Requiring Proof of Understanding

Abstract

The American School is often criticized for failing to help children develop study habits which enable them to do independent, logical thinking. Teachers of a given grade are inclined to blame instructors of the preceding grade for the child's inability to grapple with simple principles of logic and independence of thought. Complaints concerning the child's lack of ability to solve problems dealing with quantitative situations come from many quarters. Often teachers make the remark: “My children do fairly well with the arithmetical computation involved in solving examples but t hey have much difficulty with the solution of ‘verbal problems’ in arithmetic.” The expression “verbal problems” is generally employed to refer to the word description of a quantitative stituation for which the solution is not indicated. It is to be regretted that arithmetical verbal problems are not solved with less difficulty; however, it is equally regrettable that children do not understand what is involved in the various processes and operations indicated by use of abstract symbols. The fact is that many teachers are not aware of what is actually involved in the several arithmetical operations and processes they attempt to teach. Several practices which may help children to understand better why they do certain things in arithmetic, as well as help them to see what is involved in the fundamental operations performed with the abstract symbols, will be indicated.