A true story
	About these Web Pages      This project started as a purely academic computer science problem of writing an applet that would visualize the multiplication table. As soon as it was done, we realized its potential as a teaching tool for elementary education in math. With the rapidly increasing popularity of the Internet this tool should be easily accessible in schools and homes for helping teachers and parents to teach the multiplication table. To make it even more accessible, we have decided to write it in a form of standing alone software in Visual Basic. This version can be used on any PC with Windows 95 or Windows NT.      Finally we have decided to distribute all this software freely for noncommercial educational purposes to all who want to better our children's understanding of elementary math. This means that beside using the multiplication table applet (MT Applet) straight from these pages via Internet, you can download all these pages and use them with the help of a browser on your computer. You can also download the Visual Basic version of the multiplication table and use it within Windows 95 or Windows NT. Full information about downloading and installation is provided in our Download page.        Edward Kluk, Professor Emeritus Dpt. of Natural Sciences    Michael Frank, Dpt. of Math & Computer Science    Mats Mangru, Dpt. of Math & Computer Science	It happened about 30 years ago in a different country on a different continent. One day I received a phone call from the second grade math teacher who taught my daughter Dorota. She was not satisfied with Dorota's mastering of the multiplication table. "Is she giving you incorrect answers?" I asked, "Her answers are correct, but they are not instant, she waits one or two seconds and than gives an answer." she replied. "Well" I said "this is not Dorota's fault. I should be blamed for it, because I have forbidden Dorota to memorize the multiplication table. Telling a child to memorize multiplication table sends a wrong message suggesting that all of math can be memorized instead of understood. Important in math learning is understanding structures and relationships between them. In the long run, memorizing math leads to a catastrophe because math is about formulating and solving problems, not about recitation.". "So," I continued "instead of memorizing that 3 x 7 = 21 you should think about it as 3 x 7 = 7 + 7 + 7 = 14 + 7 = 21. This approach demands mastery in addition from a child, but it
	clearly shows a relationship between addition and multiplication. Consequently you can find 6 x 7 = 3 x 7 + 3 x 7 = 21 + 21 = 42. Or 9 x 7 = 10 x 7 - 7 = 70 - 7 = 63. This is a creative way to learn multiplication table that teaches children how math truly works.". The teacher agreed with me and there were no more problems with math for a quite a while.      One day,five years later, Dorota came from her school a little bit agitated. She showed me her math notebook and said "Look, my teacher marked all my last homework problems with inequalities as solved incorrectly. But all solutions there are correct." Indeed I had found all these solutions correct. I visited with the seventh grade math teacher and she admitted her mistake. After all everybody may have a bad day. Correcting hundreds of homework problems is a hard work and after a while one can easily lose concentration.      This event assured my wife and myself that learning math by understanding as opposed to memorizing, pays off. Dorota had never any problems with her math or related classes in High School or University. options