Didactics of Mathematics in the 1st 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 2,00 Maria de Fátima Mendes   2,00

Teaching language

Portuguese

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

To know the didactics of mathematics’ basic conceptual tools to teach in primary educations (6 to 10).
To develop the ability to reflect on teachers' professional practice, analyzing teaching episodes and students’ written productions.
To develop autonomy and the ability to work in cooperation with others, encouraging future teachers to assume a perspective of continuous professional development.
Develop the ability to research in mathematical education by integrating into the work developed by research teams.

Syllabus

The teaching and learning of numbers and operations, algebraic thinking, geometry and measure and data analysis in primary education (6 to 10 years old):
-Concepts and mathematical ideas that support the development of each student.
- Organizing teaching from what each student knows and is able to do.
- Mathematical tasks: types, nature, articulation, and potentialities.
- Non-curricular and curricular materials that teachers can use and/or adapt.

Demonstration of the syllabus coherence with the UC intended learning outcomes

This CU aims to develop the didactical mathematical knowledge of future primary teachers. It focuses on didactic themes associated with the topics and mathematical contents of the essential learnings of this cycle. The syllabus focuses on the key issues of didactics of 1st cycle Mathematics.
Associated with the learning of these topics and mathematical contents, milestones of their evolution are identified, documents and curricular materials are analysed - tasks, manipulative materials and interactive digital materials (digital games, applets and specific educational software) - that can support student learning and pedagogical differentiation strategies in mathematics.

Teaching methodologies

The work to be developed will favor the active participation of students, either individually or in groups, seeking to deepen their knowledge related to the themes of the program. The activities to be carried out are centered on four structuring domains of the teacher's work:
1. Represent mathematical ideas
2. Plan Mathematics classes
3. Evaluate students' knowledge
4. Mathematical reasoning
Students will develop specific knowledge in each of the above areas and deepen their ability to reflect on the effectiveness of their teaching practice.
Domain 1. Represent mathematical ideas. Mathematical ideas and processes can be represented in many different ways. It is important that the teacher has a solid knowledge that allows him to imagine, analyze and relate various mathematical representations and concepts, processes and ideas to explore them properly and effectively support students' mathematical learning.
Domain 2. Planning Mathematics classes. Careful lesson planning is essential to promote quality learning. In fact, getting students interested in Mathematics and developing solid knowledge requires careful planning that integrates mathematical knowledge about the topics to be taught with the didactic knowledge necessary to adequately manage the situations that are foreseeable to arise in the classroom.
Domain 3. Evaluate students' knowledge. Evaluating is much more than proposing and classifying tests. It involves the analysis of interactions between students and with students and their written productions, and also the identification of patterns of evolution in the work carried out by each one. In order to be able to effectively support students' learning, it is essential to know how to assess what students know and to be able to predict how they can explore tasks and respond to the challenges posed by the teacher.
Domain 4. Mathematical reasoning. Developing mathematical reasoning is a central objective for teaching Mathematics, so future teachers need to understand its nature and be able to use strategies that promote it in students. The discussion of mathematical ideas and processes is fundamental to promote the learning of Mathematics. It is therefore important to reflect on the selection and use of tasks that favor the emergence of mathematically powerful discussions, to analyze how they can be explored and to think about how to prepare and conduct these discussions with a view to promoting students' mathematical reasoning.

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

Expected learning outcomes: a) adequate use of current curriculum guidelines for teaching mathematics in primary grades; (b) mobilize fundamental concepts of mathematics education to delineate meaningful contexts for the learning of mathematics in primary grades; (c) present a critical attitude concerning the texts and episodes analyzed during the CU classes; (d) adequate use of the acquired knowledge in planning and conducting classes including student evaluation; (e) plan, collect and analyze data in context of a research focused on mathematics learning.
Thus, the activities to be developed will include: (i) reading and discussion of articles focused on teaching and learning mathematics in the primary school; (ii) exploration and critical analysis of mathematical tasks and other curriculum materials; (iii) preparation of classroom interventions focused on CU themes.

Assessment methodologies and evidences

Students may opt for continuous assessment or final exam.
The continuous evaluation will be a continuous process of retroactive regulation that will contemplate products elaborated either individually or in groups.
Continuous assessment will focus on the work carried out throughout the UC and includes the following elements and respective weights: (i) characterization work of children's numerical knowledge (in pairs) (25%); (ii) preparation of a didactic guide in the field of geometry (in group of 4) (25%); (iii) planning a class on MR (in pairs) (25%) and (iv) reflection on the class carried out (individual) (25%).
The Guides relating to the different evaluation products will be specified in specific documents.
The final exam involves a written test that will focus on all the syllabus.

Attendance system

Students who have a special status (see ESE / IPS Frequency and Assessment Regulations) and are unable to meet the stated frequency conditions should contact the UC teacher within 15 days of commencement of classes.

Bibliography

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Breda, A.; Serrazina, L.; Menezes, L.; Oliveira, P., Sousa, H. (2011). Geometria e medida no ensino básico. DGIDC. (http://www.esev.ipv.pt/mat1ciclo/temas%20matematicos/070_Brochura_Geometria.pdf)
Brocardo, J., Delgado, C., & Mendes, F. (2010). Números e operações: 1.º ano. DGIDC. http://hdl.handle.net/10400.26/5144
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Graça Martins, E., Loura, L., Mendes, F. (2007). Análise de dados. ME. http://www.esev.ipv.pt/mat1ciclo/2008%202009/analise_dados.pdf
Haylock, D. (2018). Mathematics explained for primary teachers. Sage.
Martins, G. O., et al. (2018). Perfil dos Alunos à Saída da Escolaridade Obrigatória. DGE. https://dge.mec.pt/sites/default/files/Curriculo/Projeto_Autonomia_e_Flexibilidade/perfil_dos_alunos.pdf
Mendes, F., Brocardo, J., Delgado, C., Gonçalves, F. (2010). Números e operações: 3.º ano. http://hdl.handle.net/10400.26/5145
ME-DGE (2021). Aprendizagens Essenciais de Matemática. http://www.dge.mec.pt/aprendizagens-essenciais-ensino-basico
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
Ponte, J. P., Brocardo, J., & Oliveira, H. (2003). Investigações matemáticas na sala de aula. Autêntica.