Measurement concepts are difficult for students of all ages (including adults). Some specific difficulties have been well documented by researchers:
Given these difficulties, math teachers need to use a variety of tools and teaching aides to help students develop skills and meaning relative to measurement taks. Tandi Clausen-May (UK) has recently posted some Powerpoint demonstrations that use dynamic measurement visuals to help students.
- Distinguishing between linear and area units in given situations
- Realizing the effect of changes in linear dimensions on area
- Using the correct vocabulary--perimeter vs. area vs. circumference
- Understanding the concept of area itself, separate from the use of a magical formula
The best of her work includes two visual demonstrations, both recently described in her article (see reference below). First, using an innovative approach I have not seen previously, Tandi uses moving points on circles and hexagons to illustrate why the value of pi is greater than 3. Second, Tandi explains why A=(pi)r2 is the appropriate formula for calculating the area of a circle by dynamically unfolding a "beaded" circle into a triangle. These demonstrations are good, innovative, and useful.
Less useful are her demonstrations as to either why A = lw is the formula for calculating the area of a rectangle or how this formula relates to the calculation of the area of a triangle or parallelogram.
And my thanks to Janet Mock (WWU) for connecting me with Tandi's ideas.
Source: T. Clausen-May's "Going Round in Circles," Micromath, Nov. 2006, pp. 42-44