Math think-alouds: Build essential daily math skills through verbal problem solving

Instructor, April, 2002 by Robyn Silbey

Close your eyes. Think about the steps you go through to group students for an activity. How do you determine the number of groups and the number of students in each group? What mental math skills do you use to figure it our? Verbalizing your solution process-or sharing your thoughts with students so that they can effectively crawl inside your brain--is what's known as a "think-aloud." Jeffrey Wilhelm writes, "Think-alouds make invisible mental processes visible to children." (See "Think-Alouds Boost Reading Comprehension," Instructor, Nov./Dec. 2001, page 26.) Math think-alouds engage students and help them make their way step-by-step through a solution process, reasoning right along with you. Best of all, math think-alouds can be used quite effectively both in school and at home.

Research has proved that young children can comprehend spoken words and ideas before their speech is fully developed. Similarly, your students can understand a more complex or difficult solution process than they can execute independently. By thinking aloud, you share a thought process that may be too sophisticated for them to come up with on their own, but one which they are able to comprehend by hearing. Once such a solution is learned and practiced by children, they can begin to apply it independently to other math problems they encounter.

THINK-ALOODS IN SCHOOL

Here are several math think-alouds that you can share with your students during the course of the school day.

* Find elapsed time

* Work with money

* Estimate measurements

* Interpret classroom data (lunch count, weather)

Find Elapsed Time

Think aloud about how many minutes until the class needs to be ready for their next class, a special activity such as an assembly or guest speaker, or lunch. Even if your students have not yet learned how to calculate elapsed time, they should be familiar with the concept of time and the terms used to measure it. (If you are teaching primary grades, limit the elapsed time think-alouds to either hours or minutes, rather than both, so that your thought processes are within students' reach.)

You might say, "I know lunchtime is at 12:00. It's 11:40 now. I can count by fives to see how many minutes until lunchtime: 11:45, 11:50, 11:55, 12:00. I counted by five minutes four times, so that's 20 minutes in all. Lunch is in 20 minutes."

Other elapsed time think-alouds include finding:

* The number of minutes or hours since the school day began

* The number of minutes in a class

* The total number of hours spent at school in a day

After several elapsed-time think-alouds, some students will begin to pick up the process. Ask: How does such a skill help us? How often might we use it?

Work With Money

Think aloud about how much money will be collected if seven cartons of milk are ordered for 50[cents] each. You may begin by saying, "One carton of milk is 50[cents] If I skip-count by 50[cents] seven times, I can find the total cost: 50[cents], $1.00, $1.50, $2.00, $2.50, $3.00, $3.50. So 7 cartons of milk at 50[cents] each is $3.50." You may wish to emphasize that there is more than one way to arrive at the total cost by adding, "Let me check to make sure that's right. I'll use a different strategy this time. If one carton of milk costs 50[cents], then two cartons cost $1.00. I have three groups of two cartons, that's $3.00. And 50[cents] more for the seventh carton would make a total of $3.50." Invite students to offer additional strategies, perhaps involving multiplication, repeated addition, or other mental math.

Estimate Measurements

Older students may benefit from hearing you think aloud about how to arrange their papers in a bulletin board display. You may say, "We want to display your work on the bulletin board. Each paper is about 9 inches wide and 12 inches long. We will also need space between each paper. The bulletin board is about 30 inches wide. I can fit 7 papers in a row--that's 63 inches--with plenty of space between each paper. The board is about 60 inches tall, so I can make 4 rows (48 inches) with space in between. That means I can display 4 rows of 7, or 28 papers on the board."

Interpret Data

Other math think-aloud topics that fit naturally into your day involve data analysis of daily occurrences. Think aloud about how to compare the number of sunny days with cloudy ones, how many more days until the end of the month, or how many more students buy than bring lunch one day. To highlight estimation, think aloud about how to estimate the number of tiles on the floor, or about how many buttons are worn in the classroom on one day.

THINK-ALOUDS AT HOME

Math think-alouds need not be limited to the classroom--parents can also think aloud about their daily math routines! Here are several think-alouds that parents can use to heighten children's awareness of math at home. Send the ideas home in a newsletter or e-mail, or share them during parent-teacher conference night.

* Estimate the time required to pick up the car pool or arrive at sports practice on time.