# Mathematics

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## Contents

## Equation Construction and Display

### Tools

There are a variety of tools that are available for the purpose of constructing equations, providing text expressions that can be converted to equations, and displaying equations.

The most common text expression syntax is LaTeX or a derivative with probably the most common form of display being a conversion of the equation to an image file. However, is demonstrated with ASCIIMathML simple text expressions can now be be converted to MathML on the fly.

Some tools for creating and displaying equations on-line that may be of interest to those teaching mathematics are:

- Moodle offers in core a basic TeX filter and an Algebra filter. These are simple but not simplistic. An overview of using these tools can be found at the Using TeX Notation pages. Be aware that these packages are subsets of complete TeX packages and the conventions used are designed more for ease of use within Moodle rather than as complete TeX packages.
- ASCIIMathML, which both converts equations into MathML on the fly and provides a text expression syntax more easily mastered than Tex, though the filter will convert TeX expressions as well. The ASCIIMathML 2.0.2 zip provides all the files necessary for setting ASCIIMathML up as a Moodle filter as well creating run-time graphs with ASCIIsvg. An on-line calculator is also included. Just recently an ASCIIMathML export format for DragMath was added to version 0.7.2, available here, so that you have access to both a GUI and text expression syntax for creating and displaying equations. Quick and GIFless. ASciencePad is also available and consists of htmlarea enhanced with the ASCIIMathML functionality.
- Tim Hunt's Moodle MathTran Module converts Tex into images on the fly. You can also use mathtran_img.js on a page by page basis.
- The jsMath filter, which does a similar job but using Javascript on the user's computer
- MathJax_filter, a next generation for jsMath from David Cervone et al that now includes MathML and web font features: [1] A discussion regarding deploying the beta release can be found here: [2]
- Calculated question type
- DragMath equation editor, a WYSIWYG equation editor that integrates easily with the Moodle HTML editor.
- WIRIS, is a suite of math and science tools. www.wiris.com/moodle/
- MathType, an equation editor that allows you to type or handwritte math expressions. Based on MathML and a Javascript interface.
- Wiris Quizzes, a set of question types for math and science topics

- MathML polyfill support (for Chrome) implementation using custom elements [3] (can be added to Moodle via theme custom HTML)

Mathematics teachers may also be interested to follow the work of York University Maths department, who are working on some projects to augment Moodle, particularly its Quiz module for online assessment, for example by integrating a system which is able to mark algebraic and trigonometric answers to open-ended questions.

### Accessibility Display Matrix

**Note:** This section is a work in progress. Please use the page comments for any recommendations/suggestions for improvement. *(August 2008)*

■ Feature Key appears below the matrix.

Notation | Tex/LaTex | ASCIIMath | MathML | WIRIS |
---|---|---|---|---|

Ease of Use | Plain text system. Knowledge of LaTeX notation required. Being a plain text system, LaTeX notation is straightforward to create and edit. | Plain text system. Easy to learn. Notation simple. Being a plain text system, ASCIIMath is very easy to create and edit. | XML-based. Not easy to create and edit: an editor is required. | Visual interface for MathML. Toolbar navigation is accessible. LateX plain text notation is also available. |

Conversion to Braille | Output directly to Braille display via screen reader (fn 2) | ASCIIMath notation is converted to MathML or LaTeX. Please refer to those formats for details. | Converted to suitable textual format and Brailled using screen reader (fn 3) | Image alternative text outputs directly to Braille display via screen reader (fn4) |

Transmission via TTS | Notation spoken "as-is" via screen reader (fn 2) | ASCIIMath notation is converted to MathML or LaTeX. Please refer to those formats for details. | Converted to suitable textual format and spoken using screen reader. Note that MathPlayer add-on for IE has TTS functionality built-in (fn 3). | Image alternative text spoken via screen reader (fn 4) |

**fn1.**
MathPlayer claims to do math-to-speech by parsing the MathML, not by parsing TeX. See http://www.dessci.com/en/products/mathplayer/tech/accessibility.htm where it is stated:

All of these examples were written in Microsoft Word and MathType and exported to MathML using MathType’s “MathPage” technology. MathPage technology was added to MathType in version 5.0. No special work is needed to author the expressions to make them accessible. Any product that exports MathML will produce pages that MathPlayer can speak.

For a larger real life example, see this page. Also, MSN Encarta uses MathML on many of their web pages that contain math, so much of their Math should be accessible using MathPlayer.

**fn2. **
The alt attribute of the rendered graphic is spoken and/or Braillled. As LaTeX is a plain text notation, the notation can be spoken and Brailled by the screen reader directly. This does, of course, assume an understanding of LaTeX notation on the part of the screen reader user.

**fn3. **
In the case of Internet Explorer, screen readers require the MathPlayer plugin to be installed before MathML is rendered (IE does not include native MathML support). By using MSAA, the screen reader can obtain a textual version of the math notation from MathPlayer, which it can then TTS and Braille. Note that MathPlayer also contains built-in TTS functionality (employing MS SAPI) which can be used to speak the math notation without having to employ a screen reader. See [4] for further details. At time of writing, screen reader support for Firefox is via MSAA and a special custom, Firefox-specific IAccessible2 interface (to reveal text attributes and character positions). Math notation is spoken via a screen reader which interrogates these interfaces.

