The Mathematics Curriculum in Primary and Lower Secondary Grades

A new national curriculum for compulsory school was implemented in 2011. It contains general goals, guidelines, syllabi, and knowledge requirements.¹³ One central difference from the previous curriculum is a concretization of the syllabi and the core content of the different school subjects.¹⁴ Students in TIMSS Grade 4 were taught according to the curriculum from 2011, while students in TIMSS Grade 8 were taught according to the curricula from 1994 and 2011.

The national mathematics curriculum for compulsory school begins with an overall statement of purpose describing the role of mathematics in society and human activity, and presenting arguments that defend the importance of learning and teaching mathematics. Furthermore, the syllabus outlines overall goals for creating student learning opportunities in mathematics, which may be summarized as follows. Mathematics instruction should give students the opportunity to develop their ability to:

Formulate and solve problems using mathematics, and assess strategies and methods implemented
Apply and analyze mathematical concepts and their interrelationships
Select and implement appropriate mathematical methods to perform calculations and solve routine problems
Apply and follow mathematical reasoning
Use mathematical expressions to represent questions, calculations, and conclusions and to demonstrate reasoning

This part of the syllabus is the same for Grades 1 to 9. The next part of the syllabus, a description of core content, is divided into three tiers: Grades 1 to 3, Grades 4 to 6, and Grades 7 to 9. Core content descriptions are fairly short, and the syllabus does not prescribe the order in which content should be covered or introduced within each tier. The syllabus presents content in six categories, which are the same for all three tiers: Understanding and Use of Numbers; Algebra; Geometry; Probability and Statistics; Relationships and Change; and Problem Solving. The syllabus emphasizes problem solving, identifying it as part of the overall aim that guides teachers in creating learning opportunities, and as a component of core content. The specific core content for each tier is presented below.

The final part of the mathematics curriculum contains assessment criteria that are based comprehensively on the list of competencies presented above, but not correlated to separate competencies. Few explicit references to core content occur in the assessment criteria. Criteria are formulated for three of the five levels in the grading system, in a fairly short and dense way. One example of a formulation of assessment criteria for a passing grade is: “Pupils can solve simple problems in familiar situations by choosing and apply¬ing a strategy with some adaptation to the type of problem. Pupils describe their approach and give simple assessments of the plausibility of results.”

The core content of the mathematics curriculum in Sweden may be summarized as follows:

