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Understanding Basic Concepts in Spatial Measurement

Photo of a young girl using a ruler on a piece of paper.

To help prevent students from having misconceptions about measurement, Jack Smith and his colleagues at Michigan State University (MSU) are analyzing curricula that elementary school teachers and children currently use in schools to learn spatial measurement (length, area and volume).

Credit: Thinkstock


a rectangle whose perperimeter is surrounded with 18 square tiles.

The following example illustrates a misconception when determining the perimeter of a 2-D shape: A student is asked to find the perimeter (the length of the continuous line forming the boundary of a closed geometric figure) of this 2-D rectangle. The student is told that the perimeter of the rectangle can be found by surrounding the rectangle with square tiles, including tiles at each of the four corners. The student claims that the perimeter of the rectangle is 22 tiles. However, the actual perimeter is 18 tiles. The student is not distinguishing the edges of the tiles as length units from the square tiles that are area units--the ability to visualize the difference is crucial in understanding what one is measuring.

Credit: Courtesy of Jack Smith, MSU

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