Assessed competences

Mathematics

As part of the pilot project to extend the Luxembourg School Monitoring Programme “Épreuves Standardisées” (ÉpStan) to international public schools, all five grade levels of the European Public Schools (P1, P3, P5, S1 and S3) and all five grades of the Michel Lucius International School (Stage 1, Stage 3, Stage 5, 7e and 5e) have been taking part in the ÉpStan mathematics tests since November 2022.

The competence tests in mathematics are based on the learning objectives of the Luxembourgish curriculum.

In the three grade levels of primary school as well as in the first grade level of secondary school (S1 and 7e, respectively), the mathematics test contains tasks referring to the following competence areas: “Numbers and operations”, “Space and shapes” as well as “Sizes and measures”. The tasks are presented in a decontextualized and/or contextualized way (providing arithmetic problem solving). In order to minimize the demands in terms of reading comprehension, the instructions are presented in very simple language and include many illustrations.

In the third grade of secondary school (S3 or 5e), the mathematics test covers the following competence areas: “Numbers and operations”, “Figures of area and space”, “Dependency and variation” and “Data”. Depending on the complexity of the problem and the required solution, the tasks are divided into four difficulty levels, which are based on the number of calculations to be performed or the digital units to be processed.

In the three grade levels of primary school, the mathematics test is conducted in the respective section language. In the two grade levels of secondary school, the mathematics test is offered in German, French and English. Students can change the language at any time while working on the tasks.

Regarding schools that follow the Luxembourgish curriculum, the ÉpStan allow to monitor whether, at the beginning of each learning cycle, the students have achieved the learning objectives of the previous cycle as described in the curriculum. For international public schools following an alternative curriculum (e.g., European curriculum), the learning objectives referred to should only be considered as a broad reference framework. The actual competences of students following an international curriculum are likely to exceed the learning objectives of the Luxembourgish curriculum in some domains, while staying below in others.

Further details on the mathematics test can be found under the heading “Assessed competences” of the respective grade level. Sample tasks in the three languages offered (German, French, and English) can be consulted in the download area of this section.

Test development and pre-testing

The tests evaluating mathematical skills are developed and compiled by experienced elementary and secondary school teachers, together with scientific staff from LUCET. New items are continuously developed for the ÉpStan every year. To validate the content, format and practicability of the newly developed test material, it must be tested with students attending the relevant grade levels. After the competence tests, therefore, students take part in a pre-test where they answer the newly developed test material. Students’ performance in the pre-test is not included in the ÉpStan results and thus, not reported back, as the focus is on the testing and the psychometric evaluation of the new items rather than on individual performance.

The pretest only takes place in the schools that follow the Luxembourgish curriculum.

For schools following an international curriculum, the tasks of the mathematics test are translated into the different section languages. These translations are then checked for linguistic fit by experienced teachers who teach in the respective language section of an international public school.