The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

The antioxidant requirement for plasma membrane repair in skeletal muscle.

Vitamin E (VE) deficiency results in pronounced muscle weakness and atrophy but the cell biological mechanism of pathology is unknown. We previously showed that VE supplementation promotes membrane repair in cultured cells and that oxidants potently inhibit repair. Here we provide three independent lines of evidence that VE is required for skeletal muscle myocyte plasma membrane repair in vivo. We also show that when another lipid-directed antioxidant, glutathione peroxidase 4 (Gpx4), is genetically deleted in mouse embryonic fibroblasts, repair fails catastrophically, unless cells are supplemented with VE. We conclude that lipid-directed antioxidant activity provided by VE, and possibly also Gpx4, is an essential component of the membrane repair mechanism in skeletal muscle. This work explains why VE is essential to muscle health and identifies VE as a requisite component of the plasma membrane repair mechanism in vivo