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 textbooks.


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 attributes.


<math role=ĦħlemmaĦħ>...</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 argumentation.


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, §Ùmega, 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 03:04:12 UTC