Math can be learned at any age

Math class : In-depth learning is what counts

What is the quality of math teaching in secondary school?

The quality of mathematics teaching in German schools in 2018 was recently examined by the Institute for Quality Development in Education (IQB) in the study "IQB-Bildungtrend 2018" (Henschel, Rjosk, Holtmann & Stanat, 2019). In total, over 24,000 ninth graders from all over Germany in 2018 provided information about how they perceive the deep structures of their math lessons (class management, support, cognitive activation), their interest in mathematics, their trust in their own math skills and their anxiety who are preoccupied with mathematics. In addition, the young people worked on a math test. The more than 2,000 teachers of the students surveyed also stated how often they use certain visual structures (forms of learning and organization, methods of internal differentiation) in their mathematics lessons.

In terms of the forms of learning and organization used, frontal or classroom teaching as well as quiet work predominate, which are regularly used by around 80 percent of the teachers surveyed.

The results show that math teachers continue to design their lessons very traditionally and with comparatively few variations in 2018: The forms of learning and organization used predominate in frontal or classroom teaching as well as quiet work, which are regularly used by around 80 percent of the teachers surveyed. With the exception of small group work, which around 60 percent of the teachers also use more frequently, more cooperative (e.g. peer tutoring, project learning) or individualized forms of learning (e.g. subject-related learning, weekly plan work, free work) are used comparatively rarely and more selectively . This could also be related to the fact that the preparation and implementation effort is higher than with traditional forms of learning. In line with this, it was also shown that teachers often use performance-differentiating methods that can be easily integrated into individual or idle work phases.

The majority of the teachers stated, for example, that they let more capable young people prepare for work and support them with extra tasks, as well as varying tasks for young people with different abilities in silent work. It is interesting that there tend to be differences between the types of school and that teaching in the non-grammar school types is characterized somewhat more by innovative (cooperative and individualizing) forms of learning and differentiating methods than at the grammar school.

In-depth structures in mathematics lessons are assessed positively

In addition, the information provided by ninth graders on class management, support and cognitive activation shows that these characteristics are overall quite positive and in some cases very similar between the federal states. When comparing the federal states, however, it is noticeable, for example, that young people in the eastern German states, in which a very high average level of proficiency in mathematics is achieved, assess their teaching in a particularly well-structured and cognitively challenging manner. At the same time, however, the young people in these countries also stated that dealing with mistakes and individual support from the teacher are comparatively less constructive.

In addition, differences between school types become clear again, which indicate that different teaching cultures dominate at the grammar school and in the non-grammar school types. According to this, lessons at the grammar school are more disciplined or less disturbed in the collective perception of the students, stimulate a more in-depth cognitive examination of the subject matter and are characterized by a more positive error culture than in the non-grammar school types. At the same time, the interaction between teachers and young people in mathematics lessons in non-grammar schools is perceived as more supportive and appreciative than in grammar school.

Visual or deep structures - which is more decisive for learning success in mathematics lessons?

The IQB Education Trend 2018 also examined the extent to which the visual and depth structures of mathematics lessons are related to the skills, interest, self-confidence in the abilities and anxiety of the students. The results indicate once again that it is primarily the depth (structures) that matters. In this way, good mathematical skills are achieved primarily by young people, in whose classes the teachers organize their lessons in a particularly cognitively activating way and encourage their students to think deeply and deal intensively with the learning content. Adolescents also achieve somewhat better mathematical skills when teachers use more innovative forms of learning and organization in their lessons, but the practical relevance of this effect is rather small. In addition, it was found that adolescents reported a greater interest in mathematical topics and a reduced experience of anxiety if they were well supported by their teachers and felt that their interests were taken seriously. The visual structures played no role.

Conclusion: it depends on the depth!

Overall, in agreement with previous studies, the results indicate that learning success is less related to how teachers organize learning in the classroom, i.e. what forms of learning and organization or methods they use. Rather, it is more important how well the pupils are encouraged to deal intensively with the topic of the lesson and how much the young people feel constructively supported and taken seriously.

And this also applies against the background of the increasingly heterogeneous student body in recent years. Particularly in the non-grammar school types, in which the heterogeneity in student performance is more pronounced and increased than in the grammar school, positive changes can be seen in the deep structures. According to this, teaching in non-grammar schools was perceived as more structured and cognitively more challenging in 2018 than it was six years ago, when young people were asked about their teaching in the study “IQB country comparison 2012”. Strengthening the deep structures for high-quality teaching seems to be increasingly successful, especially in non-grammar schools.

This development is encouraging because teaching research also discusses that so-called high-risk groups of students could benefit to a particular degree from high quality teaching, and initial studies support this assumption (Cadima et al., 2010; Seiz et al., 2016). This also means that dealing with heterogeneous learning groups initially requires high quality in the deep structures. The use of particularly diverse methods or forms of learning tends to have a structuring role, and ideally it favors the degree of cognitive activation in the classroom. It is therefore to be hoped that measures for lesson development as well as training and further education offers for teachers will increasingly target the deep structures of teaching.

The full report on the 2018 IQB education trend can be downloaded here.