The Mathematics Curriculum in Primary and Lower Secondary Grades

The mathematics curriculum was reviewed and updated after the evaluation of the school reform in 2011 to provide more knowledge to and higher expectations from students through all grades. Mathematics covers numbers, geometry, algebra, calculus, and statistics in Grades 1 to 13. The mathematics curriculum for Grades 1 to 9 contains:

General goals
Lists of topics to be taught for each grade
Lists of optional topics to be taught according to teachers’ discretion
Didactical recommendations
Lists of basic standards of knowledge that are expected from the majority of students at the end of each three year period
Minimal standards of knowledge for each grade that are required for student advancement to the next grade

Additionally, the curriculum describes expected approaches to problem solving, policies on homework, individualizations and differentiation, and development of mathematical competencies. It also specifies cross-curricular topics to be taught to link mathematics with other subjects, policies on assessments, and use of ICT and calculators, and lists expected manipulative tools and didactical material to be available in classes for learning mathematics.²²

In elementary school, according to the curriculum, mathematics is aimed at developing basic mathematical competence needed for expressing mathematical ideas and accepting mathematics as a cultural value. Mathematics in school should develop students’ mathematical thinking and use of procedures and technologies; teach facts, structures, and skills; link students’ knowledge of mathematics with other areas; and build students’ confidence and positive attitude toward work and mathematics.

The mathematics topic areas covered for Grades 1 to 8 are as follows:

Grades 1 to 3—Mathematics instruction covers geometry and measurement (orientation in space; basic geometrical shapes; symmetry; and basic measurement units of length, mass, volume, money with recognition of prices written as decimal numbers, and time); arithmetic with algebra (natural numbers up to 1,000 including 0, arithmetic operations with natural numbers up to 1,000, expressions, rational numbers, and parts of a whole); logic and mathematical language (sets, data presentations and diagrams with basic combinatorics, sorting and ordering, and relations); and mathematical problem solving (modeling of everyday situations and patterns).
Grade 4—In geometry and measurement, students learn to draw and recognize characteristics of line segments, lines, and rays; draw rectangles, squares, disks, and circles with the help of rulers and compasses; and perform operations with units of length, mass, volume, and time. The topic area of arithmetic and algebra includes adding and subtracting numbers up to 10,000 (optional: larger numbers), multiplying and dividing by two-digit numbers, using appropriate operations to solve problems, solving expressions with brackets, and solving simple equations and inequalities with reasoning. The topic area of rational numbers includes learning how to divide a whole into equal parts and write simple fractions (optional: recognizing equivalent fractions). Students learn to present sets and subsets, develop reading literacy, model situations with mathematical expressions, conduct a study with collection and presentation of the data, and solve combinatorial problems with manipulatives.
Grades 5 to 7—In geometry, students learn to construct parallel and perpendicular lines, angles, triangles, and circles; draw shapes; calculate area and perimeter of rectangles and triangles, and volume of cubes and cuboids; and draw nets. They learn about linear transformations. They encounter angles, and construct and calculate with them. In algebra, students learn to solve equations and inequalities with one unknown, evaluate expressions with more than one variable given values of the variables, and use simple linear relations. Students formally encounter negative numbers in Grade 5, decimal numbers in Grade 6, and percentages and general fractions in Grade 7 to perform comparisons and calculations in problem solving. Functions are introduced in Grade 7 through drawing tables and graphs and recognizing increasing or decreasing relationships between two variables. Students learn to collect, order, present, and critically interpret data, use electronic spreadsheets, and calculate with fractions and percentages on calculators. They learn to use the mean in solving problems. In problem solving, the focus is on development of reading literacy, combinatorial problems, modeling, patterns, and mathematical solutions of real problems.
Grade 8—In geometry, students learn how to use the Pythagorean theorem to calculate the length of sides of triangles, as well as the area and volume of trapezoids, rhombuses, circles, cubes, and cuboids from formulas. They calculate the area and circumference of circles (optional: calculating the length of arcs and area of sectors from formulas). In arithmetic, students learn to work with negative numbers and the absolute value of numbers, to continue sequences, and to use exponents and roots. They learn to use a calculator for work with negative and rational numbers. In algebra, students learn to value and calculate with expressions with more than one variable, transform patterns into expressions with variables, and recognize and present linear relations and link them to percentages. Functions are extended into functions of real variables, the coordinate system in a plane, and relationships between variables. Students learn to read graphs and represent sets of points on a number line, as well as present relationships between two discrete variables and two continuous variables with graphs. Besides solving equations, students learn how to recognize identical and equivalent equations and solve general inequalities, and how to model abstract situations or sequences by expressions with variables (i.e., the number of sides in the n^th figure). They model abstract (geometrical) situations, critically value models, and interpret their results.

With regard to the TIMSS framework, the Slovenian national curriculum covers most of the content included in the assessments. Among some important topics of mathematics that were tested in TIMSS but are covered in Grade 9 only are topics from geometry (e.g., similar triangles) and probability, solving systems of linear equations, graphs of linear functions, and median, mode, and range.²³