Xronos and Ximera Projects
Xronos and Ximera Projects
It is easiest to see Xronos in Action! The following links are actual assignments used at the University of Florida this semester. All pages were ultimately written, published, and maintained by myself, in close coordination with the course coordinator and any other relevant instructors or authors.
MAC1140 - Precalculus Algebra.
This is the course I coordinate and developed. When I took this course over I had pedagogical differences with the original course materials and got permission to rewrite the course materials from scratch. I took the opportunity to demonstrate some of the power of the Xronos platform. Until this point, Xronos had primarily been used as a homework assignment platform but I wanted to demonstrate that it can be used to develop an entire online curriculum, complete with embedded lecture materials, practice problems, and interactive content. Every semester I continue to add more features and content, polling the students with a number of suggestions and soliciting feedback to see what additional content is most preferred.
MAC2311 - Calculus 1
This was our pioneering course. As such it has the oldest assessments, but also the most well tested.
MAC2312 - Calculus 2
Like all the calculus courses, this course uses static problems that were randomly generated initially but are now static and the same for all students.
MAC2313 - Calculus 3
This is a homework assignment from the most recent course to use Xronos, and is thus still being beta tested. This assignment demonstrates one of the powerful aspects of Xronos; the ability to write custom validators. In this case, to validate equivalent planar functions that may be constant multiples of the supplied "correct" answer by the author.
MAC2234 - Survey of Calculus 2
This is a homework assignment from a course also in beta testing, and is using a different paradigm involving entirely randomly generated problems for each assignment.
MAC1114 - Trigonometry
This is a homework written entirely by a 5th year graduate student with minimal training; demonstrating the power and low barrier of entry to become a content author using Xronos.
The Ximera project was started at Ohio State University (OSU) by Jim Fowler and Bart Snapp as a way to allow individuals to convert LaTeX files into both a pdf textbook, and an online interactive textbook. This free and open source project was developed over several years until a working prototype was hosted at OSU. Although they provided free hosting for any institution interested in using the project, student data was necessarily hosted on the OSU servers.
Although theoretically the server code was written to be configurable so that other institutions could host their own servers for a Ximera installation, in practice much of the content was hardcoded to OSU configurations as the primary goal was getting a working prototype. Like any open source development environment with large voluntary contributions, Ximera had considerable inconsistency and variability in code style, and even programming language.
When I joined the project I specifically wanted to install a local server at the University of Florida, where I was a graduate student at the time pursuing my PhD in mathematics. We wanted a local server so that we would have sole possession of our student data, but also because we wanted to add and/or modify features of the existing system to suit our specific needs; sometimes in ways that conflicted with the architectural vision of the original programmers.
Over the first year of my involvement I spent most of my time streamlining and rewriting code, adding in comments to make it clearer what code was doing and what needed to be fixed or modified, and generalizing the configuration process to make it vastly easier for other institutions to install their own servers. For these contributions I was asked by Jim and Bart to join them as the third primary developer of Ximera, eventually joining the board of directors for Ximera.org (a nonprofit organization founded for the project to disassociate it from OSU).
Due to the extensive modifications I made to the original code; most but not all of which were eventually accepted and merged into the master code, it became necessary to distinguish between the OSU server version and the UF server version at various stages of development. For this reason we decided to name the UF server version Xronos, while the OSU server version remained Ximera.
By this point most of the changes made to the original code for Xronos have been merged into the Ximera master codebase. Originally I developed a number of new and improved features for UF, which we deployed in Xronos, including;
Randomization Tools, including Sage generated problem content.
Formatting improvements for footnotes, problems, nested problems, and inline dropdown answers.
Developed best practices and third party tools for writing and filtering databases of problems utilizing LaTeX, python or sage programming options.
Developed over half a million problems for use in calculus 1 and calculus 2.
Written guides and documentation of commands to use when writing problem sets.
Development of best practices for writing guiding problems and help features.
Xronos and Ximera have a number of features that make it genuinely better than most of the paid products currently used.
Free!
Currently University of Florida students are saving in excess of $200,000 per semester as a result of not needing to buy subscriptions to paid homework sites.
Open Source!
Xronos and Ximera are both committed to maintaining open source, free platforms. We deliberately license the code to make it difficult/impossible to monetize; to ensure that the underlying platform remains free and available to everyone that wants to use it. We envision Xronos to be a platform which helps everyone regardless of: race, gender, geographic location, or university enrollment, to learn and grow. Especially those that are under represented or lack the financial capability often required by other online education companies and tools.
Community!
The Ximera and Xronos community view content as a community resource. We are happy to share part, or all, of our course content with others for free. Currently OSU has interactive textbooks for the entire Calculus sequence as well as linear algebra, and UF has an interactive textbook with embedded lecture videos for precalculus algebra without trigonometry; all freely available to anyone who wants them.
Ximera Correctness Algorithm!
Ximera and Xronos use a multilayer algorithm to determine if a students input is the same as the answer provided by the content author. Among the many algorithms used, is a scatter test. This test applies the student and author functions on a scattering of points just off the real axis in the complex plane. If the results are equal for the two functions for enough points, then the two functions are determined to be equal. This is a consequence of the Identity Theorem from complex analysis; meaning that, up to an issue of machine level precision, mathematically the two functions really are equal regardless of their symbolic form. This allows for any equivalent form written by a student to be accepted as correct, which avoids the vast majority of complaints by students when it comes to online homework submissions.
Feedback and Custom Validators!
Xronos supports feedback which can be customized using custom validators (written in javascript) to allow an author to give immediate and dynamic feedback to students based on what they provided as an answer. For example; you can include a number of predictable incorrect answers and the feedback associated with them, allowing for a better response than "incorrect" to help the student learn and get the correct answer.