RE: MathML and Digital Textbooks

Hi Adam,

You really introduce a lot of topics!

I work in a company that is a provider of mathematical technology
worldwide with great experience in Span.

There are pioneers that master the technology but, when we speak about
the general usage, we usually find that new technologies must cope first
with non-mathematical specific areas. For example, publishers of digital
textbooks must cope with infrastructure, content licensing, single sign-
on, targeting mobile devices, etc.

Despite this, we are beginning to experience the change in giving to
MathML the role it deserves. Since now, the source of a formula, usually
MathML, was discarded in favor of the raster image. Now, MathML is kept
and brings added value, for example, the re-edition of the formulas, drag
and drop, accessibility and many other exciting features.

In our company, we are working in providing a whole set of solutions for
mathematics for the Web.  This includes: formula edition and rendering,
accessibility, computer algebra systems applied to education and using
all this technologies together for assessment.

Daniel Marques
CTO at Maths for More.

-----Original Message-----
From: Adam Sobieski []
Sent: viernes, 17 de febrero de 2012 4:02
Subject: MathML and Digital Textbooks

Math Working Group,

Greetings. I would like to introduce some topics for discussion regarding
mathematics, mathematics education, technology, the web and digital

Several nations currently have digital textbook programs underway
including, but not limited to, India, Singapore, South Korea and Ukraine.
Recently, the United States of America announced that it intends to
modernize its school equipment over the course of the next five years.

Digital books and textbooks are applications of hypertext and MathML
technologies. While the current set of features are exciting to educators
and education theorists, a discussion of new features, including numerous
features specifically applicable to mathematics education, is underway.
Technical topics include: clipboarding, drag and drop, handwriting
recognition, multitouch, speech recognition and synthesis, and widgets.
Many contemporary research topics, previously discussed in web-related
and other contexts, can now be considered with the important new usage
scenarios of digital books and textbooks.

Mathematics and Clipboarding, Drag and Drop

Clipboarding and dragging and dropping mathematics, or content including
mathematics, is very useful and can be enhanced by means of the content
layer of MathML. We can envision college students dragging and dropping
content between digital textbooks, mathematics or engineering software,
and document authoring software, possibly even between tablet and desktop
computers in their work areas.

Some new features for clipboarding and drag and drop, in general, include
provenance for interoperability with document authoring software where
conveniences for users are provided pertaining to content motion,
citations and reference sections.

Mathematics and Handwriting Recognition

Handwriting recognition is an interesting input technique for mathematics
on computers. Presently, some web-based projects make use of the <canvas>
element for handwriting recognition. In theory, either <canvas> or
<input> elements can connect to platform handwriting recognition
components. While applications already exist that can output MathML from
recognized handwriting, topical are means of doing so for webpages and
for digital books and textbooks.

Providing contextual information to recognition components can enhance
handwriting recognition results. Handwriting recognition, or speech
recognition, in digital mathematics textbooks, can facilitate exercises
or quizzes beyond multiple choice formats. The input of free-form
mathematics on computers can be convenienced by handwriting and speech
recognition technologies.

Mathematics and Multitouch

Multitouch has applicability to mathematics. Beyond writing with a
fingertip or stylus, users can tap upon and zoom onto math equations
using the spread gesture, possibly opening contextual or equation-
specific content. With multitouch gesture recognition, mathematics
equations and objects on webpages and in digital books and textbooks can
have multiple navigational dimensions such as tapping and spreading.

Mathematics and Speech Recognition, Synthesis

Speech recognition and synthesis are other interesting areas of research
and with regard to mathematics. In EPUB3, Pronunciation Lexicon
Specification (PLS), Synchronized Multimedia Integration Language (SMIL),
and Speech Synthesis Markup Language (SSML) are utilized. Elements of
HTML and MathML can be indicated in SMIL and/or annotated with SSML. For
purposes of visually synchronizing document content with playback of an
audio overlay, EPUB3 provides a publication-specified CSS3 class name,
with a default being -epub-media-overlay-active.

As with handwriting recognition, providing contextual information can
enhance speech recognition results. Such contextual information can be
from the metadata of websites, webpages, article elements, document
elements, or specifically <input> elements. Speech recognition accuracy
can be enhanced by contextual information and upcoming technologies can
be enhanced by speech recognition components which, like handwriting
recognition, include modes for outputting text and MathML.

Mathematics and Document Structure

A role attribute exists for accessibility, device adaptation, server-side
processing, and complex data description. Similarly, in EPUB3, a type
attribute exists. Such attributes can allow secondary structure to be
indicated on XML trees. Beyond complex data description, such attributes
can enhance search and navigation. Examples include mathematics proofs
and arguments, the structures of which can be indicated using such

<math role=”lemma”>...</math>

Mathematics and Proof and Argumentation

While the previous topic indicates that the structures of proofs and
argumentation can be annotational atop hypertext, digital books and
textbooks can also include data files while making use of client-side
computation to render resulting hypertext content. In such files, the
discussion text can be as annotational and client-side computation can
output sections of hypertext and mathematics from the data files.
Advantages include the automatic adaptation of navigation options when
new content files are added, including navigation of multiple discussions
of multiple mathematical proofs. Where ink and paper textbooks ordinarily
provide a sequence of discussion and reasoning, a digital textbook can
provide students multiple parallel routes of discussed proofs and

With regard to argumentation, there exist an Argument Interchange Format
(AIF), Argument Markup Language (AML) and Legal Knowledge Interchange
Format (LKIF). In addition to those are formats that accompany automated
reasoning software, such as HOL, Mizar, PVS, Coq, Otter/Ivy,
Isabelle/Isar, Alfa/Agda, ACL2, PhoX, IMPS, Metamath, Theorema, Lego,
Nuprl, Ωmega, B method, and Minlog.

In August of 2011, at the 23rd International Conference on Automated
Deduction, the first PxTP workshop discussed ideas about formats and data
exchange for mathematical proofs and argumentation.

Mathematics and 3D Interactive Visualization

Digital textbooks can include 3D interactive graphics for mathematical
concept introduction and visualization. MathML, possibly with
annotational XML, can be an input format for general-purpose
visualization applets or widgets. Such applets or widgets can
additionally make use of cascading stylesheets computed styles for
specific <object> elements in hypertext.


Each contemporary research and development topic indicated can enhance
the web as well as digital books and textbooks. Entirely new techniques
for authoring mathematics textbooks may result from upcoming new uses of
technology in classrooms. In addition to the exciting capabilities and
features that already exist, are topics pertaining to upcoming
capabilities and enhancements to features.

Kind regards,

Adam Sobieski

Received on Friday, 17 February 2012 13:23:04 UTC