Introduction to Mathematics Teaching

Scholar Year: 2017/2018 - 2S

Courses

Head Teacher Responsability Ana Maria Dias Roque Lemos Boavida 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 2 6,40 Ana Maria Boavida   3,20 Joana Brocardo   3,20

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 (pre-school 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 decision-making;
• Expresses an attitude of self-reliance 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 pre-school 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 will have a theoretical and practical character. The methodology is focused on a problem-solving 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.

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 upper-primary 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) the individual responses to a set of questions presented by the teacher during classes (50%).
If students do not get a rating higher or equal to 9.5 on the weighted average of (a) and (b) and a rating higher than 7 points in (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.

Attendance system

The option for continuous assessment modality requires the participation of at least 75% of the UC lessons.
It is advisable to consult the Regulation of Frequency and Evaluation of ESS / IPS, in particular Articles 24 and 25. The students with special status who can not meet the frequency conditions mentioned above should contact the teacher responsible for the UC.

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. 3-28). 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, Pre-K-grade 8. Reston: NCTM.
Mendes, M. F., & Delgado, C. (2008). Geometria, Textos de apoio para Educadores de Infância. Lisboa: ME-DGIDC.
Mendes, F., Brocardo, J., Delgado, C. & Gonçalves, F. (2010). Números e operações: 3º ano. Lisboa: ME/DGIDC.
Ministério da Educação e Ciência (2013). Programa e Metas Curriculares de Matemática do Ensino Básico (disponível em http://dge.mec.pt/metascurriculares/index.php?s=directorio&pid=17)
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 3-5. Portsmouth: Heinemann.
O'Connell, S. (2007). Introduction to Problem Solving, Grades PreK-2. 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 Pré-Escolar. Lisboa: Ministério da Educação/Direção-Geral da Educação (DGE)
Small, M. (2014). Uncomplicating fractions to meet Common Core Standards in Math, K-7. Reston: NCTM
Sheffield, L., & Cruikshank, D. (2005). Teaching and learning mathematics: Pre-kindergarten through middle school. Danvers: Wiley Jossey-Bass Education
Van de Walle, J. & Lovin, L. (2006). Teaching Student-Centered Mathematics Grades K-3. Boston: Pearson.
Van de Walle, J. & Lovin, L. (2006). Teaching Student-Centered Mathematics Grades 3-5. 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/