Funktionale Zusammenhänge auf den Punkt gebracht. Oder: Warum sich Funktionen nicht gerne „verschieben“ lassen

Beim Thema „Funktionen“ fokussiert der Mathematikunterricht häufig auf die Betrachtung von Graphen und deren Charakteristika unter Verwendung algebraischer Werkzeuge. Schülerformulierungen wie „Ich verschiebe die Funktion“ lassen erkennen, dass ein problematisches Verständnis von Funktionen im Sinne graphischer Objekte vorliegt. Der Beitrag stellt Überlegungen an, wie die Formalisierung der Abhängigkeit von Größen stärker ins Blickfeld gerückt werden kann und illustriert dies an Aufgabenformate

Von der Arithmetik zur Algebra

Arithmetik ist mehr als das Berechnen von Termwerten, Algebra ist mehr als das Umformen von Termen: Bereits in der Arithmetik kann das inhaltliche Verständnis für Algebra geweckt werden. Die Struktur einer Situation spiegelt sich in der Struktur von Termen wider, und Terme können als universales Werkzeug für die Darstellung strukturgleicher Situationen verwendet werden. Dazu werden Aufgabenformate vorgestellt, die das inhaltliche Verständnis für Terme und Termstrukturen anbahnen können

Aufgabenadäquates Rechnen bei Dezimalbrüchen oder Warum vermeintlich einfache Aufgaben so fehlerträchtig sind

In diesem Beitrag werden in Bezug auf das flexible Rechnen mit Dezimalbrüchen zwei Aspekte beschrieben: Einerseits typische Fehler von Schülerinnen und Schülern, die auf ein nicht aufgabenadäquates Arbeiten hindeuten, und andererseits Ansätze zur Entwicklung von Aufgaben, die das flexible Rechnen mit Dezimalbrüchen fördern können

Integrated training in using different Coordinate Measuring Systems to support Digital Manufacturing

Highly qualified labour force is a key resource for growth. In modern manufacturing, the competent use of advanced measuring equipment for inspection and digitization of parts is an essential competence that is needed for both advanced product/process engineering and quality control. Coordinate Metrology (including 3D digital measuring technologies) is by far the most important tool for these specialized activities. As widely reported, the individuals operating the measuring systems - with their decisions - are frequently one of the most relevant error sources in Coordinate Metrology operations, especially when dealing with new measuring technologies supporting Digital Manufacturing (e.g. Computed Tomography, Fringe-projection, Reverse Engineering). The paper reports the intermediate results of an initiative aiming at innovating training in Coordinate Metrology, focused on supporting the needs of SMEs in the supply chain of the automotive industry. The main target group are industry employees operating in SMEs that are newcomers on 3D measuring technologies. An integrated concept for training in Coordinate Metrology has been developed using a blended learning approach, based on a 10-steps structure and incorporating the learning outcomes required to operate different measuring systems in a consistent way

Integrated training in using different Coordinate Measuring Systems to support Digital Manufacturing

International audienc

Geometrical Product Specification and Verification as toolbox to meet up-to-date technical requirements

The ISO standards for the Geometrical Product Specification and Verification (GPS) define an internationally uniform description language, that allows expressing unambiguously and completely all requirements for the geometry of a product with the corresponding requirements for the inspection process in technical drawings, taking into account current possibilities of measurement and testing technology. The practice shows that the university curricula of the mechanical engineering faculties often include only limited classes on the GPS, mostly as part of curriculum of subjects like Metrology or Fundamentals of Machine Design. This does not allow students to gain enough knowledge on the subject. Currently there is no coherent EU-wide provision for vocational training (VET) in this area. Consortium, members of which are the authors of this paper, is preparing a proposal of an EU project aiming to develop appropriate course

A New Albite Microanalytical Reference Material from Piz Beverin for Na, Al and Si Determination, and the Potential for New K-Feldspar Reference Materials

Determination of alkali elements is important to Earth scientists, yet suitable and reliable microanalytical reference materials are lacking. This paper proposes a new albite reference material and evaluates the potential for future K-feldspar reference materials. The proposed Piz Beverin albite reference material from Switzerland yields a homogeneous composition at the centimetre- to micrometre-scale for Si, Al and Na with \u3c 2000 μg g-1 total trace elements (mostly heterogeneously distributed Ca, K and Sr). EPMA and LA-ICP-MS measurements confirm a composition of 99.5(2)% albite component, which is supported further by bulk XRF measurements. A round robin evaluation involving nine independent EPMA laboratories confirms its composition and homogeneity for Si, Al and Na. In addition, a set of five distinct clear K-feldspar samples was evaluated as possible reference materials. The first two crystals of adular and orthoclase yield unacceptable inhomogeneities with \u3e 2% relative local variations of Na, K and Ba contents. The three other investigated sets of K-feldspar crystals are yellow sanidine crystals from Itrongay (Madagascar). Despite distinct compositions, EPMA confirms they are each homogeneous at the centimetre to micrometre scale for Si, Al and K and have no apparent inclusions; further investigation to find larger amounts of these materials is therefore justified