Mathematical User Interfaces
Workshop 2013

At the Conferences on Intelligent Computer Mathematics
University of Bath, UK, July 10^th, 2013

Proceedings

The proceedings, including the papers below, of the workshop are also part of the proceedings of Workshops and Work in Progress at CICM, volume 1010 of CEUR-WS (ISSN 1613-0073).

Programme

The following papers have been presented at the workshop on July 10th in room 8W 2.1.

08:30-10:00 Session 1: Understand

Chair: Helena Mihaljevic-Brandt

• Jan Wilken Dörrie and Michael Kohlhase
  MathMap: Accessing Math via Interactive Maps
  World Math literature is growing at an alarming rate (3.3M journal articles today increasing by 120k a year). While much of that can be retrieved online, we lack technologies to navigate and understand the space of math literature. The MathMap project wants to develop and deploy novel interfaces that empower interested parties to find their way. We conjecture that such maps can act as cognitively adequate access mechanisms to many large-coverage MKM systems.
  The first concrete interface is an interactive map generated from publication data. We have developed a prototype map generation service based on MSC classifications and deployed the maps resulting from ZBMath data in OpenStreetMap. It is accessible at map.mathweb.org.
• Andrea Kohlhase
  Spreadsheets: From Data Interfaces to Knowledge Interfaces
  Documents of type ``spreadsheet'' are considered user interfaces to numeric data as they allow authors to create, modify and display these data in distinct layouts like tables or diagrams and readers to interpret them. We tend to believe that enhancing software semantically means that we are lifting its value. In particular, if we enhance spreadsheets semantically can we lift their data interface status to a knowledge interface status? We used the repertory grid methodology to conduct a study on the difference between spreadsheets and spreadsheets semantically enhanced with the SACHS extension. Our research shows that, indeed, from the perspective of users adding semantics turns spreadsheets into knowledge interfaces.
• Mihnea Iancu, Felix Mance and Florian Rabe
  The Scala-REPL + MMT as a Lightweight Mathematical User Interface Scala is a general purpose programming language that includes a read-eval-print loop (REPL). MMT is a general representation language for formal mathematical knowledge implemented in Scala. Independent recent developments permit combining them into an extremely simple user interface.
  Firstly, Scala introduced string interpolation -- a convenient syntax that permits escaping back and forth between strings and arbitrary Scala expressions (while preserving type safety). Secondly, MMT introduced a notation-based text syntax and a rule-based evaluation engine for its mathematical objects (which are based on OpenMath).
  Combining these, users can enter and work with MMT objects in the Scala-REPL with so little overhead that it essentially behaves like a dedicated MMT-REPL -- except for also providing the full power of Scala. Implicit conversions (e.g., between integers represented in MMT and Scala integers) further blur the distinction between meta- and object language.
  MMT is highly extensible: Users can add new type systems and logics as well as new theories and notations and evaluation rules. Thus, we obtain a REPL-style interface for any language represented in MMT with essentially no effort.

10:00-10:30: coffee break

10:30-12:30: Session 2: Learn

Chair: Paul Libbrecht

• Eric Andres, Bastiaan Heeren and Johan Jeuring
  Towards Automatic Generation of Domain-Specific Mathematical Input Support
  Providing input when solving a mathematical problem in a technology-enhanced learning system is often a challenging task for a learner. Input editors either provide clickable palettes to construct terms, or require knowledge of some linear syntax. To alleviate this problem, the learning environment ActiveMath was extended with a new interface supporting learners with providing a stepwise solution in the fraction domain. The interface allows learners to insert intermediate steps using pre-defined templates such as “The least common multiple of _ and _ is _”, where a blank can be filled in using a dedicated simple input field. Developing similar interfaces for other mathematical domains is labor intensive and error prone. In this article, we investigate how the IDEAS domain reasoners can be used to derive the necessary information for the automatic generation of such templates, by making the structure of domain rules explicit using OpenMath expressions.
• Anjo Anjewierden, Ellen T. Kamp and Ton de Jong
  Ziggy: Very Interactive Trigonometry
  In this paper we describe a highly interactive touch-based application to teach the basics of trigonometry to secondary school students. The application, called Ziggy, lets students ``touch'' and ``push'' triangles, dynamically modifying the shape and size, and observe the effect on the angles, sides and the trigonometric ratios. We describe the pedagogical rationale behind Ziggy, the user interface and provide details on the implementation. An early version of Ziggy has been tested in small-scale experiments in the classroom.
• Jean-François Nicaud and Christophe Viudez
  Implementation of Dynamic Algebra in Epsilonwriter
  Dynamic Algebra is “doing algebraic calculations on a computer by direct manipulation”. We have implemented Dynamic Algebra in the Epsilonwriter application. For that purpose, a “Theory of Movements in Formulas” (TMF) has been elaborated. It describes, in a precise context, how we can move a sub-expression in a formula with preservation of equivalence. It has been implemented in Epsilonwriter for the Pedagogical Dynamic Algebra mode. Dynamic Algebra in Epsilonwriter has other modes with more complex actions of different classes: equivalent drag & drop internal to a formula, external drag & drop, on click calculations and rewriting rule application. This makes Epsilonwriter a very powerful and flexible calculation tool for step by step calculations; and a tool able to provide explanations. Epsilonwriter contains different options to control the possible movements and the feedback on them. It has been developed to help students learn formula structure and transformations, and to help every user produce step by step explained calculations.
• Rui Hu and Stephen Watt
  InkChat: A Collaboration Tool for Mathematics
  We investigate the question of how multimodality can be used in computer-mediated mathematical collaboration. To demonstrate our ideas, we present InkChat, a whiteboard application, which can be used to conduct collaborative sessions on a shared canvas. It allows participants to use voice and digital ink independently and simultaneously, which has been found useful in mathematical collaboration.

