For a learnable mathematics in the digital cultures

I begin with some general remarks concerning the co-evolution of representational forms and mathematical meanings. I then discuss the changed roles of mathematics and novel representations that emerge from the ubiquity of computational models, and briefly consider the implications for learning mathematics. I contend that a central component of knowledge required in modern societies involves the development of a meta-epistemological stance – i.e. developing a sense of mechanism for the models that underpin social and professional discourses. I illustrate this point in relation to recent research in which I am investigating the mathematical epistemology of engineering practice. Finally, I map out one implication for the design of future mathematical learning environments with reference to some data from the "Playground Project"

Cross-lingual Word Clusters for Direct Transfer of Linguistic Structure

It has been established that incorporating word cluster features derived from large unlabeled corpora can significantly improve prediction of linguistic structure. While previous work has focused primarily on English, we extend these results to other languages along two dimensions. First, we show that these results hold true for a number of languages across families. Second, and more interestingly, we provide an algorithm for inducing cross-lingual clusters and we show that features derived from these clusters significantly improve the accuracy of cross-lingual structure prediction. Specifically, we show that by augmenting direct-transfer systems with cross-lingual cluster features, the relative error of delexicalized dependency parsers, trained on English treebanks and transferred to foreign languages, can be reduced by up to 13%. When applying the same method to direct transfer of named-entity recognizers, we observe relative improvements of up to 26%