Interactive Mathematics?Probability is a major sub-page of the Alexander Bogomolny?s Cut The Knot! site reviewed elsewhere in MERLOT. It is a collection of approximately 20 classic problems having to do with Probability including the famous Monty Hall problem, the birthday coincidence, and Buffon?s needle. All materials are designed to engage the reader in thoughtful and sometimes interactively experimental solution attempts. Many 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 can be used to provide fun and instructive activities in probability.
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.
Identify Major Learning Goals:
The primary goal is to use examples from the area of probability to help readers experience mathematical topics in a positive and interactive way and to help them learn to appreciate the beauty and fascination of math. 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 the 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 and includes several classic probability examples, misuse of statistics and an application to biology. The textual material is thoroughly and accurately conveyed and the numerous java applets are well designed and accompanied by excellent solution descriptions including extensions and applications in related fields. References to original sources are presented and credits are given to individual puzzle-solvers. 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 Cut the Knot! site.
Potential Effectiveness as a Teaching Tool
The emphasis of this site is on teaching and learning?in this case the use of probability examples to stimulate critical thinking. 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 but primarily written for high school and college audiences.
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 main site has a very simple and effective design with general navigation bars appearing on every page; in the Probability pages, 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. The internal search feature 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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