Mathematics 1 (5-10) Module 2

In this course students will work with mathematics didactics and mathematical subjects that are important to anyone who will teach mathematics in grade 5-10, with special emphasis on geometry. This involves work related to measurements and computations, and classical geometry with constructions and transformations. We will use compasses, rulers, and dynamic geometry software. We will also look at different proofs and argumentations, and the process of discovery. A central part of this work will be the role of communication in the classroom.

Learning outcome
Knowledge
The student
- has in-depth understanding of the mathematical topics that the students work on in grade 5-10 -- particularly different aspects of geometry related to measurements and computation -- as well as analytical geometry and transformations
- has insight into the use of different teaching materials, both digital and physical, as well as the opportunities and limitations such teaching material provides for learning
- has knowledge of various methods for teaching geometry
- has knowledge of effective oral expression, reading, and the ability to use digital tools
- has knowledge of the process of discovery in mathematics: experimentation, developing hypotheses, verification and falsification, generalization, and how to facilitate student participation in these processes of discovery
- has knowledge about the theories of learning, and the connection between various views on learning, subject matter, and knowledge
- has knowledge of common interaction patterns and communication related to mathematics teaching
- has knowledge of the importance of different forms of representation in mathematics, especially in geometry, and the challenges that relate to transitions between representations
- has some initial knowledge about research methods in mathematics didactics and ethical issues related to research involving students

Skills
The student
- can plan, implement, and evaluate mathematics teaching for all pupils in grade 5-10, with a focus on variation and student activities, based on theory and practice
- has strong practical skills in oral and written communication regarding mathematics, and the competence to promote such skills in the classroom
- can use methods that promote students' wonder, creativity, and ability to work systematically with exploratory activities, justifications, arguments, and proofs
- can assess students' learning in order to plan and adjust the lessons
- can communicate with students individually and in different groups
- can listen to students, evaluate and make use of the students input, and institutionalize this knowledge
- can analyze and evaluate students' ways of thinking, argumentation, and strategies

General competence
The student
- has knowledge of the importance of mathematics as general education, and its interaction with cultural, philosophical, and social development
- has knowledge of the role of mathematics in other subjects and in society in general
- has knowledge of the importance of mathematics as it applies to citizens’ participation in a democratic society

Teaching methods comprise class lessons, collaborative and individual work with assignments, discussions, and some oral and written presentations. The process of discovery and learning should promote the students' independence, analytical skills, and critical reflection.