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Investigated was the question of whether understanding is explained by means of concepts referring to tasks, being domain-specific for certain subject matter areas, or is it explained by concepts which extend across tasks and are not domain-specific? Also explored were: (1) which explanatory concepts are present, that is, which steps and conditions of understanding are thematized in the explanations? and (2) do explanatory concepts differentiate according to success and failure in understanding or by sex? A two-dimensional table was constructed for coding explanations of 20 male mathematics teachers in grades 5 and 6 of schools in West Germany. Results indicated a marked predominance of explanations referring to domain-specific tasks as compared to explanations extending across tasks. The order of frequency of steps and conditions of understanding are noted, and sex differences in a few categories were found. The discussion focuses on: (1) reference to the task and type of explanation; and (2) obtaining explanations referring to task: problems and opportunities. (MNS)

This set of five papers, written in German with abstracts in English, was collected by the Institut fuer Didaktit der Mathematik (Institute for the Teaching of Mathematics) at the University of Bielefeld in West Germany. In the first paper, Bauersfeld used a transcript of a videotaped scene of group work out of school as a basis for analyzing regularities in the communication within the group. The second paper, by Krummheuer, focuses on frame analysis within an eighth-grade class beginning algebra, and depicts difficulties in the communication process. In the third paper, Reiss proposes that the teacher's job is primarily managerial, with the guiding process a linguistic one. Heymann, in the fourth paper, presents two case studies investigating the implicit classroom theories of two mathematics teachers. The final paper, by Lorenz, considers learning difficulties in primary mathematics lessons. (MNS)

This set of five papers, written in German with abstracts in English, was collected by the Institut fuer Didaktit der Mathematik (Institute for the Teaching of Mathematics) at the University of Bielefeld in West Germany. In the first paper, Bauersfeld considers domains of subjective experiences as the best issue for an interactive theory of mathematics learning and teaching, using transcripts and interpretations of classroom discourse. Krummheuer, in the second paper, deals with communication problems between teacher and pupils, using instances from beginning algebra. Lorenz discusses learning problems in primary mathematics education in the third paper, describing work with underachieving students. In the fourth paper, Voigt uses transcripts of several lessons introducing probability calculus to make a microethnographic study of typical problem-solving processes with mathematical tasks. Bussman, in the final paper, attempts to show that current paradigms in mathematics education literature thematize both teaching-learning processes and educational processes, but neglect mathematical abilities. (MNS)

The prerequisites, the process, and the outcome of the implementation of the competency based teacher education program at the University of Houston are examined and analyzed. The following components comprise the framework for analysis of this innovation: (1) goals and basic assumptions, scope of the pursued change, and characteristics of the innovation under conditions of implementation; (2) sociocultural background, economic factors, changes in science, technology, and the profession; (3) personnel, financial and technological resources, curriculum and student assessment, laws and regulations, and management of the program; (4) innovation strategies, processes of decision making, and relations between the existing structures and the change process; and (5) the effects of the innovation, advantages and disadvantages for persons involved, main barriers to implementation, and future development of the innovation. Appendixes include a discussion of the methods of investigation and questionnaires submitted to students, teacher educators, and former students. An outline of the structure of the pilot program and the proficiency analysis rating instrument used in this study are also appended. (JD)

This paper focuses on mathematics education in Technical and Vocational Education (TVE) in West Germany. The "dual system" of TVE, a part-time college/part-time on-the-job training scheme that normally leads to a certificate of a qualified worker after three years, is reviewed. Entrance tests for the trainee posts focus heavily on aspects of mathematics. Qualifications tested include: decimals and various fractions; proportions; change of measurements; rule of three; percentages; and some geometry. Lessons for selected students center around topics such as basic arithmetic, percentages, and proportions. Special areas for particular occupations covered include graph-, table-, and diagram-reading and interpreting, basic algebra, and advanced calculating techniques. Criticisms concerning this topic-oriented approach are presented. (MP)

The mathematics and experimental science courses in the programs of the upper secondary school in the Federal Republic of Germany (FRG) are discussed. The paper addresses: (1) the two "secondary levels" within the FRG school system, indicating that the Secondary I-Level (SI) comprises grades 5 through 9 or 10 while the Secondary II-Level (SII) comprises grades 10 or 11 through 13; (2) developments in SI, examining curricula, syllabi, the introduction of a tenth grade in the Hauptschule, and other topics; (3) recent reform of the Gymnasiale Oberstufe (GYO), the senior high school, discussing mathematics and science requirements, students' science course selection behavior, areas of concern (such as the problem of incorporating more applications in science and mathemematics curricula), curriculum development issues, and related concerns; and (4) vocational education and the "Kollegschule" of Nordrhein-Westfalen as a model for the integration of profession-oriented and general education. The newly organized GYO provides courses which represent a much broader spectrum of subjects, such as informatics and jurisprudence. In addition, subjects are divided into compulsory and optional domains and are assigned to one of three different areas. They include language, literature, arts (area I), social sciences (area II), and mathematics, sciences, and technology (area III). (JN)