Eye Opener is a sub-page of the Alexander Bogomolny?s Cut The Knot! site reviewed elsewhere in MERLOT. It is a collection of approximately 40 interactive java applets that help to solve or prove mathematical problems by using a visual approach. Please see these related reviews:
These applets can be used to introduce students to a variety of mathematical problem solving techniques.
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 systems and browsers is highly variable with particular difficulties on older MACs and older versions of browsers. MacRuntimeJava 2.1 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 of the main Cut the Knot site is 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. The examples on this particular page use a visual approach to problem solving.
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?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. This page opens with a visual paradox regarding the area of a rectangle where moving shaded areas appears to show that two algebraically different areas are the same. A simple algebra/factoring proof shows why they are not the same. Among the 42 applets some other notable examples are: Chocolate bars ? how many moves does it take to break a rectangle into constituent squares? (algebra proofs); Flipping pancakes ? rearranging a stack of pancakes by order of size ? somewhat reminiscent of the classic Tower of Hanoi type problem (discussion of permutations); Frogs and Toads ? sliding board pieces in either two or three dimensions ? plus a link to an internet version called traffic.
All of the applets are visually appealing and allow various parameters to be changed. The story settings are attention catching and include significant mathematical explanations.
Chocolate applet has difficulties with MAC OS and Explorer
Potential Effectiveness as a Teaching Tool
The emphasis of this site is on teaching and learning and 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 section of Cut-the-Knot contains a wealth of educationally effective materials.
Ease of Use for Both Students and Faculty
The pages have a very simple and effective design with general navigation bars appearing on every 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.
Note comments above concerning difficulties with some combinations of older browsers and Mac operating systems.
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