The Challenges, Reforms, and Future Prospects of Elementary and Lower Secondary Mathematics Education in Germany

Keeping its original form of an interview, this article presents a discussion about the challenges, reforms, and the prospects of mathematics education in Germany. The interview addresses aims and goals, contents and processes of mathematics teaching. Compared with the guiding ideas some years ago, more emphasis is put on modeling today. The idea that every student should have enough mathematics knowledge and the disappointing results of Germany in the PISA-2000 comparison may have caused this change. Moreover, Germany faces, like other countries do, some basic problems in mathematics teaching, addressed here as the balance problem, the coherence problem, the curriculum problem, the classroom organization problem, the computer problem, and the teacher education and development problem. The interview also tries to show how these problems are going to be tackled in Germany. For the prospects, being able to apply mathematics in the real world, being able to understand the mathematical concepts and rules, and having the potential of cultivating the own thinking are the main concerns of mathematical literacy in Germany

Heinrich Besuden 1924 – 2019

Am 11. Oktober 2019 verstarb Prof. Dr. Heinrich Besuden im Alter von 95 Jahren. Heinrich Besuden gehörte zu den Persönlichkeiten, die unsere Disziplin der Mathematikdidaktik nachhaltig beeinflusst haben

Die „eine“ und die „andere“ Mathematik: Assoziationen zu einem grundlegenden Aspekt der Mathematikdidaktik

Welche Implikationen hat es für die mathematikdidaktische Arbeit, welche Eigenart der Mathematik man für das jeweilige Problem wählt? Diese Frage umkreise ich in 15 Assoziationen und orientiere mich dabei an zwei bekannten und einem aktuellen Beispiel

Relation of Gallbladder Motility to Viscosity and Composition of Gallbladder Bile in Patients with Cholesterol Gallstones

Background/Aims: Increased viscosity and supersaturation of cholesterol in gallbladder bile, as well as an impaired motility of the gallbladder, are considered to be important factors in the pathogenesis of cholesterol gallstones. However, the relation of these parameters has not yet been determined. Material and Methods: Bile viscosity (mPa.s) was measured by rotation viscosimetry and the composition of gallbladder bile was determined using standard methodology. Gallbladder motility was calculated as ejection fraction in percent of total volume 45 min after a test meal using ultrasonography in patients with gallstones prior to elective cholecystectomy. Results: The study included 35 patients with cholesterol gallstones. Viscosity of gallbladder bile ranged between 0.9 and 12.5 mPa.s (median 2.2 mPa.s) and an ejection fraction of the gallbladder of 55.4 +/- 18.3% (mean +/- SD) was determined. No significant correlation (r = 0.19, p < 0.2) between the 2 parameters could be calculated. Analysis of the composition of gallbladder bile revealed a positive correlation of all components to biliary viscosity but not to the motility of the gallbladder, with the exceptions of a negative correlation (r = 0.39, p < 0.02) between mucin concentration and the ejection fraction at 45 min after the test meal. Conclusions: The motility of the gallbladder appears to be unrelated to the viscosity of gallbladder bile or gallbladder bile composition. The negative correlation between the ejection fraction of the gallbladder and mucin concentration of gallbladder bile suggests that chronic inflammation of the gallbladder wall is associated with both an impaired motility of the gallbladder and increased mucin release into gallbladder bile. Copyright (C) 2009 S. Karger AG, Base

what is and what might be the legacy of felix klein

Felix Klein was an outstanding mathematician with an international reputation. He promoted many aspects of mathematics, e.g. practical applications and the relation between mathematics and natural sciences but also the theory of relativity, modern algebra, and didactics of mathematics. In this article about the The Legacy of Felix Klein we firstly refer to his ideas in university teaching of mathematics teacher students and the three books "Elementary Mathematics from a higher (advanced) standpoint" from the beginning of the last century. Secondly we refer to his interests in school mathematics and his influence to the "Merano Resolution" (1905) where he pleaded for basing mathematics education on the concept of function, an increased emphasis on analytic geometry and an introduction of calculus in secondary schools. And thirdly we especially discuss the meaning and the importance of Klein's ideas nowadays and in the future in an international, worldwide context

Degrees of Competence and Models of Difficulty for the PISA-Test of Mathematical Literacy

Die nationalen Ergänzungen des Untersuchungsprogramms für PISA haben den mathematischen Teil der Studie wesentlich erweitert. Dies betrifft die theoretische Konzeption zur mathematischen Grundbildung - dargelegt in einem nationalen Rahmenkonzept, das das internationale Framework ergänzt und erweitert, ebenso wie die Aufgabensammlung und die Stichprobe; zudem wurden in Deutschland eine Reihe von Zusatzuntersuchungen zur curricularen und Konstrukt-Validität der Aufgaben durchgeführt. Im vorliegenden Beitrag wird auf der Basis dieser Ergänzungen das Konzept der mathematischen Grundbildung und seine Operationalisierung differenziert dargestellt. Getrennt nach der Art des mathematischen Arbeitens - Ausführung technischer Prozeduren, rechnerisches Modellieren und begriffliches Modellieren - wird untersucht, welche Anforderungsmerkmale die Schwierigkeit der Aufgaben bestimmen. Die Stufen mathematischer Kompetenz lassen sich damit aus didaktischer und psychologischer Sicht charakterisieren. (DIPF/Orig.