**fn4.**
The alt attribute of the rendered image is filled with a textual version of the math notation. Screen readers can read the alternative text without additional plugins.

## Using Java for Curriculum

### Java Tools for Building Applets for Interactive Demonstration

These tools can be integrated in or used with Moodle Resources

#### Java Sketchpad

http://www.dynamicgeometry.com/JavaSketchpad/About_JavaSketchpad.html, is an applet developed by Key Curriculum Press. The applet has been the focus of quite a bit of discussion and demonstrations and discussions are widely available. An introductory article from the Journal of Online Mathematics can be found here: http://mathdl.maa.org/mathDL/4/?nodeId=508&pa=content&sa=viewDocument. Usage focuses largely on Geometry

#### CabriJava

http://www-cabri.imag.fr/cabrijava/, an applet offered by the University of Cabri, also focuses on interactive geometry. Quite a number of examples employing CabriJava can be found here: http://www.mathsnet.net/cabri/index.html.

#### Descartes

http://descartes.cnice.mec.es/, is an applet developed under the auspices of the Spanish Ministerio de Educacion Politica Social y Diporte. An English introduction can be found here at http://descartes.cnice.mec.es/ingles/index.html. The Ministery has produced an extensive Mathematics curriculum using Descartes, which is available in English and can be freely downloaded and used. Much of what is available is still only in Spanish so anyone interested in doing translation work please post to the Moodle Math Tools forum.

#### Sympl

http://www.sympl.org/, an open source Java application/applet for creating interactive graphs.

### Additional Curricular Use of Applets

- Euclid's Elements - http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
- Tutorials employing applets (applets can be downloaded and used in Moodle) http://www.analyzemath.com/
- Ultrastudio.org - Applet-capable wiki with over 100 educational applets and explaining articles next to them, best covering mathematics (especially complex plane) but also physics and many other topics. CC-BY-SA texts, most of applets open source - http://ultrastudio.org/#Mathematics.

### Applet Tools

- Graphing - http://www.langara.bc.ca/mathstats/resource/GraphExplorer/
- Geometry Construction - http://www.cs.rice.edu/~jwarren/grace/
- GeoGebra - http://www.geogebra.org/
- Physics Applets for Drawing (PAD) - http://www.wku.edu/pads/ These can make interactive activities that can both check for correctness and give guiding feedback. Includes modules for graphs (2D functions), vectors (even in/out and other lines and arrows and bar-graphs), motion analysis, equation recognition and more. Uses don't have to be just for Physics. Math, of course. VectorPAD can be used for placing markers (as points, lines, small pictures, arrows) on a picture, that could be used in almost any subject. They can be incorporating in SCORM packages which can interact with Moodle. There is no Moodle module now (july 2009) for using them directly, but that would add a lot more power (compared to SCORM), like being able to save states, turn on/off feedback, etc.
- GraphApplet 1.05: both calculator and graphapplet - http://www.lundin.info/graphapplet.aspx
- Physlets: large suite of applets about physics but includes advanced graphing too. A time dependent 3D example (Swedish!)

### Java Applet Collections

- Probability and Statistics

- http://www.mste.uiuc.edu/murphy/JavaOverview/default.html
- Math and Physics - http://www.falstad.com/mathphysics.html
- Curves - http://www-groups.dcs.st-and.ac.uk/~history/Java/index.html
- Chaos and Fractals - http://math.bu.edu/DYSYS/applets/index.html
- For sale, but extensive - http://www.cut-the-knot.org/Curriculum/index.shtml

## Mathematics Assessment

Assessment is a key driver for mathematics. There are a number of ways of getting students to answer mathematical questions through Moodle.

- WebWork, see http://webwork.maa.org/wiki/Main_Page http://webwork.math.rochester.edu/docs/docs/, and http://webwork.maa.org/moodle/ is an independent web application for assessing student Math progress, and there is a Moodle Module for interfacing WebWork to Moodle that can be found here: http://moodle.org/mod/data/view.php?d=13&rid=332, though the resources on the WeBWork wiki are probably more current as the code in the Moodle CVS has not been updated for some time.
- STACK provides very mathematical questions for the Moodle quiz module. These are supported by the CAS Maxima. The home page for STACK can be found on http://stack.bham.ac.uk/
- WIRIS quizzes wiris.com/quizzes
- Random variables and graphics
- Automatic evaluation of open answers
- Syntax checking of answers

## See also

Using Moodle forum discussions:

- Best practices for teaching Math(s) in Moodle
- How do you deal with the challenge of writing equations?
- How do you deal with the challenge of drawing graphs and diagrams?
- How do you deal with the challenge of interactive exercises and simulations?
- How can I have a student enter a fraction as an answer?
- What are the components of an exemplary high school Moodle course?