The relationship between practised monitoring activities and performance, especially in mathematics was examined within three nested studies. The first study deals with problems of faulty term rewritings submitted to three groups of subjects-10th to 13th graders, differing in their mathematical performance-whose task was to find the mistakes. Moreover, a questionnaire on the practice and appreciation of monitoring activities was developed. The third study, first, repeats the first study with a similar population and secondly adds interviews with some of the subjects while solving additional items concerning faulty term rewritings. Studies 1 and 3 show similar success in finding mistakes and in the replies to the questionnaire within the various groups. Furthermore, the third study points up that the subject's answers do neither predict the practised monitoring nor the success in the test. However, the success correlates significantly with the practised monitoring. For a deeper understanding concerning the role of metacognition in explaining performance, the second study examined two of the groups who had already been involved in the first study. These were assigned some problems of a matrices test as used in cognitive psychology. While trying to solve the problem, their eye movements were recorded by means of an eye-tracker. Afterwards they had to justify their solutions in an interview. The eye movements were analysed, the verbal comments classified. Again, the groups differ in their problem solving success, dependant on the quality of the monitoring practised. Altogether, the results of the three studies elucidate the importance of practised metacognitive monitoring activities not only for success in school algebra, but furthermore the ability and the willingness to do it is deeper anchored in a person than just a trained behaviour for school algebra.

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We report on a German-Indonesian design research project, which aims to significantly increase the mathematical skills of secondary school students. Since results of international comparative studies have shown that there exists a relationship between metacognition and learning success, a learning environment for the beginning with secondary school mathematics in class seven has been developed, in order to significantly enhance metacognitive and discursive activities of students and teachers. The effectiveness of the approach has been tested in a secondary school several times. In this paper the theoretical background for the design of the learning environment is described, some sample exercises are presented and student productions from the project lessons analysed. AbstrakDalam artikel ini kami melaporkan proyek penelitian desain Jerman-Indonesia yang bertujuan untuk meningkatkan kemampuan matematika siswa di sekolah menengah secara signifikan. Karena hasil dari studi banding internasional menunjukkan bahwa ada hubungan antara metakognisi dan keberhasilan proses belajar, maka dirancang sebuah lingkungan belajar untuk siswa kelas 7, yang bertujuan untuk meningkatkan kegiatan metakognitif dan diskurs bagi siswa dan guru. Efektivitas pendekatan ini diuji beberapa kali di sekolah menengah. Dalam artikel ini disajikan latar belakang teoritis yang digunakan untuk pengembangan lingkungan pembelajaran, beberapa contoh tugas yang diberikan kepada siswa dan analisis hasil kerja siswa.