane figures and in space, isometries, different magnitudes, and measurement processes, algebraic thinking and data representation and analysis:
• Mathematical concepts and notions that support the evolution of each student;
• Fundamental milestones of evolution;
• Teaching mathematics from what each student knows and is capable of doing;
• Mathematical tasks that promote learning: types, nature, articulation and potentialities;
• Curricular and non-curricular materials that the teacher can use and/or adapt to support pedagogical differentiation in the classroom.
• Digital technologies in the classroom of the 2nd cycle: intentionality, organization, and adequacy.

Demonstration of the syllabus coherence with the UC intended learning outcomes

This course aims to support the construction of the didactic knowledge of the future teacher of Mathematics in the 2nd cycle. It focuses on the didactical themes associated with the topics and mathematical contents of the Essential Mathematics Learning of this cycle, following those already covered in the 1st cycle. Associated with the learning of these topics and mathematical contents, milestones of their evolution are identified, curriculum documents and materials - tasks, manipulative materials, and digital technologies (digital games, applets, and specific educational software) - that can support students' learning are analyzed and strategies of pedagogical differentiation in mathematics are discussed.

Teaching methodologies

The work to be developed will privilege the active participation of students, both individually and in groups, seeking the deepening of knowledge related to the themes of the program. The activities will include discussion of didactic texts, analysis of documents and exploration and analysis of the potentialities of tasks, manipulative materials, and digital technologies. The tutorial monitoring will aim at guiding the study, clarifying doubts, and monitoring the work to be developed. It can be done in person or remotely, via Moodle and zoom platform.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

The learning outcomes expected in this CU are at four levels: use appropriately the current curricular guidelines for Mathematics teaching in the 2nd cycle; mobilize key ideas and concepts of Mathematics didactics to design meaningful contexts for Mathematics learning in the 2nd cycle; present a critical and reasoned attitude in the analysis of texts and episodes worked on in the CU and use carefully and critically the acquired knowledge. Thus, the activities to be developed within this CU will include: discussion of articles focused on teaching and learning of Mathematics in the 5th and 6th years; exploration and analysis of the intentionality of mathematical tasks; exploration and analysis of the suitability of manipulative materials; exploration of applets and specific educational software. Besides the analysis of mathematical tasks, students will be involved in their adaptation and in the construction of indications on how to explore them, which reflect the official curricular guidelines for the 5th and 6th years of schooling, and which allow differentiated learning in mathematics.

Assessment methodologies and evidences

The assessment will focus on the work developed throughout the course and includes the following elements and respective weights:
• participation in class activities (10%);
• making a proposal to explore a digital resource for 2nd cycle students (topic Rational numbers - fractions, decimals and percentages) and presenting it to the class (20%) - in groups of 4 and one of 3;
• written analysis, in pairs, of episodes on rational numbers (30%) - individual;
• realisation of a proposal to use a digital resource for 2nd cycle students (Geometry or Data) and presentation to the class (20%) - in groups of 4 and one of 3;
• analysing an article on a topic related to the teaching and learning of mathematics (20%) - in groups of 4 and one of 3.

Attendance system

Students with Special Status must agree alternative forms of participation and assessment with the teacher responsible for the course, in accordance with the RFA.

Bibliography

Breda, A., Serrazina, L., Menezes, L., Oliveira, P., & Sousa, H. (2011). Geometria e medida no ensino básico. DGIDC. https://www.researchgate.net/publication/270051243_Geometria_e_medida_no_ensino_basico#fullTextFileContent
Canavarro et al., (2021). Aprendizagens Essenciais. http://www.dge.mec.pt/aprendizagens-essenciais-ensino-basico
GTEC. (2017). Estratégia Nacional de Educação para a Cidadania. DGE. http://dge.mec.pt/sites/default/files/Projetos_Curriculares/Aprendizagens_Essenciais/estrategia_cidadania_original.pdf
Martins, G., & Ponte, J. (2011). Organização e tratamento de dados. DGIDC. https://repositorio.ul.pt/bitstream/10451/49830/1/Martins%2C%20Ponte%20OTD_revisto2%202011.pdf
Martins, G. O., Gomes, C. S., Brocardo, J. L., Pedroso, J. V., Acosta Carrillo, J. L., Ucha, L. M., Encarnação, M., Horta, M. J., Calçada, M. T., Nery, R. V., Rodrigues, S. V. (2018). Perfil dos Alunos à Saída da Escolaridade Obrigatória. DGE. http://dge.mec.pt/sites/default/files/Curriculo/Projeto_Autonomia_e_Flexibilidade/perfil_dos_alunos.pdf
NCTM (2007). Princípios e Normas para a Matemática Escolar. APM e IIE.
NCTM (2017). Princípios para a ação: assegurar a todos o sucesso em matemática. APM.
Ponte, J., Branco, N., & Matos, A. (2009). Álgebra no ensino básico. DGIDC. http://repositorio.ul.pt/bitstream/10451/7105/1/Ponte-Branco-Matos%20%28Brochura_Algebra%29%20Set%202009.pdf
Santos, E., Brunheira, L., Martins, I., Serra, S., & Martins, C. (2022). Aprendizagens Essenciais em Matemática para o Ensino Básico. Coletânea de tarefas. 5.º ano de escolaridade. DGE. https://aem.dge.mec.pt/sites/default/files/resources/coletanea_5ano.pdf
Van Galen, F., et al. (2008). Fractions, percentages, decimals, and proportions. Sense Publishers.
Recursos diversos: https://aem.dge.mec.pt/pt/recursos