CALUMATH

CALUMATH is a web-based program that facilitates the construction of interactive, educational web pages involving mathematics. Using CALUMATH, web pages suitable for use in K-12 and college level classrooms can be constructed. Pages typically include graphs, animations, and the web tools, such as boxes, drop-down menus, and buttons, to allow students to interact with them.

CALUMATH is free software: see the license information at the left for full details. Educators and students are encouraged to use and share CALUMATH web pages.

To see the types of pages that can be constructed using CALUMATH, click on the Classroom Pages button on the left or the Features link at the top of this page. To read more about CALUMATH, click on the links at the left.

What is CALUMATH?

The purpose of CALUMATH is to create high quality, interactive, mathematics web pages for use in classrooms and at home.

CALUMATH is free software designed for the creation of interactive web pages involving mathematics. CALUMATH pages are written entirely in HTML, which is the standard markup language for web pages, and JavaScript, a well-known programming language native to web browsers that allows pages to be dynamic. Web pages constructed using CALUMATH can display graphs or animations and contain all of the items commonly found in web pages, such as text boxes, drop down menus, and buttons that allow the user to provide input, make selections, manipulate graphs, answer questions, and interact with the pages in a meaningful way. In response to user interaction, items on the page can appear or disappear, graphs can be drawn or modified, new windows opened, new information displayed, or contrasting scenarios presented. Correct user answers can be challenged with a new scenario to see if the answer was the result of a memorized algorithm. Incorrect user responses can lead to activities that help the user see their response as problematic in terms of other knowledge the user possesses.

The interactive CALUMATH web pages are constructed using the CALUMATH Page Maker, a web page interface designed for the easy construction of CALUMATH pages. The CALUMATH Page Maker main menu is a table listing all of the mathematical and web objects that can be created using CALUMATH. When a page author selects an object, a screen appears with boxes and menus pertaining to the construction of the object. The author selects the properties of the particular object that she wants, and clicks a button to finish. This returns her to the main menu where the process can be repeated. Using this procedure, functions and random numbers can be defined, graphs created, points plotted, and tangent lines drawn. In the same manner, titles, paragraphs, tables, menus, text boxes, and buttons can be created. The actions that occur when a user clicks on a button or graph are also created in a similar fashion. No knowledge of HTML or JavaScript is required.

The CALUMATH Page Maker can load any saved CALUMATH web page, regardless of who authored it. When this is done and the Edit button is clicked, a window opens that reveals the structure of the page and lists all the items created. This gives someone who did not construct the page the ability to modify it and save it to their own web site.

CALUMATH is not tied to a particular mathematical content or grade level and can be employed at any level of the K-12 school curriculum and at the junior college and university levels. CALUMATH pages employ standard HTML and JavaScript, ensuring that they will not become obsolete as technology changes. CALUMATH is open-source software and is licensed under the GNU license.

Everything in CALUMATH runs in a web browser, therefore you do not need to install anything on your computer. You can download the entire CALUMATH web site and save it to your hard drive and open CALUMATH web pages by clicking on the files; there is nothing to install. When you interact with CALUMATH web pages on the internet, all calculations are done on your computer, no further connection with a web site is necessary. This means that instructors can create CALUMATH pages and place them on their web sites just as they would place any other web page there. In particular, you do not need to configure your web server in order to host CALUMATH pages.

The five parts to CALUMATH:

1. There are the CALUMATH web pages themselves that have been constructed. Click on the button at the left to see pages used in College Algebra at Purdue University Calumet. Samples of pages showing the great variety of CALUMATH capabilities can be seen by clicking the Features link above.
2. There is a suite of College Algebra quiz questions that are integrated with the Blackboard course management system. A student opens the quiz in Blackboard, however the questions displayed contain CALUMATH web pages that the student can manipulate. In addition to asking routine problems, CALUMATH pages can require students to draw or drag graphs, or define functions that possess requested properties. Each quiz is automatically graded by Blackboard when the student submits the quiz.
3. CALUMATH contains a small computer algebra system that performs symbolic calculations.
4. The CALUMATH Page Maker is the heart of the CALUMATH system. This user-friendly web page is used to construct interactive CALUMATH web pages. It also allows you to modify CALUMATH pages created by others. To view the page, click on the CALUMATH Page Maker link at the top of the page.
5. Behind the scenes, the CALUMATH program is quietly working in the background. The CALUMATH program is written in JavaScript, so it is native to web browsers and allows matematics and web tools to be combined into interactive web pages in a seamless manner.

