## A five-day doctoral course, 7,5 points (hp)

**Aims**

The course is open to PhD students who are working in mathematics education in the Nordic countries, whose research explores the teaching and learning of Arithmetic and /or its processes, e.g. problem solving, misconceptions and learning difficulties.

The aim of this course is to engage students in a discussion of theoretical and empirical research on the teaching and learning of arithmetic to students of across all years of compulsory school.

An emphasis is placed on:

- research-based specifications of arithmetic-specific goals (What should be learned? What can be learned? Which priority is given to particular aspects and why? Misconceptions, and learning difficulties)
- The analysis of learning processes and learning outcomes in different arithmetic-specific learning environments and classroom cultures.
- Current approaches to the design of rich arithmetic-related learning environments

**Other information**

**Prerequisites and conditions for acceptance on the course**

Course members must be current members of a doctoral program in mathematics education, pedagogy, didactics or equivalent at a university or equivalent.

**Course content**

The course will engage students in a discussion of theoretical and empirical research on the teaching and learning of arithmetic to students across all years of compulsory school.

An emphasis is placed on:

- Examining research-based specifications of arithmetic-specific goals (What should be learned? What can be learned? Which priority is given to particular aspects and why? Misconceptions, and learning difficulties);
- Analysing learning processes and learning outcomes in different arithmetic-specific learning environments and classroom cultures;
- Critically analysing current approaches to the design of rich arithmetic-related learning environments;
- Critically analysing current teacher education practices.

**Learning outcomes**

On course completion students will understand international perspectives on the teaching and learning of arithmetic in order to be able to

- critically analyse research on the interplay between conceptual understanding and procedural fluency
- critically compare arithmetic teaching practices in different cultural contexts
- critically analyse, current curricular specifications
- design a research intervention task in arithmetic.

**Teaching**

Instruction will comprise seminars, workshops and discussions as well as group and individual exercises. Participation in all elements is mandatory. Where special circumstances exist, the examiner, after consultation with the course leader, may condone students’ failure to attend particular elements.

**Assessment**

- The course will be assessed by means of both written assignment and oral presentation
- The only grades awarded will be Pass or Fail.
- Students who fail either component are entitled to four further examinations, as long as the course is given. Students who fail the examination twice have the right to ask that another assessor is appointed to determine the grade. The application should be made to the Board.