Studio di ausili tecnologici compensativi di supporto all'iter di apprendimento matematico secondario e universitario degli studenti con dislessia

Data coming out from various researches carried out over the last years in Italy on the problem of school dispersion in secondary school show that difficulty in studying mathematics is one of the most frequent reasons of discomfort reported by students. Nevertheless, it is definitely unrealistic to think we can do without such knowledge in today society: mathematics is largely taught in secondary school and it is not confined within technical-scientific courses only. It is reasonable to say that, although students may choose academic courses that are, apparently, far away from mathematics, all students will have to come to terms, sooner or later in their life, with this subject. Among the reasons of discomfort given by the study of mathematics, some mention the very nature of this subject and in particular the complex symbolic language through which it is expressed. In fact, mathematics is a multimodal system composed by oral and written verbal texts, symbol expressions, such as formulae and equations, figures and graphs. For this, the study of mathematics represents a real challenge to those who suffer from dyslexia: this is a constitutional condition limiting people performances in relation to the activities of reading and writing and, in particular, to the study of mathematical contents. Here the difficulties in working with verbal and symbolic codes entail, in turn, difficulties in the comprehension of texts from which to deduce operations that, once combined together, would lead to the problem final solution. Information technologies may support this learning disorder effectively. However, these tools have some implementation limits, restricting their use in the study of scientific subjects. Vocal synthesis word processors are currently used to compensate difficulties in reading within the area of classical studies, but they are not used within the area of mathematics. This is because the vocal synthesis (or we should say the screen reader supporting it) is not able to interpret all that is not textual, such as symbols, images and graphs. The DISMATH software, which is the subject of this project, would allow dyslexic users to read technical-scientific documents with the help of a vocal synthesis, to understand the spatial structure of formulae and matrixes, to write documents with a technical-scientific content in a format that is compatible with main scientific editors. The system uses LaTex, a text mathematic language, as mediation system. It is set up as LaTex editor, whose graphic interface, in line with main commercial products, offers some additional specific functions with the capability to support the needs of users who are not able to manage verbal and symbolic codes on their own. LaTex is translated in real time into a standard symbolic language and it is read by vocal synthesis in natural language, in order to increase, through the bimodal representation, the ability to process information. The understanding of the mathematic formula through its reading is made possible by the deconstruction of the formula itself and its “tree” representation, so allowing to identify the logical elements composing it. Users, even without knowing LaTex language, are able to write whatever scientific document they need: in fact the symbolic elements are recalled by proper menus and automatically translated by the software managing the correct syntax. The final aim of the project, therefore, is to implement an editor enabling dyslexic people (but not only them) to manage mathematic formulae effectively, through the integration of different software tools, so allowing a better teacher/learner interaction too.

Kernel Methods for Tree Structured Data

Machine learning comprises a series of techniques for automatic extraction of meaningful information from large collections of noisy data. In many real world applications, data is naturally represented in structured form. Since traditional methods in machine learning deal with vectorial information, they require an a priori form of preprocessing. Among all the learning techniques for dealing with structured data, kernel methods are recognized to have a strong theoretical background and to be effective approaches. They do not require an explicit vectorial representation of the data in terms of features, but rely on a measure of similarity between any pair of objects of a domain, the kernel function. Designing fast and good kernel functions is a challenging problem. In the case of tree structured data two issues become relevant: kernel for trees should not be sparse and should be fast to compute. The sparsity problem arises when, given a dataset and a kernel function, most structures of the dataset are completely dissimilar to one another. In those cases the classifier has too few information for making correct predictions on unseen data. In fact, it tends to produce a discriminating function behaving as the nearest neighbour rule. Sparsity is likely to arise for some standard tree kernel functions, such as the subtree and subset tree kernel, when they are applied to datasets with node labels belonging to a large domain. A second drawback of using tree kernels is the time complexity required both in learning and classification phases. Such a complexity can sometimes prevents the kernel application in scenarios involving large amount of data. This thesis proposes three contributions for resolving the above issues of kernel for trees. A first contribution aims at creating kernel functions which adapt to the statistical properties of the dataset, thus reducing its sparsity with respect to traditional tree kernel functions. Specifically, we propose to encode the input trees by an algorithm able to project the data onto a lower dimensional space with the property that similar structures are mapped similarly. By building kernel functions on the lower dimensional representation, we are able to perform inexact matchings between different inputs in the original space. A second contribution is the proposal of a novel kernel function based on the convolution kernel framework. Convolution kernel measures the similarity of two objects in terms of the similarities of their subparts. Most convolution kernels are based on counting the number of shared substructures, partially discarding information about their position in the original structure. The kernel function we propose is, instead, especially focused on this aspect. A third contribution is devoted at reducing the computational burden related to the calculation of a kernel function between a tree and a forest of trees, which is a typical operation in the classification phase and, for some algorithms, also in the learning phase. We propose a general methodology applicable to convolution kernels. Moreover, we show an instantiation of our technique when kernels such as the subtree and subset tree kernels are employed. In those cases, Direct Acyclic Graphs can be used to compactly represent shared substructures in different trees, thus reducing the computational burden and storage requirements.