It is long been my opinion that learning only 80% of the material presented in a given class almost certainly assures failure in a follow-on class that requires this material as a prerequisite. For example if you learn only 80% of math 101 you will have great trouble in passing math 102.
Math builds on itself.
It you multiply 386 times 497, you have to do around 36 operations (addition, multiplication, carry, and so forth) correctly in order to get the correct answer. With 98% accuracy in these operations you have about a 50% chance of getting the correct answer, (.98)**36.
I recently heard of a study attemping to document this. This study showed that if you get a C in math 101 you have only a 25% chance of getting a C or better in math 102.
If anyone knows of a study like this I would appreciate hearing about it. Also if you have any data that could be used in this type of analysis I could use the help.
Ward Woodruff AMATH Division Woodruff Consulting, Inc.