Grades 1 to 3
- Understanding and Use of Numbers
  - Natural numbers and their properties, how numbers can be divided, and how they can be used to specify quantities and order
  - How the positioning system can be used to describe natural numbers, symbols for numbers, and the historical development of symbols in different cultures
  - Parts of a whole and parts of a number, how parts are named and expressed as simple fractions, and how simple fractions are related to natural numbers
  - Natural numbers and simple numbers as fractions and their use in everyday situations
  - Properties of the four operations (addition, subtraction, multiplication, and division), their relationships, and their applications in different situations
  - Methods of calculating with natural numbers (i.e., performing mental arithmetic, estimating, using written methods, and using calculators) and implementing the methods in different situations
  - Assessing plausibility when performing simple calculations and estimates
- Algebra
  - Mathematical similarities and the importance of the equals sign
  - How simple patterns in number sequences and simple geometrical forms can be constructed, described, and expressed
- Geometry
  - Basic geometrical objects (e.g., points, lines, distances, quadrilaterals, triangles, circles, spheres, cones, cylinders, and cuboids), their basic properties, and how they are related
  - Constructing geometrical objects; using scale for simple enlargement and reduction
  - Common terms used to describe the position of objects in space
  - Symmetry (e.g., in pictures and nature) and how it can be constructed
  - Comparisons and estimates of mathematical quantities—measurement of length, mass, volume, and time in common contemporary and older units of measurement
- Probability and Statistics
  - Random events in experiments and games
  - Simple tables and diagrams, and how they can be used to categorize data and depict results from simple investigations
- Relationships and Change
  - Different proportional relationships, including doubling and halving
- Problem Solving
  - Strategies for mathematical problem solving in simple situations
  - Mathematical formulation of questions based on simple, everyday situations
Grades 4 to 6
- Understanding and Use of Numbers
  - Rational numbers and their properties
  - The positioning system of numbers in decimal form, the binary number system, and number systems used in different cultures in history (e.g., the Babylonian number system)
  - Numbers in fraction and decimal form and their use in everyday situations
  - Numbers in percentage form and their relationship to numbers in fraction and decimal form
  - Methods of calculating with natural numbers and simple numbers in decimal form (i.e., estimating, performing mental arithmetic, and using written methods and calculators) and applying the methods in different situations
  - Assessing plausibility when estimating and performing calculations in everyday situations
- Algebra
  - Unknown numbers and their properties, and using symbols to represent unknown numbers
  - Simple algebraic expressions and equations in situations relevant to students
  - Methods of solving simple equations
  - How patterns in number sequences and geometrical patterns can be constructed, described, and expressed
- Geometry
  - Basic geometrical objects (e.g., polygons, circles, spheres, cones, cylinders, pyramids, and cuboids), their basic properties, and how they are related
  - Constructing geometrical objects and using scale, including in everyday situations
  - Symmetry in everyday life, in art, and in nature, and how symmetry can be constructed
  - Methods of determining and estimating circumference and area of two-dimensional geometric figures
  - Comparing, estimating, and measuring length, area, volume, mass, time, and angles using common units of measurement; taking measurements using contemporary and older methods
- Probability and Statistics
  - Probability, chance, and risk based on observations, experiments, or statistical material from everyday situations; comparisons of probability in different random trials
  - Simple combinatorial analysis in concrete situations
  - Tables and diagrams presenting the results of investigations; interpretation of data in tables and diagrams
  - Measures of central tendency (i.e., average, mode, and median) and how they are used in statistical investigations
- Relationships and Change
  - Proportionality and percent, and how they are related
  - Graphs depicting different types of proportional relationships in simple investigations
  - The coordinate system and strategies for scaling coordinate axes
- Problem Solving
  - Strategies for mathematical problem solving in everyday situations
  - Formulating mathematical questions from everyday situations
Grades 7 to 9
- Understanding and Use of Numbers
  - Real numbers, their properties, and their use in everyday and mathematical situations
  - Development of the number system from natural numbers to real numbers; methods of calculation used in different historical and cultural contexts
  - Using exponents to express small and large numbers, and using prefixes
  - Methods of calculating with numbers in fraction and decimal form (i.e., estimating, performing mental arithmetic, and using written methods and digital technology) and implementing the methods in different situations
  - Assessing plausibility when estimating and performing calculations in everyday and mathematical situations, and in other subject areas
- Algebra
  - Variables and their use in algebraic expressions, formulas, and equations
  - Algebraic expressions, formulas, and equations in situations relevant to students
  - Methods for solving equations
- Geometry
  - Geometrical objects, their properties, and how they are related
  - Representing and constructing geometrical objects; using scales to reduce and expand two- and three-dimensional objects
  - Similarity and plane symmetry
  - Methods of calculating area, circumference, and volume of geometrical objects, and converting between units
  - Geometrical theorems and formulas and the need to argue for their validity
- Probability and Statistics
  - Standard probability and methods of calculating probability in everyday situations
  - How combinatorial principles can be applied in simple everyday and mathematical problems
  - Tables, diagrams, and graphs, how they can be interpreted and used to present the results of students’ own and others’ investigations, and using digital tools to create them; how coordinates and measures of dispersion can be used to assess results of statistical studies
  - Assessment of risk and chance based on statistical information
- Relationships and Change
  - Percent as a means of expressing change and rate of change, and calculations using percent in everyday situations and in different subject areas
  - Functions and linear equations—how functions can be used to examine change, rate of change, and other relationships
- Problem Solving
  - Strategies for problem solving in everyday situations and in different subject areas, and evaluation of strategies and methods implemented
  - Formulating mathematical questions from everyday situations and in different subject areas
  - Simple mathematical models and their application in different situations