# Learning about Area by Working with Building Plans

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• 1 University of Northern Iowa, Cedar Falls, IA 50614-0607
• | 2 Malcolm Price Laboratory School, University of Northern Iowa, Cedar Falls, IA 50613

Area measurement is one of the most difficult topics in measurement that teachers cover in the K–6 curriculum. Several authors (Nitabach and Lehrer 1996; Outhred and Mitchelmore 2000) have noted that students' difficulties with area stem from an overreliance on the area formula, with little accompanying understanding of its conceptual basis. Students in the early elementary grades measure objects directly with instruments such as rulers, and in this sense, they see the units that they are “counting.” Calculating the area of a rectangle by means of the a = l × w formula, however, involves a shift in thinking, because area is derived from measurements that have been obtained with a ruler, rather than by directly counting units. When using the formula, students do not have to think about units covering space or an object. When designing a unit of instruction on area measurement, we began the process with this question: How could we help students see how direct measurement (counting units) is connected to indirect (a = l × w) measurement? Another way to frame the question is this: How can students better understand the conceptual basis of area measurement?

## Footnotes

ELANA JORAM is interested in elementary school and middle school students' understanding of measurement and algebra.

VICKI OLESON is interested in supporting the development of number sense in all areas of the middle school mathematics curriculum.

## Contributor Notes

Mathematics Teaching in the Middle School
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