घuसना — to sneak in

The verb घuसना is so articulate as to be almost a one-word justification for learning Hindi. Its range of meanings, or rather its suggestions and attitudes, is a real challenge for lexicographers, whose various glosses can only hint at what घuसना has to say.Asian Studie

A proof of P!=NP

We show that it is provable in PA that there is an arithmetically definable sequence $\{\phi_{n}:n \in \omega\}$ of $\Pi^{0}_{2}$-sentences, such that - PRA+$\{\phi_{n}:n \in \omega\}$ is $\Pi^{0}_{2}$-sound and $\Pi^{0}_{1}$-complete - the length of $\phi_{n}$ is bounded above by a polynomial function of $n$ with positive leading coefficient - PRA+$\phi_{n+1}$ always proves 1-consistency of PRA+$\phi_{n}$. One has that the growth in logical strength is in some sense "as fast as possible", manifested in the fact that the total general recursive functions whose totality is asserted by the true $\Pi^{0}_{2}$-sentences in the sequence are cofinal growth-rate-wise in the set of all total general recursive functions. We then develop an argument which makes use of a sequence of sentences constructed by an application of the diagonal lemma, which are generalisations in a broad sense of Hugh Woodin's "Tower of Hanoi" construction as outlined in his essay "Tower of Hanoi" in Chapter 18 of the anthology "Truth in Mathematics". The argument establishes the result that it is provable in PA that $P \neq NP$. We indicate how to pull the argument all the way down into EFA

तनाव — tension

There’s maybe just enough time to write this note before the English loanword !"शन completely ousts the fine word तनाव from Hindi usage! The two words are in fact related to each other, which may account for the…er…tension between them.Asian Studie

‘It’s just a wait and see thing at the moment’. Students’ preconceptions about the contribution of theory to classroom practice in learning to teach

This paper reports on an exploration of the preconceptions held by Primary PGCE students about the relationship of theory to classroom practice in learning to teach. Preconceptions about learning to teach have been found in the past to be unsophisticated and unhelpful, yet durable. Linking theory and practice within teacher education is notoriously difficult and studies report scepticism about the value of research findings and theory in everyday classroom practice. Furthermore, the nature of teachers’ professional knowledge is itself uncertain and highly complex. Unlike many previous investigations into student teacher thinking, this small-scale case study captures participants’ views before the start of their training and explores the research question through three key issues: what constitutes teacher knowledge, where this knowledge is learned and how these different facets of knowledge relate to one another. While many of the complexities of teaching are yet to be understood fully in this pre-course phase, these participants prove to be far from naïve and begin the course open to a range of forms of learning, with a positive view of the potential contribution of theory to practice. The insight into this starting point leads to some potentially important implications for future course design. The research relates to an English university, but the debate is significant to teacher education more widely