Mathematics 1 (5-10) Module 1: Numburs and and mathematical understanding

In this module, students explore key topics in mathematics education and mathematical content relevant for teaching mathematics in grades 5-10, with a particular focus on numbers and number sense. A central theme is the concept of comprehensive mathematical competence and how it is reflected in the current national curriculum. The course includes discussions on various perspectives and attitudes toward mathematics as a subject and its teaching. Emphasis is placed on developing both conceptual understanding and procedural knowledge. Students will examine how learners can be supported in developing their understanding of numbers—from whole numbers to rational and real numbers—and in building strategies for arithmetic operations. An important aspect of the course is the use of multiple representations of numbers and operations. Topics such as fractions, fraction operations, and their connections to decimals and percentages are covered, along with prime numbers, divisibility, and factorization. A key teaching practice addressed in the course is the selection, analysis, and adaptation of different types of tasks and teaching resources (both analog and digital), with a focus on their potential to support learning.

Knowledge

Upon completing the course, the student will:

• have in-depth knowledge of numbers and arithmetic as taught in grades 5-10;
• be able to explain the significance of different forms of representation—particularly within number and arithmetic—for the development of students’ conceptual understanding and procedural knowledge;
• be able to describe what mathematical competence entails, as well as different perspectives and attitudes toward mathematics as a subject;
• be able to explain various types of mathematical tasks and the learning opportunities they offer;
• be able to describe the structure of the place value system and its didactical implications.

Skills

Upon completing the course, the student will:

• be able to engage with number theory problems beyond the scope of the primary and lower secondary mathematics curriculum;
• be able to analyze and adapt mathematical tasks to support students’ development of mathematical competence, especially conceptual understanding and procedural knowledge;
• be able to plan varied teaching activities that foster students’ curiosity and creativity;
• be able to analyze students’ thinking and problem-solving strategies;
• be able to evaluate different teaching resources and how they can support students’ development of number sense.

General Competence

Upon completing the course, the student will:

• be able to articulate the importance of mathematics as a general education subject, both in school and in society;
• be able to explain aspects of mathematics teaching that support students’ development of comprehensive mathematical competence;
• be aware of their own views on mathematics and how these may influence their future teaching practice.

The course employs a variety of teaching and learning methods, including lectures, individual and group work on tasks, discussions, and both oral and written student presentations. Exploratory learning processes are emphasized to promote students’ critical reflection and their development toward becoming mathematics teachers.