A Study on the Teaching of 'Intensive Quantity' in Elementary-school-Mathematics

摘要

Quantity is classified into extensive quantity and intensive quantity. The length, magnitude, and weight are typical examples of the extensive quantity. The population density and average speed are examples of the intensive quantity. Teaching of intensive quantity in the fifth grade of elementary schools has been investigated with particular reference to the presentation materials and procedures of intensive quantity. Our findings include the following：1. Children are able to understand intensive quantity as one quantity, but not as a set of two extensive quantities, which indicates that they have already had the perspective of representing intensive quantity by numbers. Comparison aIone does not help pupils grasp intensive quantity, although Comparison approach is a common practice in classroom situation.2. We need to teach children to be aware of representing explicitly the density or speed by the concept of "average".3. If we are to help children understand the meaning of representing intensive quantity by numbers, we need to teach not only a common intensive quantity but also an inverse intensive quantity：children need to observe that the greater a numerical value is, the higher a common intensive quantity is and the lower an inverse intensive quantity is. This observation is to make sure that they fully understand that there exists intensive quantity as well as extensive quantity.