
Introduction to Mathematics Teaching
Scholar Year: 2023/2024  2S
Code: 
EDB30015 

Acronym: 
IDM 
Scientific Fields: 
Didáticas Específicas 
Courses
Acronym 
N. of students 
Study Plan 
Curricular year 
ECTS 
Contact hours 
Total Time 
LEB 
62 
Study Plan 
3º 
4,0 
48 
108,0 
Teaching language
Portuguese
Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)
• Demonstrates knowledge and understanding of fundamental mathematical themes and about the process of learning of these themes in the early years (preschool and the first six years of schooling), linking them with the mathematical processes of problem solving and mathematical reasoning, taking into account with the results of actual research and curricular guidelines;
• Problematizes the main challenges of mathematics teaching in the early years in the light of assumptions and theoretical foundations of pedagogical and educational processes in mathematics;
• Analyzes and discusses educational potentialities of different resources for the teaching of Mathematics and reflects on their use in order to enrich the learning opportunities;
• Conceives powerful experiences of learning mathematics mobilizing and integrating knowledge about the teaching of mathematics in the early years, resources, concepts, mathematical processes and procedures;
• Reveals autonomy in identifying and addressing educational issues, bearing in mind the benefits and risks in decisionmaking;
• Expresses an attitude of selfreliance concerning mathematics;
• Communicates in a clear, coherent and rigorous way, using different formats.
Syllabus
• 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.
Demonstration of the syllabus coherence with the UC intended learning outcomes
The choice of the syllabus stems from the importance of future educators and / or primary school teachers understand how children of preschool 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
Teaching methodologies
The lessons of this course (whether they HP, HS, HPS) will have a theoretical and practical character. The methodology is focused on a problemsolving pedagogy so that the theoretical information is mobilised in situations of practical nature and vice versa. In this context, it is crucial involvement and engagement of students in the proposed tasks, in particular during the lessons. These tasks may or may not entail prior preparation, will be varied in nature and will remit to different types of work (individual work, small group, with the whole class). The working processes will include (a) analysis and discussion of documents: theoretical and practical papers focused on relevant themes related to the syllabus; episodes of classroom and students productions; (b) exploration and discussion of mathematical tasks and of their educational potentialities; (c) oriented bibliographic search on important topics of the course; (d) tutorial guidance concerning the organization of the study, clarifying doubts and monitoring the preparation of the essay.
All resources to support the teaching will be made available on the moodle platform.
Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes
This course is included in the area of Didactics and is the first in mathematics education that students attend. It is intended to provide them with resources they are able to mobilize in the future profession of childhood educators or primary and upperprimary teachers. The option of a problem solving pedagogy stems from the fact that these professionals, in their action, 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 a theoretical and practical character focused on the teaching and learning of mathematics in conjunction with classroom episodes that allow the 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 are essential both to support students’ study as to the preparation of the essay.
Assessment methodologies and evidences
The assessment will be focus on the work developed throughout the course and will be an ongoing process of retroactive regulation that will include moments of individual and group work and activities of written and oral expression.
The students may choose the modality of continuous evaluation or final exam.
Concerning the first modality, the evaluation elements are (a) the development and presentation of an essay focused on teaching and learning of mathematics (50%) and (b) one test that may performed facetoface or remotely, just take the written format or, if the teacher considers it necessary, include an oral component. Any of the products (a) and (b) have a weight of 50%
If students do not get a rating higher or equal to 9.5 on the weighted average of (a) and (b), may hold a final examination as those who do not have opted for the modality of continuous evaluation. This exam will involve the realization of a written test, which will be focused on all topics of the syllabus.
If the results obtained in online or facetoface assessment, appears to indicate the existence of fraud, it will be taken into account the provisions of Despacho No. 40 / President / 2021 promulgated by the IPS President.
Bibliography
Main Bibliography
Boavida, A., Paiva, A., Cebola, G., Vale, I., & Pimentel, T. (2008). A experiência matemática no ensino básico. Lisboa: ME/DGIDC.
