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).
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.
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
- 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
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
16:00-18:00: Session 4: Evaluation & Demonstration
Chair: Christoph Lange
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
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
OpenDiscoverySpace: a new social portal to share learning resources across Europe
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).
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.
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.
- 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
The programme committee review work is indebted to the following persons in the review process:
Corneliu-Claudiu Prodescu, and