14:00-15:30: Session 3: Input

Chair: Andrea Kohlhase

• Vadim Mazalov and Stephen Watt
  Recommendation Systems in Mathematical Character Recognition
  In handwritten text there are usually several accepted styles for forming each character. We hypothesize that in the handwriting of individuals there is a correlation among the styles used for characters, and that these correlations may be used to anticipate which styles particular writers will use for symbols that have not yet been seen.
  This approach may prove useful in the setting of mathematical handwriting recognition, where there are many symbols and it would be onerous to require writers to provide samples of every one in order to personalize handwriting recognition. We describe preliminary experiments using ideas from the area of recommendation systems to predict which styles writers will likely use for symbols they have not yet written.
  The experiments demonstrate a certain degree of similarity between character styles of users, as well as similarity between users with respect to the styles they provided. We also explain a method for efficient training of the classifier by proposing character styles that are likely to represent the handwriting of the given author. These ideas may be used to enhance usability of the training application.
• Daniel Marques
  Edition with Arabic mathematical notation
  This paper is related to user interfaces for editing formulas and the challenges that introduce the Arabic mathematical notation. A brief introduction to Arabic mathematical notation is provided with special attention to the MathML format and the difficulties that the formula editor should solve.
• Deyan Ginev
  NNexus Glasses: A Drop-in Showcase for Wikification
  This paper describes a general drop-in approach for showcasing web services and web user interfaces, provided they are accessible through or realized via JavaScript and CSS. We utilize the Greasemonkey extension for Firefox to invade the client with user scripts, which load the desired new functionality, as if looking at the web through an enhanced pair of glasses. Such demos have so far typically required access and modifications to the production server of the target website.
  The approach is particularly valuable for mock-integration with closed, proprietary platforms and/or sites serving content under restrictive copyright licenses. A potential use case is to aid an "elevator pitch" to a company interested in MKM technologies, by supplementing it with a drop-in demo on their live system.
  To exemplify, the paper presents a case study of using the recent rewrite of the NNexus auto-linker for mathematical concepts to invade the closed web platforms of Zentrallblat Math and DLMF with wikification links.

16:00-18:00: Session 4: Evaluation & Demonstration

Chair: Christoph Lange

• Jan Willem Knopper and Hans Cuypers
  Interactive Mathematical Videos
  Over the last ten to fifteen years video has become an important means of communications through the world wide web. The video tools incorporated in mobile phones and other devices make it easy to create videos. These videos are then easily distribute via YouTube, Vimeo or other channels. Also in education of mathematics videos and screencasts are playing a more and more prominent role, witnessed by the popularity of the Kahn Academy.
  On the other hand, mathematical software for online and blended education has become mature and nowadays there exist various software packages, both commercial and open source, that provide the user various ways of interactive mathematics, ranging from interactive and dynamic geometry packages like geogebra, cinderella and sketchpad, to automatically generated and graded exercises in Webworks, STACK or MapleTA and systems combining these functionalities like ActiveMath and MathDox.
  In this note we report on some experiments in which we have tried to combine the use of video with the interactive mathematical software package MathDox to obtain interactive mathematical videos. The tools we use to obtain the integration of video with interactive MathDox pages is the Popcorn JavaScript framework developed by Mozilla.
  In the sequel we first describe MathDox and Popcorn.js and then report on our experiments to combine the two to obtain interactive mathematical videos.

The demonstration session of the MathUI workshop is an exhibit where each software is demonstrated by their authors. It starts at 16:30 with an elevator pitch of 90 seconds per demo and finishes at 18:00. The following demonstrations are accepted:

