Die Rolle der Mathematik in der Mathematikdidaktik

Es gibt verschiedene fachliche Perspektiven, aus denen ein mathematischer Unterrichtsgegenstand betrachtet werden kann. Sie sind je für sich wichtig und erst ihr Zusammenspiel erzeugt das rechte Hintergrundwissen für den Unterricht. Die folgenden Ausführungen möchten diese Auffassung am Beispiel der Bruchrechnung exemplarisch entfalten

Zur algebraspezifischen Ausprägung mathematischer Denkhandlungen

In unseren Überlegungen gehen wir davon aus, dass mathematische Denkoperationen spezifische Ausprägungen bzw. Idealisierungen allgemeiner menschlicher Denkhandlungen sind (Wille 2001 im Anschluss an Kitcher 1984). Harel unterscheidet in diesem Zusammenhang "mental acts" and "ways of thinking" (Harel 2008). Mental acts bezeichnen allgemeine Denkhandlungen, die überall im menschlichen Denken eine Rolle spielen, ways of thinking sind bereichs- oder disziplinspezifische Ausprägungen von diesen (ebd.). Danach können wir das Anliegen unseres Vortrages so präzisieren: Wir möchten allgemeine Denkhandlungen ausweisen, die auch in der Algebra eine Rolle spielen, und ihre algebraspezifischen Ausprägungen charakterisieren

Medin aggregation causes cerebrovascular dysfunction in aging wild-type mice

Medin is the most common amyloid known in humans, as it can be found in blood vessels of the upper body in virtually everybody over 50 years of age. However, it remains unknown whether deposition of Medin plays a causal role in age-related vascular dysfunction. We now report that aggregates of Medin also develop in the aorta and brain vasculature of wild-type mice in an age-dependent manner. Strikingly, genetic deficiency of the Medin precursor protein, MFG-E8, eliminates not only vascular aggregates but also prevents age-associated decline of cerebrovascular function in mice. Given the prevalence of Medin aggregates in the general population and its role in vascular dysfunction with aging, targeting Medin may become a novel approach to sustain healthy aging

Small-Animal PET Imaging of Amyloid-Beta Plaques with [11C]PiB and Its Multi-Modal Validation in an APP/PS1 Mouse Model of Alzheimer's Disease

In vivo imaging and quantification of amyloid-β plaque (Aβ) burden in small-animal models of Alzheimer's disease (AD) is a valuable tool for translational research such as developing specific imaging markers and monitoring new therapy approaches. Methodological constraints such as image resolution of positron emission tomography (PET) and lack of suitable AD models have limited the feasibility of PET in mice. In this study, we evaluated a feasible protocol for PET imaging of Aβ in mouse brain with [11C]PiB and specific activities commonly used in human studies. In vivo mouse brain MRI for anatomical reference was acquired with a clinical 1.5 T system. A recently characterized APP/PS1 mouse was employed to measure Aβ at different disease stages in homozygous and hemizygous animals. We performed multi-modal cross-validations for the PET results with ex vivo and in vitro methodologies, including regional brain biodistribution, multi-label digital autoradiography, protein quantification with ELISA, fluorescence microscopy, semi-automated histological quantification and radioligand binding assays. Specific [11C]PiB uptake in individual brain regions with Aβ deposition was demonstrated and validated in all animals of the study cohort including homozygous AD animals as young as nine months. Corresponding to the extent of Aβ pathology, old homozygous AD animals (21 months) showed the highest uptake followed by old hemizygous (23 months) and young homozygous mice (9 months). In all AD age groups the cerebellum was shown to be suitable as an intracerebral reference region. PET results were cross-validated and consistent with all applied ex vivo and in vitro methodologies. The results confirm that the experimental setup for non-invasive [11C]PiB imaging of Aβ in the APP/PS1 mice provides a feasible, reproducible and robust protocol for small-animal Aβ imaging. It allows longitudinal imaging studies with follow-up periods of approximately one and a half years and provides a foundation for translational Alzheimer neuroimaging in transgenic mice