VU-PPMD240 .

Credits (ECTS):15

Course responsible:Stine Marie Fykse Haraldsen

Campus / Online:Taught campus Ås

Teaching language:Norsk

Course frequency:Annually

Teaching and exam period:The course starts in the spring semester, and has teaching/assessment in the spring semester.

About this course

  • Number theory: Mathematical induction, division and divisibility, greatest common divisor and least common multiple, Euclid's algorithm, prime numbers, Eratosthenes' sieve, diophantine equations, congruence arithmetic, linear congruences, Fermat's little theorem, group theory, applications including RSA encryption. Programming of selected topics.
  • Problem solving: Introduction to problem solving, problem-solving tactics such as use of symmetry, extremal principle, Dirichlet's box principle, and invariants. Selected topics among graph theory, complex numbers and generating functions.
  • Mathematics Education: Review and exploration of the varied ways of thinking and working in mathematics, based on curricula, competence goals and principles for good mathematics teaching. Planning, implementation and assessment of and for learning. One work requirement in the subject will require knowledge sharing in own faculty.

Adapted education will be integrated in the mathematical and mathematics education content of the subject.

Learning outcome


  • You are familiar with basic concepts and theorems from mathematical theory, and areas of application for these.
  • You have knowledge of mathematics education principles and theories that together provide a varied repertoire of learning strategies and work and assessment methods in mathematics.
  • You have knowledge of curricula and competence goals in mathematics aimed at grades 8-13.You are aware of academic and motivational challenges for students, and how mathematics teaching can be adapted for different students.
  • You have knowledge of how ICT and digital tools can be used in planning, implementation and assessments in mathematics.


  • You can apply covered theory to solve problems within number theory.
  • You can use the covered problem-solving techniques to explore and solve various problems.
  • You can plan, implement and assess teaching based on research and experience-based knowledge and the school's governing documents.
  • You can lead and facilitate teaching sequences that lead to good academic and social learning processes.
  • You can use varied working methods, adapt the teaching, and create a motivating and inclusive learning environment.
  • You can use forms of assessment that contribute to promoting learning in the subject.You can use ICT to promote good learning and assessment practices in mathematics.

General competence:

  • You can, with the help of knowledge from other parts of mathematics, judge the validity of mathematical formulations of problems and solutions to these.
  • You can, with a high degree of independence, reflect on your own teaching practice in mathematics, further develop your own mathematics education competence through professional literature, research and experience, and contribute to both colleagues' and the school's development.
  • You can communicate mathematics education issues, orally and in writing.You can orient yourself in, and critically relate to, professional literature.
  • One-way online lectures and two-way online exercises. 3 gatherings of 5 days each during the semester on campus in Ås. In addition to the gatherings, there is also an offer with calculation exercises. Mathematics education principles are reviewed at gatherings. Between the gatherings, students should use the principles in practice and reflect on this.

    During the semester, there will be mandatory submissions in mathematics and mathematics education.

  • The course has a combined assessment consisting of two parts that are equally weighted: The course has one written mid term test (3.5 hours) in number theory. In addition, students must submit a written (semester) assignment in mathematics education.

    In the problem-solving part of the course, there is compulsory work that must be approved to receive a grade in the subject. The evaluation in number theory and the semester assignment are equally weighted in grading and together constitute the entire grade for the subject.

    Written exam Grading: Letter grades Permitted aids: B2 Calculator handed out, other aids as specified Term paper Grading: Letter grades