Gihan Dias

Computer Aided Evaluation of Multi-Step Answers to Algebra Questions

This paper presents a system that automatically assesses multi-step answers to algebra questions. The system requires teacher involvement only during the question set-up stage. Two types of algebra questions are currently supported: questions with linear equations containing fractions, and questions with quadratic equations. The system evaluates each step of a students answer and awards full/partial marks according to a marking scheme. The system was evaluated for its performance using a set of student answer scripts from a government school in Sri Lanka and also by undergraduate students. The system accuracy was over 95.4%, and over 97.5%, respectively for the aforementioned data sets.

Automatic Identification of Errors in Multi-step Answers to Algebra Questions

This paper presents a system that automatically identifies errors made by students in answering algebra questions that require multiple steps. The types of algebra questions we consider include linear equations with fractions and quadratic equations. We have already developed a system that is capable of grading multi-step answers to the aforementioned two types of questions and awarding full/ partial credit according to a marking scheme. The error identification module works on top of this previous system. It was evaluated using data from two sources: government schools and a tuition class in Sri Lanka. The mistakes identified by the system were compared against feedback by two independent teachers. The results showed that the system identified the student mistakes with more than 85% accuracy for both types of questions.

Automated assessment of multi-step answers for mathematical word problems

We present a system to automatically grade the mathematical word questions. The questions that we currently consider are at the level of GCE (General Certificate of Education) Ordinary Level (O/L) Mathematics paper standard in Sri Lanka. The solutions to these questions are open-ended multi step answers. The system uses a regular expression based information retrieval approach to validate the expressions in the answers. The implemented system properly evaluates student answers using a marking rubric and awards full/partial marks. We have tested the performance of the system using 500 answer scripts for five different questions from 50 students. The grades given by the system are compared against the manual grading marks and only one answer was graded wrongly. Therefore, the accuracy of the system is 99.8%.

Computer representation of Venn and Euler diagrams

Venn & Euler diagrams are well-defined mathematical diagram types, which are the major representation methods of Set Theory. Although understanding of different diagram types such as charts and coordinate graphs has been addressed, no research has been done for Venn and Euler diagram interpretation from an image. Venn and Euler Diagrams exist in various media types such as printed format in books, raster images and vector images in electronic media. In this research, a methodology for set details extraction from a vector image is presented and Venn data representation is introduced, which can store Venn details extracted from a Venn or Euler diagram.

Tamil Morphological Analyzer Using Support Vector Machines

Morphology is the process of analyzing the internal structure of words. Grammatical features and properties are used for this analysis. Like other Dravidian languages, Tamil is a highly agglutinative language with a rich morphology. Most of the current morphological analyzers for Tamil mainly use segmentation to deconstruct the word to generate all possible candidates and then either grammar rules or tagging mismatch is used during post processing to get the best candidate. This paper presents a morphological engine for Tamil that uses grammar rules and an annotated corpus to get all possible candidates. A support vector machines classifier is employed to determine the most probable morphological deconstruction for a given word. Lexical labels, respective frequency scores, average length and suffixes are used as features. The accuracy of our system is 98.73 % and a F-measure of .943, which is more than the same reported by other similar research.

Comparison Between Performance of Various Database Systems for Implementing a Language Corpus

Data storage and information retrieval are some of the most important aspects when it comes to the development of a language corpus. Currently most corpora use either relational databases or indexed file systems. When selecting a data storage system, most important facts to consider are the speeds of data insertion and information retrieval. Other than the aforementioned two approaches, currently there are various database systems which have different strengths that can be more useful. This paper compares the performance of data storage and retrieval mechanisms which use relational databases, graph databases, column store databases and indexed file systems for various steps such as inserting data into corpus and retrieving information from it, and tries to suggest an optimal storage architecture for a language corpus.

Automatic Assessment of Student Answers Consisting of Venn and Euler Diagrams

Venn and Euler diagrams are well-defined mathematical diagram types, which are the major representation methods of Set Theory. Venn and Euler diagrams are part of major Mathematics examinations in secondary education such as London Ordinary Level and SAT. Although computer assessment of different diagram types has been addressed, no such research has been done for Venn and Euler diagrams. In this research, we present a system capable of automatically assessing student answers consisting of Venn and Euler diagrams. The student answer is compared against a model answer, and marks are allocated according to a marking rubric.

Assessment and Error Identification of Answers to Mathematical Word Problems

Mathematical word problems can be broadly divided into two categories as numerical word problems and algebraic word problems. These can be further categorised according to the domain, such as interest calculation and mensuration. Although most of the popular Mathematics examinations contain word problems, there are slight differences in the syllabi. The existing research has produced solutions for some categories of the word type problems. However, these solutions cannot be used for other types of word problems nor can these systems be used in the context of other examinations where there are differences in the grading schemes. We introduce a system that can be easily used to assess answers to both numerical and algebraic type word problems and automatically identifies the exact errors (if any) made by students by using a (teacher provided) marking rubric. The system is modularized and can be extended to support different types of word problems. If the answer contains a short textual phrase along with the numerical or algebraic expression, it is also evaluated in order to check whether the student has actually understood the question.

Automatic Assessment of Student Answers for Geometric Construction Questions

In this paper, we present a system that evaluates answers given by students for geometric construction questions and awards full/partial marks according to a marking rubric. We focus on geometric construction questions found in high school mathematics, where students only use a straightedge and compass. The assessment system is automatic, and requires teacher involvement only at question set up time.

An Episode-based Approach to Identify Website User Access Patterns

Mining web access log data is a popular technique to identify frequent access patterns of website users. There are many mining techniques such as clustering, sequential pattern mining and association rule mining to identify these frequent access patterns. Each can find interesting access patterns and group the users, but they cannot identify the slight differences between accesses patterns included in individual clusters. But in reality these could refer to important information about attacks. This paper introduces a methodology to identify these access patterns at a much lower level than what is provided by traditional clustering techniques, such as nearest neighbour based techniques and classification techniques. This technique makes use of the concept of episodes to represent web sessions. These episodes are expressed in the form of regular expressions. To the best of our knowledge, this is the first time to apply the concept of regular expressions to identify user access patterns in web server log data. In addition to identifying frequent patterns, we demonstrate that this technique is able to identify access patterns that occur rarely, which would have been simply treated as noise in traditional clustering mechanisms.