Representations in Elementary Mathematics

Base Knowledge

N/A

Teaching Methodologies

Lectures will be of theoretical and practical nature, they try to articulate the various chapters addressing to the students to perceive the connections within mathematics, through rich tasks. Whenever appropriate, texts, concrete and virtual manipulatives that favor the teaching and learning process will be used.

The assessment in this CU will be performed by students in one of two ways:
a) Continuous assessment: one written test, quoted from 0 to 8 values (40%); a group work, quoted from 0 to 6 values (30%); participation in classroom tasks, quoted, in total, from 0 to 5 values (25%); individual reflection, quoted from 0 to 1 value (5%).
b) Assessment by exam.

Learning Results

– Develop learning from representations, internal and external, of mathematical concepts or ideas.
– Explore mathematical concepts through different representations.
– Distinguish and classify different types of mathematical representations.
– Recognize opportunities and resources to trigger the representation of mathematical ideas.
– Develop representational fluency.
– Develop meaningful mathematical learning.

Program

– Systems of representation and the development of mathematical concepts.
– Representations of numbers.
– The numerical reasoning representation by young children.
– The influence of the language in mathematical representations.
– The use of diagrams as tools to think.
– “Listen” to the mathematical drawings of children.
– The use of literature to invite mathematical representations.
– Mathematics modeling and representation capabilities in mathematics.

Curricular Unit Teachers

Grading Methods

Continuing Evaluation
  • - Frequency - 40.0%
  • - Individual and/or Group Work - 30.0%
  • - Individual reflection - 5.0%
  • - Attendance and Participation - 25.0%
Examen
  • - Exam - 100.0%

Internship(s)

NAO

Bibliography

– Cucuo, A. A., & Curcio, F. (2001). The roles of representation in school mathematics: 2001 Yearbook. National Council of Teachers of Mathematics.
– Goldin, G. A. (2008). Perspective on representation in mathematical learning and problem solving. Handbook of International Research in Mathematics Education, 176-201.
– Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education, National Research Council ; Jeremy Kilpatrick, Jane Swafford, and Bradford Findell (Eds.) (2001). Adding it up : helping children learn mathematics. National Academy Press.
– McGrath, C. (2014). Teaching Mathematics Through Story – A criative approach for the early years. Routledge.
– NCTM (2014). Princípios para a Ação: assegurar a todos o sucesso em matemática. APM (Tradução em 2017).
– SPIEM (2015). Investigação em Educação Matemática – 2015, Representações Matemáticas. SPIEM. http://spiem.pt/DOCS/ATAS_ENCONTROS/atas_EIEM_2015.pdf