Classroom Problem Solving with CalculatorsAuthor(s): Joan Duea and Earl OckengaSource: The Arithmetic Teacher, Vol. 29, No. 6 (February 1982), pp. 50-51Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192017 .

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Classroom Problem Solving with Calculators

By Joan Duea and Earl Ockenga

In An Agenda for Action the NCTM has made recommendations for the mathematics classroom. One recom- mendation is that "problem solving be the focus of school mathematics in the 1980s." Another is that "mathematics programs take full advantage of the power of calculators at all grade lev- els."

To implement these recommenda- tions, successful activities and re- warding learning experiences in prob- lem solving are needed. Bulletin board displays, learning stations or centers, and calculators provide a nice blend for getting naturally curi- ous children involved in solving prob- lems.

Where do problems come from? Not always from a teacher or a text- book. Students should be encouraged to be authors, to create problems as well as to solve them.

A piece of art or a picture that has an active, interesting setting generates many problems (see fig. 1).

'There were three trucks and on each one there were 18 wheels. How many wheels were there? Three more trucks came and one of them left. The other two had 18 wheels, so how many wheels were

Joan Duea is a third-grade teacher at the Price Laboratory School and a professor of educa- tion at the University of Northern Iowa in Cedar Falls. She teaches all subjects in her elementary classroom and serves as a demon- stration teacher and supervisor of student teachers. Earl Ockenga is also a classroom teacher at the Price Laboratory School and an assistant professor on the same campus.

there?" Ryan, Chad, J.D., third grade. "The truck drove 625 miles in one day and it got 8 miles a gallon. I had a full tank of 100 gallons. How many gallons of gas were left?" Lisa, fifth grade. "Jan, the truck driver, drove his 18- wheeler across the United States, from San Francisco to Denver, with 1 male rabbit and 1 female rabbit in his empty 20-ton trailer. The chart (table 1) shows the total number of rabbits at 100-mile intervals. What is the total number rabbits at the end of the trip?" Jan and Dave, eighth grade.

Because every students can add, subtract, multiply, and divide when they are using a calculator, computa- tion does not stand in the way of either writing or solving problems. The calculator puts the emphasis on "what to do" rather than on "how to do it."

Taking ownership in problem-solv- ing situations increases students' de- sire to solve problems. Given the op- portunity, they enjoy being the collectors of materials and the build- ers of displays.

The information provided on a col- lection of empty cartons, containers, or cans brought from home by stu- dents can stimulate the development

of creative, thought-provoking prob- lems (see fig. 2). In turn, these prob- lems will challenge the students to identify the data needed and to use their estimation skills. Guessing and testing usually involve tedious com- putation, but students are willing to make initial estimates and reflect on the outcome when they know they can quickly clear the calculator and enter a better estimate.

Using materials and objects that students see and use every day gives them the opportunity to apply their problem-solving skills.

A good opportunity for students to use realistic data is provided in the collection of personal information. When students use personal data and a calculator, they extend problems. Watch your students use the calcula- tor and the code (number of beats in 15 seconds [x] 4 [x] 60 [x] 24 [x] 365 El) to determine how many times each heart beats in a year (see fig. 3).

Once students know how to com- pute the number of times the heart beats, they can be easily motivated to collect data related to pets and other animals. When a class was asked how many times a peťs heart beats in an hour, the responses were immediate:

"I've got a cat and a kitten so I can find that out." Jill "How about my checking the heart beat on my hamster?" Joy. "I have a guinea pig." Larry. "Would I hold right above my dog's paw to get his heart beat?" Renee.

When students have a code and a calculator, mathematics computation becomes insignificant. They focus on

50 Arithmetic Teacher

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the collection of data and their skills and strategies are immediately trans- ferred to new situations.

As students collect information, they look back on their findings to observe patterns and similarities (see fig. 4). In this case, students may develop hypotheses such as the fol- lowing:

"The bigger the animal, the fewer the heart beats." Sean 4 The animals that dart around seem to have more heartbeats." Ellen "Animals with slower heartbeats seem to live longer." Kathy "After playing with my dog, its heart seems to beat faster than when it's resting." Renee

Students discover that problem solv-

ing requires far more than computa- tion - it requires methods of gather- ing, organizing, and interpreting information; drawing and testing in- ferences from data; and communicat- ing results.

Once students' problem-solving in- terests have been fostered in planned situations and they recognize the val- ue of the calculator in arriving at solutions, they are ready for open- ended experiences, the generation of their own problems. An inexpensive wrist calculator can be made available to the students on a check-out basis. They are encouraged to take the cal- culator with them, as a reminder, to look for situations where they can ask "I wonder" questions. More often than not, the naturally curious stu- dents return with not only the calcula-

tor but also with the question "I won- der ... ?"

To solve the "I wonder" problems, students become involved in identify- ing the problem, collecting the data, determining the necessary operation, and then using the calculator to find the answer (see fig. 5). The speed, efficiency, and accuracy of the calcu- lator serve to eliminate many of the age-old aversions to problem solving.

The joy of problem solving will be- come contagious in the classroom as students participate in experiences that they generate. Capitalizing on their interests and curiosity for the setting, then handing them the calcu- lator as a problem-solving tool, can make better problem solvers in the 1980s. So, let's check our batteries, hit the switch, and get on with it! m

February 1982 51

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