Pattern and Structure in Early Mathematics

This course examines pupils' development of mathematical knowledge in the early years. We will investigate relationships between numbers, and examine how generalizing properties of numbers can prepare an individual for early algebraic thinking. Conceptual understanding of the place value system and patterns and structure will be highlighted in the work with algebraic thinking. The course will also analyze geometric thinking and the understanding of geometric concepts, measurement and programming. Inquiry-based learning processes will be a central topic of the course.

Knowledge

The candidate has

• in-depth mathematical knowledge for teaching at the primary level, especially early numeracy and the transition from arithmetic to algebra
• knowledge about the nature of mathematics, especially the role of patterns and structure in numeracy, geometry, placement and orientation
• conceptual understanding in geometry focusing on language's role in the learning of mathematics
• knowledge about the historical development of mathematics, especially the development of number concept and number systems

• knowledge about the use of different teaching materials, both digital and analog, and the possibilities and limitations of these materials.

Skills

The candidate can

• analyse and evaluate pupils' way of thinking, argumentation, and problem-solving methods with focus on how it affects teaching

• use work methods that promote pupils' wonder, creativity, and ability to work systematically with problem solving activities, reasoning, and argumentation
• Assess the possibilities for learning mathematics when using digital resources

General competence

The candidate has

• insight into the significance mathematics has as a generally educative subject and its interplay with culture, philosophy, and social development.
• insight into the significance mathematics has for development of critical democratic competence.

Different teaching methods will be used, such as discussions, lectures, group work, student presentations, and trial activities involving pupils. Students' active involvement is emphasized, and during the course students will undertake a certain number of tasks of varied character. These include written work assignments and oral presentations, often linked to practice. The practice field as a learning arena will play a central role. It is therefore necessary that students develop a relationship to the elementary school for which they are assigned. Ultimately, it is hoped that students will learn a great deal of their own practice.