MA-457 Basic Algebra (Autumn 2025)

The student

• has advanced knowledge regarding what it means to think algebraically and that it involves analytical and deductive processes, symbolizing and manipulation of expressions
• has deeply grounded insight into what algebra in school involves in terms of being able to explain and express relationships and structures in numbers and operation on numbers, and in functions and their structure, and explain algebra's role as a modelling language
• can explain and use the mathematical core elements as described in the curriculum (LK20), particularly Reasoning and argumentation and Abstraction and generalization
• can discover and justify results and relationships between concepts in algebra, number theory and geometry by engaging in exploration, problem solving, abstraction, generalization and use of appropriate representations
• can communicate mathematics one self has developed, and interpret and understand other’s mathematical ideas and reasoning

The course is about familiarity with numbers, operations on numbers and properties of numbers, what it means to think mathematically and what algebraic thinking means and involves in grades 5-10. In the work with reasoning and argumentation we will look at examples of proofs within number theory, geometry, algebra and probability. We will become aware of the premises and conclusions in conjectures and become familiar with different logical modes of argumentation such as direct- and indirect proofs and proofs by use of generic examples.

The course in practicum. Within the five days of practicum, students’ experience in using different teaching resources in mathematics and student active teaching methods will be facilitated.

Joint teaching, work in small groups, compulsory assignments, oral presentations.

There are mandatory work requirements that can be completed either through physical attendance or through submissions. Further specifications about the work requirements will be provided in Canvas at the start of the semester.

The course has an expected scope of work of 267 hours.

It is included 5 days practice for the teacher education students. This is a preparation for the teaching practice in the 8th semester. Other students will perform a didactic work of similar scope as practice.

The teacher education students

• approved obligatory assignments (see Canvas for more information)
• approved practice

Other students

• approved obligatory assignments (see Canvas for more information)
• approved didactic work of similar scope as practice