Towards a quantitative evaluation of the relationship between the domain knowledge and the ability to assess peer work

In this work we present the preliminary results provided by the statistical modeling of the cognitive relationship between the knowledge about a topic a the ability to assess peer achievements on the same topic. Our starting point is Bloom's taxonomy of educational objectives in the cognitive domain, and our outcomes confirm the hypothesized ranking. A further consideration that can be derived is that meta-cognitive abilities (e.g., assessment) require deeper domain knowledge

Supporting mediated peer-evaluation to grade answers to open-ended questions

We show an approach to semi-automatic grading of answers given by students to open ended questions (open answers). We use both peer-evaluation and teacher evaluation. A learner is modeled by her Knowledge and her assessments quality (Judgment). The data generated by the peer- and teacher- evaluations, and by the learner models is represented by a Bayesian Network, in which the grades of the answers, and the elements of the learner models, are variables, with values in a probability distribution. The initial state of the network is determined by the peer-assessment data. Then, each teacher’s grading of an answer triggers evidence propagation in the network. The framework is implemented in a web-based system. We present also an experimental activity, set to verify the effectiveness of the approach, in terms of correctness of system grading, amount of required teacher's work, and correlation of system outputs with teacher’s grades and student’s final exam grade

Mixed spatially varying L2L^2-BV regularization of inverse ill-posed problems

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers which allow the capturing of diverse properties of the exact solution (e.g. edges, discontinuities, borders, etc.). However, in some problems in which it is known that the regularity of the exact solution is heterogeneous and/or anisotropic, it is reasonable to think that a much better option could be the simultaneous use of two or more penalizers of different nature. Such is the case, for instance, in some image restoration problems in which preservation of edges, borders or discontinuities is an important matter. In this work we present some results on the simultaneous use of penalizers of $L^2$ and of bounded variation (BV) type. For particular cases, existence and uniqueness results are proved. Open problems are discussed and results to signal restoration problems are presented.Comment: 18 pages, 12 figure

Improved computation of individual ZPD in a distance learning system

This paper builds upon theoretical studies in the field of social constructivism. Lev Vygotsky is considered one of the greatest representatives of this research line, with his theory of the Zone of Proximal Development (ZPD). Our work aims at integrating this concept in the practice of a computer-assisted learning system. For each learner, the system stores a model summarizing the current Student Knowledge (SK). Each educational activity is specified through the deployed content, the skills required to tackle it, and those acquired, and is further annotated by the effort estimated for the task. The latter may change from one student to another, given the already achieved competence. A suitable weighting of the robustness (certainty) of student’s skills, stored in SK, and their combination are used to verify the inclusion of a learning activity in the student’s ZPD. With respect to our previous work, the algorithm for the calculation of the ZPD of the individual student has been optimized, by enhancing the certainty weighting policy, and a graphical display of the ZPD has been added. Thanks to the latter, the student can get a clear vision of the learning paths that he/she can presently tackle. This both facilitates the educational process, and helps developing the metacognitive ability self-assessment

Modeling peer assessment as a personalized predictor of teacher's grades: The case of OpenAnswer

Questions with open answers are rarely used as e-learning assessment tools because of the resulting high workload for the teacher/tutor that should grade them. This can be mitigated by having students grade each other's answers, but the uncertainty on the quality of the resulting grades could be high. In our OpenAnswer system we have modeled peer-assessment as a Bayesian network connecting a set of sub-networks (each representing a participating student) to the corresponding answers of her graded peers. The model has shown good ability to predict (without further info from the teacher) the exact teacher mark and a very good ability to predict it within 1 mark from the right one (ground truth). From the available datasets we noticed that different teachers sometimes disagree in their assessment of the same answer. For this reason in this paper we explore how the model can be tailored to the specific teacher to improve its prediction ability. To this aim, we parametrically define the CPTs (Conditional Probability Tables) describing the probabilistic dependence of a Bayesian variable from others in the modeled network, and we optimize the parameters generating the CPTs to obtain the smallest average difference between the predicted grades and the teacher's marks (ground truth). The optimization is carried out separately with respect to each teacher available in our datasets, or respect to the whole datasets. The paper discusses the results and shows that the prediction performance of our model, when optimized separately for each teacher, improves against the case in which our model is globally optimized respect to the whole dataset, which in turn improves against the predictions of the raw peer-assessment. The improved prediction would allow us to use OpenAnswer, without teacher intervention, as a class monitoring and diagnostic tool

