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Patterns and Algebra

Scholar Year: 2018/2019 - 1S

Code: EDB30022    Acronym: PA
Scientific Fields: Formação na Área da Docência
Section/Department: Science and Technology

Courses

Acronym N. of students Study Plan Curricular year ECTS Contact hours Total Time
LEB 46 Study Plan 5,0 60 135,0

Teaching weeks: 15

Head

TeacherResponsability
Joana Maria Leitão BrocardoHead

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 8,00
Joana Brocardo   8,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

Identify, analyze and represent different types of patterns and relationships present in mathematical situations in different phenomena or in everyday life, using for example the technological tools;
Explore sequences of numbers by recursion and looking for general expressions;
Using algebraic thinking in the exploration of numerical situations;
Represent and analyze mathematical situations and structures using different representations, namely the
algebraic symbols;
Solve problems using mathematical models to represent and understand quantitative relationships;
Show the ability to connect ideas, concepts and mathematical procedures;
Develop and evaluate mathematical arguments, using different methods of reasoning and evidence.

Syllabus

The contents are organized around three major themes:
(1) From Arithmetic to Algebra: develop algebraic thinking;
(2) Patterns and Functions;
(3) Modeling.

(1)
Properties of numbers and operations in different algebraic structures. The generalized arithmetic. Direct and
inverse relations of proportionality.

(2)
Numerical and geometric, repeating and growth, patterns. Linear and quadratic sequences.
From patterns to functions: development of functional thinking. Multiple representations of functions.

(3)
Construction and exploration of mathematical models. The technology to support the modeling of mathematical situations and phenomena of everyday life.
The worksheet for exploring models, to generalize from numerical tables and construct recursive and functional relationships.
The Dynamic Geometry Systems (DGS) and the applets: dynamicity, interactivity and multiple representations
offered by the technology.


Demonstration of the syllabus coherence with the UC intended learning outcomes

The development of algebraic thinking is present in situations of Mathematics, other disciplines and daily life, with roots in arithmetic and in working with numerical and geometric patterns.
The study and the generalization of the properties of numbers and operations allow you to create contexts where
different representations (numerical, graphical and symbolic) are articulated to give meaning to the algebraic work.
Modeling supported by equations and functions, and the dynamic and interactive technology, provides support for translating situations, establish conjectures, develop functional thinking and problem solving

Teaching methodologies

The teaching methods include: (a) resolution of tasks and reporting on the performed activity; (b) preparation,
presentation and discussion of written work; (c) discussion and analysis of scientific and technical papers. The
spreadsheet, DGS and applets, provide resources to value approaches to patterns and Algebra.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

Once the goals involve capabilities to explore, represent, analyse, solve problems and reason, it is necessary to promote diverse processes and activities of study, discussion and resolution of tasks. This is what happens with moments of solving practical tasks (use of knowledge), reading and discussion of issues (synthesis and argument)
and identification of core ideas (reflection in comparison with the practice).

Assessment methodologies and evidences

The evaluation will be an ongoing process which will include retroactive adjustment moments of individual work
and group activities and oral and written expression.

Attendance system

Students who participate in at least 75% of classroom sessions may include the system of continuous assessment.

Bibliography

Blanton, M. L. (2008). Algebra and Elementary Classroom: transforming thinking, transforming practice.
Portsmouth: NH Heinemann.
Brocardo, J. et al. (2006). Números e Álgebra: Desenvolvimento curricular. In I. Vale et al. (Orgs.), Números e
Álgebra na aprendizagem da Matemática e na formação de professores (pp. 65-92). Lisboa: SPCE.
Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher & M. Blanton (Eds.),
Algebra in the Early Grades (pp. 133-160). New York: Lawrence Erlbaum.
ME (2007). Programa de Matemática do Ensino Básico. (consultado em 15 de Outubro de 2008 em
http://sitio.dgidc.min-edu.pt/matematica/ Documents/ProgramaMatematica.pdf).
NCTM (2007). Princípios e Normas para a Matemática Escolar. Lisboa: APM.
Ponte, J. (2006). Números e Álgebra no currículo escolar. In I. Vale et al. (Orgs.), Números e Álgebra na
aprendizagem da Matemática e na formação de professores (pp. 5-27). Lisboa: SPCE.

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Página gerada em: 2024-03-28 às 21:41:37