Course Objectives

Mathematics 3 - module 2 covers the topics of geometry, linear algebra and didactics.

In this module, the students will deepen their insight into fundamental geometrical concepts, which will be broadened and supplemented so that they may acquire a more complete understanding of the methods and approaches used in the field of geometry. This, in turn, will enable them to solve complex theoretical and practical problems. This means that the students will become familiar with the principal concepts of geometry, such as vectors, diagrams and matrices. They will learn to interpret and apply these concepts to model and analyze realistic situations, and to solve related problems. The students will gain insight into how the concepts are linked, and broaden concepts which are studied in mathematics education. The visual aspect of geometry provides a unique approach to mathematical theory, and the students will learn of the role this can play in teaching it as a school subject. This will help them understand how geometry in school mathematics paves the way for learning important principles of applied mathematics.

Working with diagrams will give the students insight into how mathematics can model dynamic processes, while widening their understanding of the function concept. This will lead naturally to algebra, a major topic in school mathematics. The students will expand their knowledge of algebra in general, not least with respect to equations and systems of equations. They will see how one may, through concepts such as matrix and vector, formulate an algebraic theory which binds geometry and algebra together. The students will learn to use computer programs for both geometry and algebra. They will, in particular, gain practice and insight into the solution of problems in plane-geometry, such as basic construction, using such programs, and they will see how this approach may be used for teaching.

Students will gain experience from realistic teaching situations where both planning and implementation of teaching mathematics will be included, and they must be able demonstrate that they can reflect on this.

For the specialization unit Mathematics 3, development of pure knowledge of the subject will be an essential goal. Students will of course become acquainted with the mathematics that is taught in schools, where inductive methods are central, but they must also study the discipline mathematics, and gain some experience of how it is pursued as a logical-deductive science.

Course Description

Mathematics is an important part of our culture, both as a science and as a tool in a variety of fields, including other sciences. Mathematics also plays a central role in many forms of creative activity. Therefore, mathematics is a central subject in primary and secondary schools and in the general teacher education programme. Through the study of mathematics in the general teacher education programme students will encounter the subject in a variety of contexts. In addition to gaining knowledge of mathematics, there is a special focus on the nature of the subject and teaching mathematics.
Target areas are described in greater detail in the curriculum for teacher education (1999), and this will be followed with some adjustments.

Mathematics 3 Module 2 presents an introduction to geometry and algebra related to topics:

Representation and calculation using vectors – scalar products and cross-products – normal vectors and directional vectors to straight lines – vector projection – trigonometry – parameter representation of lines and planes in space – congruence representations – symmetry – basic matrice calculation – determinants – equation systems.

The topic for the subject didactics assignment in Mathematics 3 is: problem-solving and investigation as a working method in mathematics. In Part 1 of the assignment, theory and basic problems will be studied. This will form the basis for Part 2, where an examination of pupils’ work will be carried out.

Learning Methods

Mathematics 3 - Module 2 is taught over one academic year, with final examinations in May / June. Four hours teaching per week will normally be offered in each of the modules during the teaching weeks (specified in the semester schedule). A teaching sequence will consist of both lectures and exercises; however, students can expect a degree of flexibility with regards to the organization of the teaching. In addition, individual instruction will be offered in work on exercises.
Subject-didactics work will be included in Mathematics 3; the work is two-fold, with a submission at the end of each semester.

Assessment Methods

The grade in Mathematics 3 is calculated on the basis of the grades for the two 6-hour written examinations and the subject-didactics work. In calculating the final grade, the written examinations count for 80% and the subject-didactics work counts 20%.
All components must receive passing marks before the final grade may be awarded.
Letter grades from A to F will be awarded, where A is the highest grade, and E is the lowest passing grade. F is a failing grade.

Minor adjustments may occur during the academic year, subject to the decision of the Dean