Oii-web: An interactive online programming contest training system

In this paper we report our experience, related to the online training for the Italian and International Olympiads in Informatics. We developed an interactive online system, based on CMS, the grading system used in several major programming contests including the International Olympiads in Informatics (IOI), and used it in three distinct context: training students for the Italian Olympiads in Informatics (OII), training teachers in order to be able to assist students for the OII, and training the Italian team for the IOI. The system, that is freely available, proved to be a game changer for the whole italian olympiads in informatics ecosystem: in one year, we almost doubled the participation to OII, from 13k to 21k secondary school students. The system is developed basing on the Contest Management System (CMS, http://cms- dev.github.io/), so it is highly available to extensions supporting, for instance, the pro- duction of feedback on problems solutions submitted by trainees. The system is also freely available, with the idea of allowing for support to alternative necessities and developmen

Peer assessment and knowledge discovering in a community of learners

Thanks to the exponential growth of the Internet, Distance Education is becoming more and more strategic in many fields of daily life. Its main advantage is that students can learn through appropriate web platforms that allow them to take advantage of multimedia and interactive teaching materials, without constraints neither of time nor of space. Today, in fact, the Internet offers many platforms suitable for this purpose, such as Moodle, ATutor and others. Coursera is another example of a platform that offers different courses to thousands of enrolled students. This approach to learning is, however, posing new problems such as that of the assessment of the learning status of the learner in the case where there were thousands of students following a course, as is in Massive On-line Courses (MOOC). The Peer Assessment can therefore be a solution to this problem: evaluation takes place between peers, creating a dynamic in the community of learners that evolves autonomously. In this article, we present a first step towards this direction through a peer assessment mechanism led by the teacher who intervenes by evaluating a very small part of the students. Through a mechanism based on machine learning, and in particular on a modified form of K-NN, given the teacher’s grades, the system should converge towards an evaluation that is as similar as possible to the one that the teacher would have given. An experiment is presented with encouraging results

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Espectroscopía Raman Intensificada por Superficie (SERS) en la identificación de microorganismos que producen biodeterioro: patrimonio edificado con arquitectura en tierra, Vale Histórico Paulista (São Paulo, Brasil)

El objetivo de este trabajo es presentar resultados obtenidos mediante análisis por espectroscopía Raman intensificada por superficie (SERS) como herramienta novedosa para la identificación taxonómica de hongos a partir de biofilms formados en paredes de arquitectura en tierra (“pau-a-pique”, “taipa de pilão”, y adobe), en edificaciones históricas del Vale Histórico de São Paulo, representativas del período colonial brasileño, Con el objetivo de abrir la posibilidad de clasificación de hongos mediante SERS, se seleccionaron colonias puras que fueron previamente aislados de las paredes de tierra e identificados por taxonomía clásica y biología molecular. Los géneros estudiados fueron: Trichoderma, Cladosporium, Aspergillus, Neurospora, Fusarium y Penicillium. Las colonias fueron cultivadas en PDA sólido. Se realizaron extractos en acetato de etilo que fueron mezclados con nanopartículas de oro en suspensión coloidal. Se observaron bandas características de grupos funcionales en la región entre 600 y 1800 cm-1 que presentaron diferencias para cada género. Análisis estadísticos de PCA y HCA mostraron relaciones que permitieron hacer asociaciones por género. Este trabajo es el primer reporte de comunidades microbianas a partir de paredes hechas con técnicas de arquitectura en tierra con el uso de Espectroscopía SERS

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur