APPLICATION OF COGNITIVE CONDENSATION |
The following concept map for the Average Rate and Rate of Change illustrates the power of cognitive condensation.
This map clearly shows that one can learn a tremendous amount of science, mathematics, and technology by judiciously organizing knowledge using causal, logical, and functional relationships. This particular map is one of the best implementation of "less is more" of Project 2061.
Please see how this map clearly defines "the average rate" and "the rate of change" in a way that does not permit someone to confuse them again.
We are particularly pleased with ourselves for having used this map, two years in the row, to teach effectively the concept of average rate of change and of rate of change to 11th grade students of the Summer Science Institute (SSI) at the Timbuktu Academy.
The following three pages describing this concept map are self-explanatory. After the students grasped the content of these pages, we also taught them the "sum," "product," and "the ratio rules" for calculating rates of change. Of course, extensive exercises were done in class and assigned as graded homework to ensure the mastery of the concepts.
It was a delight to then see them master uniformly varied and other forms of motions using the above concepts. We told them later above derivatives!
NOTE: Average rate of change and rate of change are not the same.