The Mathematics Curriculum in Primary and Lower Secondary Grades
The current national policies on mathematics were published in the 2015 version of the new Simplified Common Objectives.15 This document defines the grade structure in the primary and lower secondary curriculum that covers mathematics instruction as follows: Grades 1 to 3, Grades 4 to 6, and Grades 7 to 9. Because the intermediate achievement goals for Grade 6 are required national goals, they also serve as the guidelines for Grade 4 mathematics instruction. Students may encounter specific skills, such as division, at different points within the curriculum, depending on the municipality, the school board, the teacher, the school curriculum, and the teaching materials (e.g., textbooks).
Overall, students are expected to develop mathematical skills and knowledge and to apply these in real situations. They learn to recognize the role of mathematics in historical, cultural, and social contexts, and take a critical approach to mathematics applications in order to fulfill their civic responsibilities effectively. Students learn independently and cooperatively how mathematics requires and promotes creativity, and how it involves instruments for problem solving, argumentation, and communication.16
Exhibit 1: Mathematical Competence Goals
| Field of Competence | After Grade 3 | After Grade 6 | After Grade 9 |
| Mathematical Qualifications | Students are able to apply mathematics in real situations | Students are able to apply mathematics with comprehensive understanding in complex situations | Students are able to apply mathematics with judgment in complex situations |
| Numbers and Algebra |
Students are able to develop methods of calculation with natural numbers | Students are able to apply rational numbers and variables in descriptions and calculations | Students are able to apply real numbers and algebraic expressions in mathematical studies |
| Geometry and Measurement | Students are able to apply geometric concepts and measurements | Students are able to apply geometric methods and calculate simple measurements | Students are able to explain geometric contexts and calculate measurements |
| Statistics and Probability | Students are able to perform simple statistical surveys and express intuitive chance sizes | Students are able to perform statistical surveys and determine statistical probabilities | Students are able to evaluate statistical surveys and apply probability |
As shown in Exhibit 1, mathematics is divided into four fields of competence in skills and knowledge (færdigheds-og vidensområder), which are divided into several subcategories. The subcategories are divided into three phases each, as follows:17,18
- Mathematical Qualifications
- Problem solving
- Phases 1 and 2—Students can formulate and solve mathematical problems. Students have knowledge about the characteristics of closed, open, and pure mathematical problems, as well as problems relating to the outside world.
- Phase 3—Students can use different strategies for mathematical problem solving and have knowledge about different strategies for mathematical problem solving with digital tools.
- Modeling
- Phases 1 and 2—Students have knowledge of and can complete simple modeling processes.
- Phase 3—Students have knowledge of and can apply simple mathematical models.
- Reasoning and thinking
- Phases 1 and 2—Students can apply reasoning in investigative work. They have knowledge of simple reasoning linked to investigative work, including investigative work with digital tools.
- Phase 3—Students can apply reasoning to develop and verify hypotheses.
- Representation and treatment of symbols
- Phases 1 to 3—Students can distinguish between everyday language and expressions with mathematical symbols.
- Communication
- Phase 1—Students can read and write simple texts and mathematics. They have knowledge about the purpose and structure of texts and mathematics.
- Phase 2—Students can communicate about mathematics orally and in writing, and have knowledge of digital media.
- Phase 3—Students can use specialist terminology and concepts orally and in writing.
- Mathematical tools
- Phases 1 and 2—Students can use tools with professional precision. They know how to apply various tools in different mathematical situations.
- Phase 3—Students can select tools according to their mathematical application, and can use various concrete materials and digital tools.
- Numbers and Algebra
- Numbers
- Phase 1—Students can use decimals and fractions in everyday situations.
- Phase 2—Students have knowledge of and can work with negative integers.
- Phase 3—Students can apply percent, simple potencies, and pi.
- Methods of calculation
- Phase 1—Students can perform calculations using all four arithmetical operations and involving estimates.
- Phase 2—Students have knowledge of and can develop methods of calculation with decimal numbers, simple fractions, and negative integers.
- Phase 3—Students can perform calculations with percent, with and without digital tools. They have knowledge of strategies for calculating percent.
- Algebra
- Phase 1—Students learn how to find solutions to simple equations using informal methods and understand the importance of the equal sign and informal methods of solving simple equations.
- Phase 2—Students can use simple algebraic expressions in calculations. They understand the role of variables in formulas, and how to use digital tools with variables.
- Phase 3—Students can use variables to depict simple situations and understand the role of variables in depicting situations.
- Geometry and Measurement
- Geometric properties and relationships
- Phase 1—Students can categorize polygons according to side lengths and angles, and are knowledgeable about types of angles and sides in simple polygons.
- Phase 2—Students are knowledgeable about calculating angles, the relative position of lines, and methods for examination of plane figures, including use of dynamic geometry programs.
- Phase 3—Students can explore geometric properties of spatial figures, and have knowledge of polyhedrons and cylinders.
- Geometric drawing
- Phase 1—Students can reproduce figures from the outside world by drawing with and without the use of digital tools. They have knowledge of geometric shapes that can represent these figures.
- Phase 2—Students can sketch and draw accurately.
- Phase 3—Students can draw figures using different methods. They have knowledge of geometric shapes for rendering dimension.
- Location and movement in the coordinate plane
- Phase 1—Students have knowledge of and can describe locations in the first quadrant of the coordinate grid.
- Phase 2—Students can describe locations across the grid, and have knowledge of the entire grid.
- Phase 3—Students can produce patterns with reflections, parallel shifts, and twists, and have knowledge of different methods, including methods using digital tools.
- Measurement
- Phase 1—Students can estimate and calculate perimeter and area, and have knowledge of different methods, including those using digital tools.
- Phase 2—Students can estimate and calculate volume, and have knowledge of different methods.
- Phase 3—Students can calculate the circumference and area of circles.
- Statistics and Probability
- Statistics
- Phase 1—Students have knowledge of and can apply and interpret graphical representations of data.
- Phase 2—Students can complete and present their own surveys, and have knowledge of methods of processing and presenting data, including methods using digital tools.
- Phase 3—Students can compare data sets from frequency and simple statistical descriptors.
- Probability
- Phase 1—Students can explore randomness and chance sizes through experimentation, and have knowledge of different methods.
- Phase 2—Students can investigate chance sizes by simulation of chance experiments, and have knowledge of different methods, including methods using digital tools.
- Phase 3—Students have knowledge of the relationship between frequency and probability, and can describe probability as it relates to frequency.