Didactics of Mathematics in the 1st Cycle

Scholar Year: 2020/2021 - 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 Joana Brocardo   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.
The syllabus focuses on key issues of the didactics of the first cycle: learning of elementary mathematical topics, milestones of its evolution and curricular materials’ analysis - tasks, manipulative materials, interactive digital materials (applets and dynamic geometry software). Globally it focuses on the teaching and learning of the following mathematical topics: operations with rational numbers in its different representations; properties of plane and space figures; isometries, different measurement systems and measurement processes, development of algebraic thinking and representation and interpretation of data.

Teaching methodologies

The work to be developed will focus on active student participation, whether in individual or in group work, looking for the deepening of knowledge related to the syllabus. The activities to be developed will include discussion of didactic texts as well as exploration and critical analysis of curriculum materials and will be focused on four structuring domains of the teacher's work: (a) Representation of mathematical ideas; (b) Planning math classes; (c) Assessment of student knowledge; (d) Mathematical reasoning.
The tutorial support, individual or group support, consists in the orientation of the student study, clarifying doubts and monitoring the preparation of the written works. The tutorial support can also be done at distance, through a collaborative platform (moodle).

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 choose either continuous assessment or final exam.
Continuous evaluation will be a continuous process of retroactive regulation that will include products developed either individually or in groups and will focus on the work developed throughout the UC. In 2019/2020, this UC is organized into two main parts: the first that runs between the beginning of the school year and January 24, 2020; the second runs from February 19, 2020, until the end of the school year. The evaluation products for each of these parts will have a weight of 50% in the final classification and will be specified in documents focused on these products.
The final exam involves the completion of a written exam that will focus on all syllabus.

Attendance system

Students who choose the continuous assessment modality must participate in at least 70% of UC classes. Those 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 (s) within 15 days of commencement of classes.

Bibliography

Boavida, A., Paiva, A., Cebola, G., Vale, I., & Pimentel, T. (2008). A Experiência Matemática no Ensino Básico. Lisboa: ME-DGIDC (https://comum.rcaap.pt/bitstream/10400.26/5566/1/A_experiencia_matematica_no_ens_basico.pdf)
Breda, A.; Serrazina, L.; Menezes, L.; Oliveira, P., Sousa, H. (2011). Geometria e medida no ensino básico.Lisboa: DGIDC; Lisboa (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. Lisboa: DGIDC.(http://area.dgidc.min-edu.pt/materiais_NPMEB/home.htm)
Brocardo, L. Serazina, & Isabel Rocha (Eds.). (2008). O sentido do número: Reflexões que entrecruzam práticas. Lisboa: Escolar Editora. (Disponível na biblioteca da ESE)
Chapin, S., O’Connor, C., & Anderson, N. (2003). Classroom discussions: Using math talk to help students learn, Grades 1-6. Sausalito, CA: Math Solutions Publications (Disponibilizado pela docente)
Graça Martins, E., Loura, L., Mendes, F. (2007). Análise de dados. Lisboa: ME (http://www.esev.ipv.pt/mat1ciclo/2008%202009/analise_dados.pdf)
Haylock, D. (2010). Mathematics explained for primary teachers. London: Sage. (disponível na biblioteca da ESE)
Mendes, F., Brocardo, J., Delgado, C., Gonçalves, F. (2010). Números e operações : 3º ano (http://area.dgidc.min-edu.pt/materiais_NPMEB/home.htm)
NCTM (2007). Princípios e Normas para a Matemática Escolar. Lisboa: APM e IIE (disponível na biblioteca da ESE)
Ponte, J. P., Brocardo, J., & Oliveira, H. (2003). Investigações matemáticas na sala de aula. Belo Horizonte: Autêntica (Disponível na biblioteca da ESE)
Ponte, J.; Branco, N. & Matos, A. (2009). Álgebra no ensino básico. Lisboa: DGIDC(http://repositorio.ul.pt/bitstream/10451/7105/1/Ponte-Branco-Matos%20%28Brochura_Algebra%29%20Set%202009.pdf)