Monitoring Student Progress in Mathematics and Science
At the end of ninth grade, students take seven compulsory school leaving examinations; after 10th grade, school leaving examinations are optional.39 The compulsory examinations cover the following five subjects: Danish (oral and written), mathematics (written), English (oral), and physics and chemistry (oral). The two remaining examinations are selected randomly for each school. Students may choose to take a further examination in an additional, optional subject. Examinations are regulated to ensure uniformity throughout the country. The Ministry of Children, Education, and Gender Equality develops the written school leaving examinations, and teachers conduct the oral examinations.
The examination in mathematics consists of two parts. Students have one hour to complete the first part, which tests their basic mathematical skills in numbers and algebra, geometry and measurement, and statistics and probability. No aids are allowed on the first part of the examination, and one grade is given. Students have three hours to complete the second part of the examination, which tests their mathematical problem solving abilities. On the second part of the examination, students are allowed to use any aids that they have been using in the classroom on a daily basis, such as calculators, and one grade is given.40 Students in Denmark are graded on a seven point scale ranging from -3 to 12 (-3, 00, 2, 4, 7, 10, and 12), which was introduced in 2007 to help standardize the Danish grading system in an international context.41 At least twice a year, students in Grades 8 and 9 are given a continual assessment grade, which is intended to provide a snapshot of their academic achievement.42
In the 2007–2008 school year, Denmark introduced a range of compulsory national tests, designed to serve as pedagogical tools to aid teachers in planning instruction for individual students according to students’ strengths, weaknesses, and potential.43 Students are required to take national tests in six subjects at different grade levels: mathematics in Grades 3 and 6; science in Grade 8; Danish in Grades 2, 4, 6, and 8; English in Grade 7; geography in Grade 8; and biology in Grade 8. The national tests are computer-based, and the questions are continuously adapted to individual students as they complete the tests. Results are published only at the national level.
Once a year every Folkeskole in Denmark is required to complete an evaluation of student well-being (Trivselsmåling).44 These evaluations typically are carried out through a digital survey in which students are required to answer 40 questions about their well-being. Teachers share results with their classes, and teachers or school administrators will share the results with parents. Evaluation results are utilized by municipalities, schools, and teachers in their work with student well-being and teaching environments. The results comprise part of municipal reports on the well-being of students, which include proposals for addressing issues of student well-being going forward. Teachers, school administrators, school boards, and municipal councils have access to all class results with the following exception: in order to protect student anonymity, the results of classes with fewer than five students are not available.