Estimation
For some reason I have always been intrigued by contests that ask people to estimate how many jelly beans or marbles or whatever are in a large jar. The skill involved in making this type of estimate is so obviously useless (except for success in the contests) that it strikes me as humorous. For a long time I thought that success in these contests was dependent entirely on luck. On further review I have come to the conclusion that skill in this type of estimation can be practiced and learned. Estimation of any quantity or any measurement is a skill that is learned through trial and error. Each time you make an estimate of something and then receive feedback about the accuracy of your estimate, you take a step in learning the skill of estimation in that particular context. The more times you make an estimate in a particular context and then receive feedback, the more skilled you will become in estimation in that particular context. It is important to note that the skill of estimation is not a general skill, but rather, it is a skill that applies only to specific contexts. The person at the amusement park who estimates people's weight is not necessarily very good at estimating their height. The person who can always make an accurate estimate of a person's age may be unable to reliably estimate weights.
Burns (2000) has noted that about half of the time when we use mathematics in daily life, an estimate is all we really need. If this is the case, and if skill in estimation is context specific, then we should be spending a lot of time building and developing our estimation skills in a variety of contexts. How much paint do I need for this job? How much money should I be saving for retirement? What is the most expensive house I can afford? How long will this tank of gasoline last me? Would I be better off to trade my car in for a hybrid? Do I have enough cash for these groceries? How long will it take me to get ready for church? Will I be able to lift or even roll that rock to move it to another part of my garden? Our lives are full of estimates of measurements from the time we wake up in the morning until the time we go to bed at night. As an enlightening activity, try keeping a log of all the times during a day when you use estimation. Write these down and then compare your list with the lists of a few of your colleagues. You will probably be surprised to find that you do a lot of estimation. If you intentionally practice your estimation by attending specifically to the feedback you receive about the accuracy of your estimates, you will gain skill and grow in your ability to estimate. If this is a reliable way for you to improve your estimation skills, then it stands to reason that it is also a reliable way for children in your classroom to improve their estimating skills. Practice-feedback, practice-feedback, practice-feedback. Nothing works better to improve skill in estimation.
If this discussion of estimation sounds different from what you experienced in school, it probably is. Often in school exercises children are asked to provide an "estimate" for a mathematics exercise that lacks context. They are taught to round the numbers of the problem and then perform an arithmetic operation on the rounded numbers. The result of this operation on the rounded numbers is said to be an "estimate." The purpose of doing an estimate in this way is to allow the student to compare the actual computed answer to the estimate to find out if the computed answer is at least close to what was expected. While there is some value in learning to do this, there are several reasons why this procedure does not rise to the level of a "powerful idea." First of all, this procedure is generally practiced on mathematics exercises that lack context. Without a real-world context, mathematics exercises are a bit like a game: they're fine if you like the game, but pointless if you don't. Secondly, the act of rounding numbers in order to produce an estimate just to compare it to a computed answer bears little resemblance to what we do when we estimate in our daily lives. Finally, we rarely need to perform both an estimate and an exact computation in daily life. Most of our daily mathematical needs can be addressed by either an estimate or an exact computation. Children, particularly the more academically capable children, seem to have an innate sense that estimation exercises of the sort we're discussing here have little value. I have observed repeatedly that such students tend to avoid doing what we ask them to do with these exercises. Rather than produce an estimate before computing an exact answer, these students tend to compute their exact answer first and then go back and produce their "estimate." These students tend to be uncomfortable with inexact answers, which is how they perceive their estimates.
Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.