• Epsilonwriter: Dynamic Algebra and Communication with Math
  Jean-François Nicaud and Christophe Viudez, Aristod SàRL, Palaiseau, France
  Epsilonwriter is Java software running on Windows, MacOs and Linux for editing text and formulas. Beyond allowing the production of documents and web pages with a very flexible formula editor, Epsilonwriter implements Dynamic Algebra, an innovative and rich mechanism for step by step calculations. Epsilonwriter also has a Chat and allows working on Live documents (several persons share a document in real time). In all cases, math formulas are easy to type and are received as objects that can be edited.
  Dynamic Algebra is doing calculations with the mouse. In Epsilonwriter, there are several Dynamic Algebra frameworks. The Pedagogical Dynamic Algebra is based on a Theory of Movement in Formulas. It aims at helping students learn the structure of formulas and reinforce their knowledge in basic transformations of formulas. The other Dynamic Algebra frameworks allow doing step by step calculations with explanations at several levels, including solving second and third degree equations. This makes Epsilonwriter a very good tool for students and also for teacher for writing documents.
  Epsilonwriter is communication software. It allows working on Live documents with formulas which includes distance tutoring. In the current Live mode, only one person can edit the document at a time; another person can edit the document when the former leave control. In a near future, the Live-multi mode will allow several persons to edit the document at a time.
  Epsilonwriter has a Chat for chatting with text, formulas, links and images.
• Lurch: The word processor that can check your math
  Nathan Carter
  Lurch is a word processor capable of checking the reasoning of proofs in the user's document. It is a pedagogical tool, intended for use by students in an introductory proofs course, to provide frequent and immediate feedback to accelerate learning the rules of logic and mathematical proof. We want the user to be able to write their document in whatever style and natural language they choose, and yet still have Lurch understand and check the validity of their mathematical inferences. Of course, the software cannot read and understand natural language, so a minimal formatting burden is placed on the user to point out to the software which sections of the document are "meaningful mathematics." The software does the rest, providing feedback on each step of the user's proof, and gentle suggestions on how to fix errors.
• Ziggy: Very interactive trigonometry
  Anjo Wierden
  Ziggy is an interactive environment for teaching secondary school students basic trigonometry (sine, cosine, tangent, Pythagoras, 180* rule). Ziggy contains instructional material explaining what basic trigonometry is, examples that can be manipulated and exercises that students can solve algebraically. Ziggy was designed for touch-devices such as the iPad but runs on all modern browsers that support HTML5/Javascript. For more information see the MathUI workshop paper.
• OpenDiscoverySpace: a new social portal to share learning resources across Europe
  Paul Libbrecht
  The central goal of OpenDiscoverySpace is the central goal of Action 68 of the Digital Agenda for Europe: ODS aims to pave the way to a generalized usage of ICT in education.
  This demonstration has presented the beta version of this portal which positions itself as much as a resources' sharing platform, as much as a training platform, and as a social network.
  ODS is federating a considerable amount of learning resources repositories in mathematics, physics, biology, language learning, and other subjects. It is based on a classification of subjects that extends the EUN LRE Thesaurus so that "almost fine grained" categorization can help to narrow down the ever lasting search for the relevant learning resource.

The evening continues in the same room with the DML Panel discussion: Fifty Shades of *DML (18:00-19:00).

Scope

MathUI is an international workshop for discussing mathematical user interfaces, i.e., ideas and studies of how users (can) interact with mathematical representations on a computer. Topics include:

• user-requirements for math interfaces
• presentation formats
• mobile-devices powered mathematics
• cultural differences in practices of mathematical languages
• didactically sensible scenarios
• spreadsheets as mathematical interfaces
• manipulations of mathematical expressions

This workshop follows a successful series of meetings held at the Conferences on Intelligent Computer Mathematics; it features presentations of brand new ideas in papers selected by a review process, wide space for discussions, as well as a software demonstration session.

Invitations

We have welcome submissions that present new ideas, features, user-studies, and software systems relevant to MathUI in the form of a description (4-8 pages) and/or a video submitted to the easychair system. The programme committee has reviewed the submission following criteria of originality and applicability. The final forms of the papers are included in the proceedings on this web page and on CEUR-WS.

Programme Committee

• David Aspinall
  School of Informatics, University of Edinburgh, Scotland
• Paul Cairns
  University of York, Great Britain
• Olga Caprotti
  University of Gothenburg, Chalmers, Sweden.
• Andrea Kohlhase (organizer)
  Jacobs University Bremen, Germany
• Paul Libbrecht (organizer)
  Center for Educational Research , MLU Halle, Germany
• Andrea Hoffkamp
  HU Berlin, Germany
• Elena Smirnova
  Texas Instruments Inc. Education Technology, USA
• Helena Mihaljevic-Brandt
  Zentralblatt MATH

The programme committee review work is indebted to the following persons in the review process: Mihnea Iancu, Christoph Lange, Azzeddine Lazrek, Christoph Lüth, Steven Obua, Corneliu-Claudiu Prodescu, and Iain Whiteside

Links

• Please advertise MathUI'13 further: find the plain-text call for submissions.
• MathUI has been announced in a number of mailing-lists as was on the Interaction Design Calendar
• The seventh Mathematical user interfaces workshop happened at CICM 2012 in Bremen, Germany. Please find proceedings and programme on MathUI'12 and in CEUR-WS joint proceedings.
• Find about previous events in MathUI workshop archive.
• This page is at
  http://cermat.org/events/MathUI/13/.