Web Browser Requirements

CALUMATH has been carefully designed to be compatible with all major web browsers, both recent and older versions. CALUMATH pages should work correctly in the following browsers:

1. Internet Explorer: Versions 5.5 and later.
2. Firefox: Versions 1.0 and later.
3. Opera: Versions 7.5 and later.
4. Safari: Versions 3.0 and later.
5. Googe Chrome: recent versions.

Browser Warnings:

Never Use the Back or Forward button of your browser to navigate through CALUMATH pages.

Pop-up windows are an integral part of CALUMATH. Your browser must allow pop-up windows for CALUMATH to function properly.

If you have a slow internet connection, the first time you open an interactive CALUMATH page, it may take about a minute to load. After that, each page should load very quickly.

Constructing CALUMATH pages is done by using the CALUMATH Page Maker. While learning how to use the Page Maker, it is recommended that you use the Firefox web browser to open the CALUMATH Page Maker.

Philosophy:

CALUMATH was designed to meet particular objectives:

1. CALUMATH is designed to be available to the widest possible audience, including all grade levels K-16. To meet this objective, CALUMATH is web-based, open source, and does not rely on plug-ins.
2. CALUMATH is designed for mathematics education and produces fully functional web pages. The page designer controls the functionality that the student can bring to a given task and the responses the page makes to user interactions. A page designer can display or not display the equation of a graph that is presented, can reveal or hide the scaling of axes in a graph, allow or preclude the student from ascertaining exact coordinates of points on the graph, and include or not include the functionality to draw tangents to a curve at a given point. This allows the page designer to take students outside of their comfort zone by not giving them the tools they would normally rely on in a given situation, thus forcing them to contemplate a scenario in more than one way. Equally importantly, the page designer chooses how students’ responses are to be evaluated by the page; for example, if a student drags a graph, the page can determine the new position and provide the student with questions dealing specifically with the new position. This cycle of capturing student’s responses or interactions with the page in order to provide new questions or scenarios is one of the distinguishing features of CALUMATH. In addition, since CALUMATH pages are fully functional web pages, CALUMATH pages can respond to the user in many ways, such as displaying a paragraph analyzing what the student did, graphing arrows that point out features to which the student should pay attention, opening a new window containing new information or graphs, or displaying buttons that provide a graph with new functionality that the student can now employ.
3. CALUMATH pages can be continually improved by the mathematics and mathematics education communities, leading to cycles of creation, evaluation, improvement, and adaptation. A previously constructed CALUMATH page can be opened by anyone using the CALUMATH Page Maker; the structure of the page will be revealed and modifications can be made. Changes can be in response to the latest research in mathematics education, assessment results, or simply because a new instructor has a fresh perspective. Once the changes are made, the instructor can post the page on their own web site, share it with their peers, the original page author, and the mathematics community in general.

License:

Copyright 2003-2011 Purdue University.

Developed by: Peter Turbek, Department of Mathematics, Computer Science, and Statistics, Purdue University Calumet.

CALUMATH is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Table of Contents

• GNU GENERAL PUBLIC LICENSE
• • Preamble
  • TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
  • How to Apply These Terms to Your New Programs

---

GNU GENERAL PUBLIC LICENSE

Version 2, June 1991

Copyright (C) 1989, 1991 Free Software Foundation, Inc.  
51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

Preamble

The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Lesser General Public License instead.) You can apply it to your programs, too.

When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things.

To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it.

For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.

We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software.

Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations.

Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all.

The precise terms and conditions for copying, distribution and modification follow.

TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you".

Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does.

1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program.

You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee.

2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions:

a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change.

b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License.

c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.)

These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it.

Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program.

In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License.

3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following:

a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,

b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,

c) Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.)

The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable.

If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code.

4. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.

5. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it.

6. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License.

7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program.

If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances.

It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice.

This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License.

8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License.

9. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation.

10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally.

NO WARRANTY

11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found.

one line to give the program's name and an idea of what it does.
Copyright (C) yyyy  name of author

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

Also add information on how to contact you by electronic and paper mail.

If the program is interactive, make it output a short notice like this when it starts in an interactive mode:

Gnomovision version 69, Copyright (C) year name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details
type `show w'.  This is free software, and you are welcome
to redistribute it under certain conditions; type `show c' 
for details.

The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program.

You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names:

Yoyodyne, Inc., hereby disclaims all copyright
interest in the program `Gnomovision'
(which makes passes at compilers) written 
by James Hacker.

signature of Ty Coon, 1 April 1989
Ty Coon, President of Vice

This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License.