Course Objectives

Mathematics 3 –Module 1 covers the topics of number theory and didactics.

In this module, the students will gain insight into the fundamental principles and methods of number theory, and learn to use this information to solve basic problems. In doing so, they will receive considerable practice in calculation techniques which are used with number theory. In addition, the students will work regularly with mathematical proofs and reasoning, in order to learn to understand and produce basic proofs which are a significant aspect of school mathematics. The course will widen the students’ understanding of number theory, and will give them an insight into the theoretical foundations of arithmetic which will allow them to see the relationship between numbers and calculation in a wider perspective.

The students will learn to use spreadsheets to solve fundamental theoretical-numerical problems which require extensive calculation, and they will become familiar with some applications which are useful in lower secondary-school mathematics. They will also learn to organize spreadsheets so that others will find them logical and practical. They will be introduced to internet pages which contain information on number theory.

The students will be familiarized with topical literature and research within the field of mathematics education, and become acquainted with the most important aspects of work methods and learning theory in mathematics. In this process, the students will also widen their knowledge of approaches to mathematics education, which will allow them to understand the importance of mathematics in the school program and explain it to parents and others.

In Mathematics 3, the students will acquire an insight into the history of some of the course’s main topics. They will gain experience in a realistic teaching situation where they will plan and carry out lessons in mathematics, and must be able to demonstrate that they can judge their own performances.

In the specialization unit Mathematics 3, a major objective will be to improve the students’ knowledge of the subject. Students will encounter mathematics as a school subject, where the inductive method is preferred, but they will also view mathematics on its own premises and acquire experience in how it is practiced 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 1 presents an introduction to number theory related to topics:

natural numbers, reasoning and proof in mathematics - factors, divisibility and remainders – the meaning of prime numbers – analysis of numerical sequences – figurate numbers and geometric shapes – diophantine equations – congruence calculation - linear congruencies and systems of such – special division rules – basic cryptography – some principle number theory functions – some basic equations in number theory – Pythagorean triple.

Didactic topics that will be focused on are problem solution and discovering, children’s perception of mathematical reasoning and proof, the development of children’s use of concepts related to numbers and some more general didactic topics. Further, the historical development of number theory will be discussed.

Topics for the subject-didactics assignment in Mathematics 1 are: Problem solution and discovering as a working method in mathematics. In Part 1 of the assignment, theory and basic questions 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 1 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.
Students in the 3rd class of the General Teacher Education programme will complete a compulsory period of teaching practice, which is described in the General Teacher Education Programme Curriculum (2003).

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 5-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