Algebra and Functions

Scholar Year: 2023/2024 - 2S

Courses

Head Teacher Responsability Catarina Raquel Santana Coutinho Alves Delgado 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 1 3,20 Margarida Rodrigues   3,20

Teaching language

Portuguese

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

 To represent and explore problems and mathematical structures, using different representations, namely the algebraic symbols;
 To model and use quantitative relations connecting various types of representations
 To evaluate the adequacy of mathematical models used to represent phenomena;
 To identify functions of various types and differentiate their properties;
 To analyze the variation in different contexts; - To identify different algebraic structures;
 To reveal the ability to connect ideas, concepts and mathematical procedures;
 To produce and to evaluate mathematical arguments related to the theme Algebra and Functions, using various types of reasoning and methods of proof.

Syllabus

 Regularities and relationships
• The equality as relation of equivalence
• Equations and inequations
• Ratio, proportion, and percentage
• Direct and inverse proportionality
• Different roles of the symbols in Algebra
• Problem solving problems involving regularities and relationships
 Functions
• The concept of function
• Types of functions: continuous and not continuous; linear and nonlinear
• Direct proportionality and inverse proportionality as functions
• Representations of functions: natural language, tables, graphs and algebraic language
• Problem solving problems involving functions
 Mathematical modeling
• Cycle of mathematical modeling
• Modeling and problem solving with technology

Demonstration of the syllabus coherence with the UC intended learning outcomes

It is intended that students expand their knowledge to understand in depth the key concepts on the theme Algebra and functions listed in the mathematics curriculum of primary and upper primary education. The program stems from the assumption that Algebra is primarily a way to reason about mathematical situations and to identify and to generalize relationships expressing them in different ways. Thus, it was considered important that the contents were worked from problems that allow manipulation of symbolic expressions and, above all, to attribute meaning to symbols and to use them as a resource to represent general ideas. The study of functions, relations, and variation is one of the aspects of Algebra. A deep understanding of the concept of function allows the interpretation and analysis of many phenomena. So, it is essential that future teachers develop their functional thinking by their involvement in activities of mathematical modeling.

Teaching methodologies

The classes of the course will mainly have a theoretical and practical orientation. Emphasis will be a working methodology based on problem solving and discussion of the solutions of these problems. The problems will have varying degrees of complexity and openness and will be explored using different ways of working (individual work, small groups, whole class). Furthermore, theoretical information related to the contents will be provided and it will be proposed that the students research information about these contents and prepare, with the supervision of the teacher, presentations to the class. There will also be tutoring sessions designed to assist students in organizing the study and clarify doubts.

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

The learning outcomes listed before are focused on learning, with understanding, of mathematical concepts and processes related to the theme Algebra and Functions. This learning requires (a) conceptual understanding, (b) procedural fluency, (c) strategic competence (related to the ability to formulate, represent, and solve mathematical problems) and (c) adaptive reasoning (associated with the capacity of logical thought, of reflection
about mathematical ideas and of explanation and justification). All these aspects are central in a problem-solving pedagogy, the main methodological option for the work in the class. The theoretical information provided by the teacher and the preparation and presentation to the class of work carried out by students enables the deepening of their knowledge about the contents of the course and the systematization of this knowledge. The individual written test and the final exam will focus on solving problems related to the syllabus, which is consistent with the methodological options.

Assessment methodologies and evidences

The evaluation elements are: i) an individual written test (50%) and ii) the development and presentation of a group work focused on a topic related to the contents of the course (50%).
Alternatively, students can solve a final exam.

Bibliography

Blitzer, R. (2021). Thinking mathematically (7th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
Musser, G. L., Burger, W. F. & Peterson, B. E. (2013). Mathematics for elementary teachers: A contemporary approach (10th ed.). Upper Saddle River, NJ: Prentice-Hall.
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). SPCE.
Ponte, J., et al. (2009). Álgebra no Ensino Básico. DGIDC – Ministério da Educação.
Setek, W. M. & Gallo, M. A. (2004). Fundamentals of mathematics (10th ed.). Upper Saddle River, NJ: Prentice-Hall.