Interactive Mathematics?Games & Puzzles is a major sub-page of the Alexander Bogomolny?s Cut The Knot! site reviewed elsewhere in MERLOT. It is a collection of approximately sixty miscellaneous games and puzzles including some well-known puzzles such as the Towers of Hanoi, the game of Nim, Cryptarithms, and Magic Squares along with a number of lesser-known but nonetheless intriguing puzzles that are designed to engage the reader in thoughtful and sometimes interactively experimental solution attempts. Most of the presentations are accompanied by well-written java applets that the author uses in an attempt to effectively draw the reader/user into exploring possible approaches; multiple solutions from various sources are often included afterwards. In addition, there is an excellent collection of links to other math resources with accompanying annotations. This site is highly interactive and one can sense the author?s fascination with mathematics and his desire to convey this to his readers.
This is a resource collection of textual materials along with a multitude of interactive java applets.
This material should be used to challenge the minds of students while simultaneously demonstrating to them that mathematics can be fun
A basic browser is all that is required to view the primarily textual material; a java-enabled browser is needed for the interactive java applets. The ability of the applets to run on different operating systems and browsers is highly variable with particular difficulties on older Macs and older versions of browsers. MacRuntimeJava2.1 may need to be installed independently of the older Mac OS and there still seemed to be difficulties with Explorer 5. Some failures resulted in particularly nasty system freezes. This is particularly true of this Games and Puzzles portion of the web site. For example,
Wythoff?s Nim does not run on Explorer 5 but does on Netscape 4.79; Towers of Hanoi does not run on either.
Identify Major Learning Goals:
The primary goal is to help readers experience mathematical games and puzzles in a positive and interactive way by simply exploring. This may help them learn to appreciate the beauty and fascination of math and to delve deeper into the explanations behind the games. In addition, in the author?s words, ?Learning starts from wondering, and another purpose of this site is to serve as a resource for things, simple but curious, related to Mathematics.?
Target Student Population:
The materials here cover a range of topics and ability-levels; most of topics are at high school and/or college levels.
Prerequisite Knowledge or Skills:
Prerequisite skills vary from basic math knowledge to college-level math knowledge, depending on the topic. All of the material is presented in an accessible manner and the many java applets invite exploration and discovery.
The content here is of the highest quality?the textual material is thoroughly and accurately conveyed and the numerous java applets are well designed and eye-catching. They are accompanied by a short history of the game and excellent solution descriptions including extensions and applications in related fields. References to original sources are presented and credits are given to individual puzzle-solvers. References for further study and related internet resources are also included. The author is an accomplished educator and software developer and has combined these talents to create an outstanding mathematical resource. He is an invited author/contributor on the Mathematical Association of America?s web site and authors a monthly column entitled ?Cut the Knot!? An archive of the column is included on the main Cut the Knot! site.
Suitable for many different levels of user; some material is beyond the general user and requires advanced math knowledge.
Potential Effectiveness as a Teaching Tool
Games and puzzles are an excellent way to attract and hold the attention of students but the main emphasis of this site is on the teaching and learning that can occur through playing those games. The author makes every effort to engage the student/reader in the exploration and discovery process; the level of interactivity is outstanding. Thoughtful solutions are presented and the reader is guided to an analytical understanding of the underlying mathematical principles involved. In some instances alternative solutions are presented; in others, applications to other mathematical fields are described. Altogether, this site contains a wealth of educationally effective materials. In addition, there is an annotated listing of other math resources on the internet that is quite excellent and potentially helpful to the reader. Suitable for many different levels of user - some material is beyond the general user and requires college-level math knowledge. The banner ads at the top of each page and the shopping links in the sidebar are relatively unobtrusive.
Ease of Use for Both Students and Faculty
The entire site has a very simple and effective design with general navigation bars appearing on every page; on the Games/Puzzles page, the reader is always just a click away from the other site features. The textual materials are interspersed with numerous cross-links that may enrich the reader?s experience. Features of the main site include an internal search feature that is quick and easy to use and comes with a thorough set of instructions and general searching tips. Several areas allow for user interaction, including a guest-book that permits posting and reading of user comments. The CTK Exchange is a moderated forum where users may ask math-related questions and interact with other forum participants. The Glossary feature is good for readers with limited math knowledge and is very nicely written.
Note comments above concerning difficulties with some combinations of older browsers and Mac operating systems.
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