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Materials in Mathematics
Scholar Year: 2023/2024 - 1S
| Code: |
EDB10050 |
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Acronym: |
MEM |
| Scientific Fields: |
Formação na Área da Docência |
Courses
| Acronym |
N. of students |
Study Plan |
Curricular year |
ECTS |
Contact hours |
Total Time |
| LEB |
20 |
Study Plan |
1º |
5,0 |
60 |
135,0 |
Teaching language
Portuguese
Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)
- Selects and uses critically diverse materials in solving mathematical problems.
- Identifies advantages and limitations of using a variety of materials, including manipulatives, in the development of mathematical thinking.
- Mobilizes concepts and procedures related to fundamental mathematical themes to solve mathematical problems and to support conclusions.
- Demonstrates the ability to connect mathematical ideas, concepts, procedures, and processes and to mobilize this knowledge to select and use materials that foster mathematical knowledge.
- Uses and incorporates, in an appropriate manner, a variety of communication tools, including ICT, to
promote their own learning.
- Reveals autonomy in identifying and solving problems.
Syllabus
- Problem solving related to several mathematical contents/processes and involving the use of different types of materials;
- The role and importance of materials in the exploration of mathematical situations.
- Critical analysis on the use of materials in the development of mathematical thinking.
- Construction of didactical materials.
Demonstration of the syllabus coherence with the UC intended learning outcomes
Mathematics is often considered a body of abstract knowledge and without any relationship with reality.
However, if we analyze the experience of who does mathematics, we note that this image is too reductive. It is a fact that mathematical concepts are not in any material or may simply be abstracted from them.
However, the materials can play an important role in assigning meaning to mathematical objects, in
problem solving, in mathematizing situations and in formulating, testing, and justification conjectures.
The objectives and syllabus of this course, stem directly from these ideas. Together they aim to enable
students to know and build various types of materials, including games, manipulatives and technological
resources, to select carefully those that may be useful to solve problems and to analyze critically how they can be used to foster mathematical understanding.
Teaching methodologies
The focus will be on the active participation of students either in individual or in group work, seeking to foster the construction of knowledge based on problem-solving activities and the use of several types of materials. The students will be encouraged to reflect on their experiences in the classroom by connecting them with the analysis of texts centered on relevant syllabus issues. In addition, students will be encouraged to design a seminar, to be achieved in the classroom, focused on the theme “The use of materials and problem-solving”. There are, also, tutorial sessions designed to clarify doubts and to support students in the organization of the study.
Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes
It is intended that students critically analyze the potentialities of materials as a resource to support the understanding of mathematical ideas. So it is necessary to give to the students the opportunity to contact various types of materials and to involve them in the exploration of problems and in the
mathematization of situations in which the materials are useful. At the same time, as learning mathematics with understanding, requires the analysis of the mathematical activity developed with the materials, it is essential to encourage reflection on this activity in order to identify the advantages and limitations of the materials. In addition, students may be, in the future, educators or teachers. Thus, it was considered important that they could (a) elaborate didactical materials, (b) analyze texts related to the educational use of materials, and (c) perform, in class, a seminar for which they would have to select problems and provide appropriate materials.
Assessment methodologies and evidences
The assessment will focus on the work carried out along the course. It will be considered the students’
participation in the classes, and the development of individual work. On continuous assessment will be considered participation in class, group work centered on the design and realization of a workshop (60% weight) and also an individual written test (weight 40%). In order for students can get approved at UC, the weighted average of the products must be greater than or equal to 10 values and the classification in the test can not be less than 7 (out of 20). Alternatively, the students can take a final exam.
Attendance system
Students who participate in activities carried out in at least 75% of classes may be included in the continuous assessment system. Students who are unable to integrate into the continuous assessment system will take a final exam.
Students with special statute, in the event that they are unable to attend classes, must negotiate with each teacher (in the first 15 days of classes) the way that will be used for their evaluation, as well as the most convenient timetable.
Students that do not meet continues assessment requirement will have a final exam.
Assement and Attendance registers
| Description |
Type |
Tempo (horas) |
End Date |
| Attendance (estimated) |
Classes |
0 |
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Total: |
0 |
Bibliography
Books and papers
Boavida, A., Paiva, A., Cebola, G., Vale, I., Pimentel, T. (2008). A experiência matemática no ensino básico. Lisboa: ME/DGIDC.
Abreu, A. (2013). O ensino e a aprendizagem de geometria com recurso a materiais manipuláveis : uma experiência com alunos do 9º ano de escolaridade (disponível em http://repositorium.sdum.uminho.pt/handle/1822/29027)
Gardner, M. (1991). Matemática, Magia e Mistério. Lisboa: Gradiva.
Hart-Davis, A. (1999). Admiráveis Puzzles Matemáticos. Lisboa: Bertrand Editora.
Lopes, A. et al. (1990). Actividades matemáticas na sala de aula Lisboa: Texto Editora
Marshall, L., & Paul, S. (2008). Exploring the use of mathematics manipulative materials: iIs it what we think it is? Edith Cowan University – Research online (disponível em http://ro.ecu.edu.au/cgi/viewcontent.cgi?article=1032&context=ceducom)
Martins, C., & Santos, L.(2010). Utilização de materiais manipuláveis num contexto de formação contínua. Actas do Encontro ProfMat2010 (disponível em https://bibliotecadigital.ipb.pt/bitstream/10198/4856/1/ProfMat2010_Martins%26Santos.pdf)
NCTM (2007). Princípios e Normas para a Matemática Escolar. Lisboa: APM.
Neto, J.& Silva, J. (2004). Jogos matemáticos, jogos abstractos. Lisboa: Gradiva.
Serrazina, L. & Matos, J. (1998). O Geoplano na sala de aula. Lisboa: APM.
Stein, M. K., & Bovalino, J. (2001). Manipulatives: One piece of the puzzle. Mathematics
teaching in the middle School, 6 (6), 356-359.
Journals
Educação & Matemática: Associação de professores de Matemática
Teaching Children Mathematics: NCTM
Mathematics teaching in the middle School: NCTM
Sites
http://nctm.org/
http://illuminations.nctm.org
http://www.atractor.pt/
http://nrich.maths.org/frontpage
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