In this article the concept of learner autonomy is applied to the foreign language classroom although some ideas might also be useful within a second language context. It begins by approaching the different problems that a foreign language context entails. It then goes on to put forward the rationale which justifies David Little's construct of developmental and experiential leaming (Learner Autonomy) as the result of both interactional and inferential input. The latter is redenned here on the basis of a pragmatic theory: Relevance Theory, first proposed by Dan Sperber and Deirdre Wilson in 1986. Finally, some hints aiming to foster learner autonomy inside and outside the classroom are reported after an experience with university students of English in Spain.
dedicated to the memory of professor e. aparicioThe Bernstein operator on the standard k-simplex and other analogous k-variate operators allow for a probabilistic representation in terms of the successive increments of a real valued superstationary stochastic process (a notion introduced in the paper) starting at the origin and having nondecreasing paths. For this class of operators, we obtain estimates of the best constants in preservation of the first modulus of continuity corresponding to the l 1 -norm, and in preservation of classes of functions defined by concave moduli of continuity. We also show that, in some special cases, such best constants do not depend upon the dimension k. To show our results, we use probabilistic tools such as couplings and Wasserstein distances for multivariate probability distributions. The general results are applied to the computation of the aforementioned constants for several classical multivariate operators.
We consider tensor product operators and discuss their best constants in preservation inequalities concerning the usual moduli of continuity. In a previous paper, we obtained lower and upper bounds on such constants, under fairly general assumptions on the operators. Here, we concentrate on the loo -modulus of continuity and three celebrated families of operators. For the tensor product of k identical copies of the Bernstein operator B n , we show that the best uniform constant coincides with the dimension k, when k ^ 3, while, in case k = 2, it lies in the interval [2,5/2] but depends upon n. Similar results also hold when B n is replaced by a univariate Szasz or Baskakov operator. The three proofs follow the same pattern, a crucial ingredient being some special properties of the probability distributions involved in the mentioned operators, namely: the binomial, Poisson, and negative binomial distributions.
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