Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

This is the final version. Available from Taylor and Francis via the DOI in this record. In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between ‘construction’ and ‘substantiation’ based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.JSPS KAKENHIJSPS KAKENH

Lattice Field Theory with the Sign Problem and the Maximum Entropy Method

Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the θ term. We reconsider this problem from the point of view of the maximum entropy method

Yokukansan Inhibits Neuronal Death during ER Stress by Regulating the Unfolded Protein Response

Recently, several studies have reported Yokukansan (Tsumura TJ-54), a traditional Japanese medicine, as a potential new drug for the treatment of Alzheimer's disease (AD). Endoplasmic reticulum (ER) stress is known to play an important role in the pathogenesis of AD, particularly in neuronal death. Therefore, we examined the effect of Yokukansan on ER stress-induced neurotoxicity and on familial AD-linked presenilin-1 mutation-associated cell death.We employed the WST-1 assay and monitored morphological changes to evaluate cell viability following Yokukansan treatment or treatment with its components. Western blotting and PCR were used to observe the expression levels of GRP78/BiP, caspase-4 and C/EBP homologous protein.Yokukansan inhibited neuronal death during ER stress, with Cnidii Rhizoma (Senkyu), a component of Yokukansan, being particularly effective. We also showed that Yokukansan and Senkyu affect the unfolded protein response following ER stress and that these drugs inhibit the activation of caspase-4, resulting in the inhibition of ER stress-induced neuronal death. Furthermore, we found that the protective effect of Yokukansan and Senkyu against ER stress could be attributed to the ferulic acid content of these two drugs.Our results indicate that Yokukansan, Senkyu and ferulic acid are protective against ER stress-induced neuronal cell death and may provide a possible new treatment for AD