Estimation and Functions
The emphasis thus far has been on solving problems by calculating an exact answer. The topic now shifts to investigate how well people can estimate answers to word problems. Many situations in our daily lives require an estimate: Do I have enough cash to pay for these books? How much paint do I need for this room? How long will it take me to drive to the dentist's office? ( Sowder, 1992)
There are a number of reasons why it is important to provide reasonable estimates to problems, and estimation has been receiving increased emphasis in mathematics education. One reason estimation is important is that people often don't know how to calculate an exact answer to a problem. Second, even when they know a correct procedure, they may not take the time to use it if an approximate answer is sufficient. For example, a person may estimate how long it will take to reach a destination without calculating an exact answer. Third, estimation provides a means to evaluate the reasonableness of an answer following calculation ( De Corte & Somers, 1982).
Estimation can also provide teachers or researchers with a measure of how well students understand a procedure. A dramatic example of how students may learn a procedure by rote with little conceptual understanding is illustrated by performance on the National Assessment of Educational Progress test ( Carpenter, Corbitt, Kepner, Lindquist, & Reys, 1980). When asked to estimate the answer to the fraction addition problem 12/13 + 7/8, 7% of the 13-year-olds selected the response 1, 24% selected the correct answer 2, 28% selected 19, 27% selected 21, and 14% selected I don't know. Carpenter and his colleagues suggested that because students actually did better on questions that required an exact answer, many students had little