Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

Using Natural Language as Knowledge Representation in an Intelligent Tutoring System

Knowledge used in an intelligent tutoring system to teach students is usually acquired from authors who are experts in the domain. A problem is that they cannot directly add and update knowledge if they don’t learn formal language used in the system. Using natural language to represent knowledge can allow authors to update knowledge easily. This thesis presents a new approach to use unconstrained natural language as knowledge representation for a physics tutoring system so that non-programmers can add knowledge without learning a new knowledge representation. This approach allows domain experts to add not only problem statements, but also background knowledge such as commonsense and domain knowledge including principles in natural language. Rather than translating into a formal language, natural language representation is directly used in inference so that domain experts can understand the internal process, detect knowledge bugs, and revise the knowledgebase easily. In authoring task studies with the new system based on this approach, it was shown that the size of added knowledge was small enough for a domain expert to add, and converged to near zero as more problems were added in one mental model test. After entering the no-new-knowledge state in the test, 5 out of 13 problems (38 percent) were automatically solved by the system without adding new knowledge

New measurement paradigms

This collection of New Measurement Paradigms papers represents a snapshot of the variety of measurement methods in use at the time of writing across several projects funded by the National Science Foundation (US) through its REESE and DR K–12 programs. All of the projects are developing and testing intelligent learning environments that seek to carefully measure and promote student learning, and the purpose of this collection of papers is to describe and illustrate the use of several measurement methods employed to achieve this. The papers are deliberately short because they are designed to introduce the methods in use and not to be a textbook chapter on each method. The New Measurement Paradigms collection is designed to serve as a reference point for researchers who are working in projects that are creating e-learning environments in which there is a need to make judgments about students’ levels of knowledge and skills, or for those interested in this but who have not yet delved into these methods

Bayesian Knowledge Tracing for Navigation through Marzano’s Taxonomy

In this paper we propose a theoretical model of an ITS (Intelligent Tutoring Systems) capable of improving and updating computer-aided navigation based on Bloom’s taxonomy. For this we use the Bayesian Knowledge Tracing algorithm, performing an adaptive control of the navigation among different levels of cognition in online courses. These levels are defined by a taxonomy of educational objectives with a hierarchical order in terms of the control that some processes have over others, called Marzano’s Taxonomy, that takes into account the metacognitive system, responsible for the creation of goals as well as strategies to fulfill them. The main improvements of this proposal are: 1) An adaptive transition between individual assessment questions determined by levels of cognition. 2) A student model based on the initial response of a group of learners which is then adjusted to the ability of each learner. 3) The promotion of metacognitive skills such as goal setting and self-monitoring through the estimation of attempts required to pass the levels. One level of Marzano's taxonomy was left in the hands of the human teacher, clarifying that a differentiation must be made between the tasks in which an ITS can be an important aid and in which it would be more difficult

BeSocratic: An Intelligent Tutoring System for the Recognition, Evaluation, and Analysis of Free-form Student Input

This dissertation describes a novel intelligent tutoring system, BeSocratic, which aims to help fill the gap between simple multiple-choice systems and free-response systems. BeSocratic focuses on targeting questions that are free-form in nature yet defined to the point which allows for automatic evaluation and analysis. The system includes a set of modules which provide instructors with tools to assess student performance. Beyond text boxes and multiple-choice questions, BeSocratic contains several modules that recognize, evaluate, provide feedback, and analyze student-drawn structures, including Euclidean graphs, chemistry molecules, computer science graphs, and simple drawings. Our system uses a visual, rule-based authoring system which enables the creation of activities for use within science, technology, engineering, and mathematics classrooms. BeSocratic records each action that students make within the system. Using a set of post-analysis tools, teachers have the ability to examine both individual and group performances. We accomplish this using hidden Markov model-based clustering techniques and visualizations. These visualizations can help teachers quickly identify common strategies and errors for large groups of students. Furthermore, analysis results can be used directly to improve activities through advanced detection of student errors and refined feedback. BeSocratic activities have been created and tested at several universities. We report specific results from several activities, and discuss how BeSocratic\u27s analysis tools are being used with data from other systems. We specifically detail two chemistry activities and one computer science activity: (1) an activity focused on improving mechanism use, (2) an activity which assesses student understanding of Gibbs energy, and (3) an activity which teaches students the fundamentals of splay trees. In addition to analyzing data collected from students within BeSocratic, we share our visualizations and results from analyzing data gathered with another educational system, PhET