Breda, A., Serrazina, L., Menezes, L., Oliveira, P., & Sousa, H. (2011). Geometria e medida no ensino básico. Lisboa: ME/DGIDC.
Brocardo, J., Delgado, C., & Mendes, F. (2010). Números e operações:1º ano. Lisboa: ME/DGIDC.
Brocardo, J., Serrazina, L., & Rocha, I. (Orgs.) (2008). O sentido do número – reflexões que entrecruzam teoria e prática (pp. 328). Lisboa: Escolar Editora.
Brocardo, J., Abreu, A., Paiva, A., Boavida, A. M. et al. (2007). A Geometria nos 1º e 2º ciclos do Ensino Básico. Setúbal: Fotoarte, Lda.
Castro, J. P. e Rodrigues, M. (2008). Sentido de número e organização de dados, Textos de apoio para Educadores de Infância. Lisboa: ME/DGIDC.
Lannin, J., Ellis, A., & Elliot, R. (2011). Developing essential understanding of mathematical reasoning, PreKgrade 8. Reston: NCTM.
Mendes, M. F., & Delgado, C. (2008). Geometria, Textos de apoio para Educadores de Infância. Lisboa: MEDGIDC.
Mendes, F., Brocardo, J., Delgado, C. & Gonçalves, F. (2010). Números e operações: 3º ano. Lisboa: ME/DGIDC.
DGE (2021). Aprendizagens Essenciais de Matemática. https://www.dge.mec.pt/noticias/aprendizagensessenciaisdematematica
NCTM (2007). Princípios e Normas para a Matemática Escolar. (trabalho original publicado em 2000 pelo NCTM). Lisboa: APM.
NCTM (2017). Princípios para a ação: Assegurar a todos o sucesso em matemática. (trabalho original publicado em 2014 pelo NCTM). Lisboa: APM.
O'Connell, S. (2007). Introduction to Problem Solving, Grades 35. Portsmouth: Heinemann.
O'Connell, S. (2007). Introduction to Problem Solving, Grades PreK2. Portsmouth: Heinemann.
Ponte, J. e Serrazina, L. (2000). Didáctica da matemática do 1.º ciclo. Lisboa: Universidade Aberta.
Pimentel, T., Vale, I., Freire, F., Alvarenga, D. & Fão, A. (2010). Matemática nos primeiros anos: tarefas e desafios para a sala de aula. Lisboa: Texto Editores Lda.
Silva, I., Marques, L., Mata, L. & Rosa, M. (2016). Orientações Curriculares para a Educação PréEscolar. Lisboa: Ministério da Educação/DireçãoGeral da Educação (DGE)
Small, M. (2014). Uncomplicating fractions to meet Common Core Standards in Math, K7. Reston: NCTM
Sheffield, L., & Cruikshank, D. (2005). Teaching and learning mathematics: Prekindergarten through middle school. Danvers: Wiley JosseyBass Education
Van de Walle, J. & Lovin, L. (2006). Teaching StudentCentered Mathematics Grades K3. Boston: Pearson.
Van de Walle, J. & Lovin, L. (2006). Teaching StudentCentered Mathematics Grades 35. Boston: Pearson.
9. Other bibliographic resources that may be useful
Journals (Library ESE/IPS)
• Educação e Matemática (APM)
• Teaching Children Mathematics (NCTM)
• Teaching Mathematics in Middle Schools (NCTM)
Sites
• Associação de Professores de Matemática: http://www.apm.pt/
• Direção Geral da Educação: http://www.dge.mec.pt
• Freudenthal Institute: http://www.fisme.science.uu.nl/publicaties/subsets/rekenweb_en/
• National Council of Teachers of Mathematics: http://www.nctm.org
• NRICH enriching mathematics: http://nrich.maths.org/public/
• Programa de Formação Contínua em Matemática da ESE/IPS: http://projectos.ese.ips.pt/pfcm/

