Mathematics 2 (5-10) Module 1:Geometry and Problem Solving in Mathematics

In Mathematics 1 course 2, the students work with topics in mathematics education and in mathematics that are important for teaching mathematics in grades 5-10, with special emphasis on geometry and problem-solving. Problem-solving is a central part of overall mathematical competence, and in this course, we will explore how to facilitate it in mathematics teaching. In geometry, work will be done on, for example, properties of 2- and 3-dimensional figures, constructions, symmetry, and measurement. The nature and historical development of mathematics are discussed in relation to the axiomatic structure of geometry and the role of definitions and proofs. The historical development of the number concept and the expansion of the number set to include negative and irrational numbers are also worked on in the course. Key teaching practices being worked on include setting clear goals for teaching, planning teaching activities, and mathematical discussions.

KNOWLEDGE

After completing the course, the student should

• have in-depth knowledge of the geometry topics students work with in grades 5-10
• have knowledge of the development of geometric thinking in pupils
• have knowledge of problem solving as a central part of mathematical competence
• be able to explain the nature of mathematics, and the role of proofs and definitions in mathematics
• be able to explain mathematics' historical development of number concepts, especially about negative and irrational numbers, arithmetic with them, and pupils' challenges within the topic
• be able to explain the importance of mathematical norms and communication for pupils' learning

SKILLS

After completing the course, the student should

• be able to familiarize themselves with and work with geometric topics beyond the mathematics subjects in primary and lower secondary school
• be able to plan, carry out and assess teaching about geometry and numbers that support pupils' learning
• be able to develop and carry out problem-solving activities with pupils in grades 5-10
• be able to use digital tools such as dynamic geometry programs and block programming in geometry teaching
• be able to set clear academic goals for teaching, develop activities and plan and carry out mathematical discussions

GENERAL COMPETENCE

After completing the course, the student should

• have knowledge of the importance of mathematics as a general education subject and its interaction with culture and philosophy
• be able to account for aspects of mathematics teaching that can support pupils' development of comprehensive mathematical competence
• be aware of his/her own view of mathematics and mathematics learning, as well as the significance it may have for future professional practice

The working methods alternate between presentations, work with joint planning, various assignments, discussions, and oral and written student presentations. Exploratory learning processes are used to promote the students' critical reflection and development towards becoming mathematics teachers.

Compulsory work

• Compulsory attendance in teaching, 75%
• Up to eight written assignments
• Participation in up to four workshops