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Dynamic Math on the Web
Design Science WebEQ™ Developers Suite is a comprehensive Java toolkit for building web pages that include dynamic math. The world's leading e-learning companies, content developers and education portals are implementing WebEQ components to create web-based learning environments that help educators engage their students in math and science on the web.
Author Math for the Web
WebEQ provides a full suite of tools for authoring math on the web.
WebEQ also includes the WebEQ Publisher which allows you to translate either MathML or WebTeX (a subset of the TeX equation language) into the same set of output formats supported by the WebEQ Editor.
Mathematical editor
Simboli matematici
Equazioni
WebEQ Editor is a point-click equation editor that is used to graphically compose equations. By using templates and symbol palettes from a customizable toolbar, you build up an equation using the mouse and the keyboard. WebEQ Editor works much like our other math editor products, MathType and the Equation Editor in Microsoft Office, but is specifically designed for working with equations encoded in MathML, the Web standard for representing mathematical expressions. WebEQ Editor can save equations as MathML markup, as images, or as applet tags for displaying the equations in a browser using the WebEQ Viewer Control.
WebEQ Editor features:
| • | Intuitive graphical editing of equations |
| - New support for prescripts and tensor indices | |
| - Better handling of multi-line equations | |
| - Expanded keyboard shortcuts for MathType compatibility | |
| • | Direct control over MathML structure |
| • | Easy control of style and display properties |
| - Set font properties per token or per expression | |
| • | Large collection of symbols |
| - Enter symbols by MathML name or Unicode number | |
| - Updated for Unicode 4 compatibility | |
| • | Customizable toolbar |
| - Support for multi-character buttons | |
| • | Sophisticated MathML export options |
| - Control namespaces, declarations, and white space handling via preferences | |
| - Set default clipboard export preferences for streamlined workflow | |
| • | Generate JPEG and PNG images, MathML or Viewer Control applet tags |
| • | Support for authoring interactive math equations |
| • | Expanded editor preferences, including new support for chemistry notation |
WebEQ Publisher converts equations and documents into a variety of formats. It is most often used to process an entire HTML page containing many equations, though it can also be used to convert one equation at a time. The Publisher understands equations written in both MathML and WebTeX (a subset of the TeX equation language) and it can generate the same formats as the Editor -- MathML, images, and applet tags.
WebEQ Publisher features:
| • | Convert math markup to Web-ready formats |
| • | Process markup in Solutions Library JavaScript code |
| • | Read entire documents or cut-and-paste markup to be converted |
| • | Send output to the screen for cutting-and-pasting or write files |
| • | Process WebTeX and MathML |
| • | Generate JPEG and PNG images, MathML or Viewer Control applet tags |
| • | Generate markup for Mozilla, MathPlayer, and cross-browser stylesheets |
Interactive web pages can be easily created by using the WebEQ Controls, which you can place on your web pages to interact with the reader. For example, the WebEQ Input Control provides a way for students to easily enter mathematical equations. After the student enters an equation, you can use WebEQ's Graph Control to graph it or the Evaluation Control to compare it with the correct answer.
To make creating interactive math pages even easier, WebEQ 3.5 introduces a Solutions Library consisting of HTML template files, sample pages and JavaScript libraries containing already written and debugged code for common operations. This lets you focus on the logic behind your interactive math page while our code takes care of the implementation details.
The WebEQ Controls include:
| • | Input Control to gather input from the student |
| • | Viewer Control to display equations |
| • | Graph Control to graph equations |
| • | Evaluation Control to evaluate and compare equations |
The Solutions Library, an important component of WebEQ Developers Suite, is a collection of JavaScript libraries and web page templates that help you create dynamic and engaging web pages. The JavaScript libraries provide a rich set of methods for creating online quizzes, interactive graphs, dynamic demonstrations, and online step-by-step expository material. The web page templates also illustrate the use of the WebEQ Controls for common tasks, such as drawing a graph of a reader-supplied equation.
The WebEQ Solutions Library also contains sample pages that were created by customizing and extending one or more of the page templates. Unlike the generic page templates, the sample pages each deal with a specific mathematical topic. Together with the tutorials, the sample pages provide you with a road map for constructing high-quality finished pages from the Solutions Library's generic templates and high-level building blocks.
