Online Education: What Works in Mathematics

Florida State University and University of Helsinki Information technology has the potential to deliver education to everybody by high quality online courses and associated services, and to enhance traditional face-to-face instruction by, e.g., web services offering virtually unlimited practice and step-bystep solutions to practice problems. Regardless of this, tools of information technology have not yet penetrated mathematics education in any meaningful way. This is mostly due to the inertia of academia: instructors are slow to change their working habits. This paper reports on an experiment where all the instructors (seven instructors and six teaching assistants) of a large calculus course were required to base their instruction on online content. The paper will analyze the effectiveness of various solutions used, and finishes with recommendations regarding best practices.

Computer Processing of Medieval Slavic Sources in the Institute of Literature at BAS Repertorium Project (1994–2004)

Mixed-content miscellanies (very frequent in the Byzantine and mediaeval Slavic written heritage) are usually defined as collections of works with non-occupational, non-liturgical application, and texts in them are selected and arranged according to no identifiable principle. It is a “readable” type of miscellanies which were compiled mainly on the basis of the cognitive interests of compilers and readers. Just like the occupational ones, they also appeared to satisfy public needs but were intended for individual usage. My textological comparison had shown that mixed- content miscellanies often showed evidence of a stable content – some of them include the same constituent works in the same order, regardless that the manuscripts had no obvious genetic relationship. These correspondences were sufficiently numerous and distinctive that they could not be merely fortuitous, and the only sensible interpretation was that even when the operative organizational principle was not based on independently identifiable criteria, such as the church calendar, liturgical function, or thematic considerations, mixed-content miscellanies (or, at least, portions of their contents) nonetheless fell into types. In this respect, the apparent free selection and arrangement of texts in mixed-content miscellanies turns out to be illusory. The problem was – as the corpus of manuscripts that I and my colleagues needed to examine grew – our ability to keep track of the structure of each one, and to identify structural correspondences among manuscripts within the corpus, diminished. So, at the end of 1993 I addressed a letter to Prof. David Birnbaum (University of Pittsburgh, PA) with a request to help me to solve the problem. He and my colleague Andrey Boyadzhiev (Sofia University) pointed out to me that computers are well suited to recording, processing, and analyzing large amounts of data, and to identifying patterns within the data, and their proposal was that we try to develop a computer system for description of manuscripts, for their analysis and of course, for searching the data. Our collaboration in this project is now ten years old, and our talk today presents an overview of that collaboration.