Here are some of the samples included with the WebEQ Developers Suite. Note that the Solutions Library requires a browser environment that supports Java\JavaScript communication and a relatively full implementation of JavaScript (including bindings to the W3C DOM). In order to view the live examples, it is recommended that only browsers which meet these requirements be used - currently, these are Internet Explorer under Windows and Mozilla\Netscape under Windows and Linux.
Quiz
The WebEQ Solutions Library contains several dynamic math logic modules to facilitate the creation of online tests and quizzes. A test can contain any number of questions drawn from four question types: multiple choice, true/false, matching, and free-form equation short answer. Tests can be either unscored or self-scoring, giving readers immediate feedback about what questions they answered correctly or incorrectly.
Animation
The WebEQ Solutions Library provides two "animator" objects that control moving items on a page along paths defined by equations, PathAnimator and FunctionAnimator. PathAnimator accepts two mathematical functions that describe the position of the object being animated as a function of time, one for x and one for y, allowing very general kinds of animation paths. FunctionAnimator is simpler. It accepts a single function of x and y and moves an object along its graph.
Step-by-Step
The WebEQ Solutions Library provides two dynamic math logic modules for step-by-step exposition. The Single-path Step-by-step module displays a single sequence of steps. The second module, the Multi-path Step-by-step, allows authors to create a tree of steps, using reader input to choose the next step at each stage. Each step consists of one or more equations and other expository text, together with optional help or explanatory text. A typical step-by-step sequence might be the steps in the solution of an algebra problem.
The Input Control is an equation editor applet that runs in a web page. It gives readers a way to enter mathematical expressions in a web page, much as the text entry controls and buttons in typical HTML forms give users a way to enter other kinds of information. Typically, an equation entered via the Input Control is passed as MathML to either JavaScript code embedded in the same web page or sent to your web server to be processed there.
Input Control features:
| • | Serves as an embedded equation editor in Web pages |
| • | Can be used to send equations to a Web server |
| • | Cross-platform support for many Web browsers |
| • | Customizable toolbar |
| • | New applet parameters for chemistry notation mode |
| • | Extensive API for manipulating properties and equations via JavaScript |
The WebEQ Viewer Control is an applet that runs in a web browser to display interactive equations. By using the Viewer Control, authors can create highly engaging and educational Web pages.
Viewer Control features:
| • | Cross-platform display of MathML expressions in Web browsers |
| • | - Corrects for client screen resolution |
| • | Automatic line breaking for long equations |
| • | Extensive API for manipulating expressions via JavaScript |
The WebEQ Graph Control is a scriptable applet for displaying graphs in a web browser. The Graph Control can plot real-valued functions and inequalities encoded in MathML. Multiple equations can be graphed simultaneously.
Graph Control features:
| • | Graphs real-valued functions and inequalities |
| • | Displays multiple equations |
| • | Customizable appearance and graphing options |
| • | Extensive API for manipulating properties and equations via JavaScript |
The WebEQ Evaluation Control is an applet that provides MathML-based computation services. Unlike the other WebEQ Controls, the Evaluation Control doesn't display anything on the screen. Instead, it is invoked from JavaScript to evaluate and compare MathML expressions.
A typical use of the Evaluation Control is checking answers in online quizzes. Most online quiz systems require multiple choice questions, or other question types that are easily checked by computer. Open-ended questions where a student must supply an answer from scratch are not possible with such systems, since determining when a free-form mathematical expression is equivalent to a given answer is difficult. The Evaluation Control, however, utilizes sophisticated mathematical algorithms to determine when two expressions are equivalent.
For example, a quiz page might contain a question whose answer is x + 2. The student enters his or her answer using the Input Control, and the Evaluation Control checks the answer:
| If the student entered: | Evaluation Control analysis: | |
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Equivalent to x + 2. |
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The additional formatting (extra spaces) is ignored. Equivalent to x + 2. |
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Equivalent to x + 2. |
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This not equivalent to x + 2. |
Evaluation and Comparison Controls features:
| • | Evaluates MathML real-valued expressions in several variables |
| • | Tests two expressions for equality |
| • | Extensive API for use from JavaScript |
| • | Incorporate static math into cross-platform pages using high-level JavaScript equation wrappers |
| • | Incorporate WebEQ Controls into cross-platform pages using high-level JavaScript control wrappers |
| • | JavaScript logic modules simplify mathematical animations, step-by-step exposition, and quizzes |
| • | Over 20 templates and sample files for common interactive math tasks |