Learning:
Calculators in the Classroom

Teachers figure they're valuable for relating complex problems, not 7 3 8.

Math teacher Douglas Tucker says calculators let his middle school students tackle tougher math problems from the real world.

On Valentine's Day, Bonnie Hagelberger's first graders at the Monroe Elementary School in Brooklyn Park, Minnesota, give a valentine to each other and to the teacher. So how many valentines are there in the whole class?

Hagelberger's six- and seven-year-olds can tackle that problem, although they can't yet solve it with paper and pencil. They also estimate the number of children in the school. They even begin thinking about negative numbers.

Hagelberger helps these children stretch their mathematical thinking with the aid of a powerful tool--the hand calculator.

Although still controversial, calculators are now common in American schools, according to Lee Stiff, president of the National Council of Teachers of Mathematics, which has strongly promoted them. Calculators are relatively scarce in first grade, but by fourth and fifth grade, they are widely used.

At the Martin Luther King, Jr. Efficacy Academy in Denver, Colorado, Douglas Tucker has used calculators with eighth graders for a unit on the ratios and proportions of the human body. They found some of the Statue of Liberty's dimensions on the Web and used them to calculate some that weren't listed. They've also done a secret-person investigation in which they try to guess the identity of someone in the school by calculating dimensions, like height, from other body measurements. These problems help students understand that ratios exist in the real world, not just in math books, Tucker explains.

"I use calculators to enhance, investigate, do more. They don't replace other ways of doing math. They reinforce them," says Tucker.

Tucker got his own introduction to calculators after a difficult first year of teaching. "I had classroom management issues--typical first-year teacher stuff," he recalls. "I was uncomfortable going page by page in the book. The students didn't like it, and I didn't like it, but I didn't know another way because that's how I learned." His principal suggested a summer in-service program, and there he learned how to make his math classes more interesting with calculators.

Despite their popularity with many math teachers and students, calculators are still controversial. NCTM leader Stiff says most of the opposition centers on the early grades. Some teachers and parents are afraid students will turn to calculators instead of learning basic number facts.

NCTM, Stiff explains, does want children to learn their number facts. "Today's students should be able to do what their parents did, but they should also do more, taking advantage of tools their parents didn't have," he says.

Tucker says he teaches children how to decide when it's appropriate to use a calculator and when it isn't. "I say to them, 'Would you use your bicycle to get from the bedroom to the bathroom? Or would you use it to visit somebody on another street? It's the same with calculators.'"

Hagelberger says more than 100 studies have confirmed that calculators don't keep children from learning number facts. But she says teachers need good professional development if they are to use calculators well.

"We have to ask, 'Will the calculator help my kids understand the material?'" says Hagelberger. "This is a tool we never used in school ourselves, either in K-12 or in college. So how can we learn to use it effectively, and not have it become the crutch the general public is fearful of?" A one- or two-hour class--even a full day of training--isn't enough, she says.

"Teachers need to see calculators demonstrated, use them in class, and reflect on their practice, both individually and with colleagues," says Hagelberger. "This takes time."

--Alain Jehlen

For more: E-mail Hagelberger at hagelberger@anoka.k12.mn.us, Tucker at doug_tucker@dpsk12.org, or Pamela Matthews of NEA's Teaching and Learning unit at pmatthews@nea.org. Visit the NCTM Web site at www.nctm.org.

Dilemma
What do you do when students' late work hours affect their studies?

I taught in inner-city high schools where many of my students went directly from school to work. They did not get off work until 10 p.m. or later. Since classes started at 7:15 a.m., they had no time for homework or outside assignments and were often so tired that keeping them awake was a real problem. Often both their grades and their health suffered.

First, I talked with the students about cutting down their hours, but most felt they had to work to help support themselves and others in the family. They were afraid they would be fired if they asked to work fewer hours.

Next I talked to their parents. Most realized their child's grades were suffering, but there was no other choice. I felt that students were being victimized by employers who couldn't find anyone else to work such late hours for such low pay, so I started writing letters to legislators. A bill was finally passed in the state legislature to limit the hours of working students. (It contained a provision, however, that parents could request these limits be waived, and no one ever verified the parents' signature.)

When nothing else worked, I called or went to the students' place of employment and explained the situation to the manager. In most cases, that worked. I worried that students would resent my interfering, but they knew I cared about them, and many expressed their appreciation. I even had students and parents asking me to speak to employers about reducing work hours.

Jo Walters
Retired
Chattanooga, Tennessee

I allow students to re-do work they have turned in to me on time. They know that they can turn in something and make it better later if time and too many other commitments kept excellence from their grasp on the given day it was due. This helps students stay positive even when they are overwhelmed with work.

I set a firm rule of accepting no late work even if the student is absent unless they or a parent call me personally to inform me that they are extremely ill. I have an answering machine on my school phone and give all students my home number, which is also tended by a machine. Both machines have a time/date stamp.

I emphasize to students and parents how this is preparation for the workplace and a lifelong skill. The self-management needed to get work in on time is the most important learning many students can do.

Leslie Van Leishout
Theater arts teacher
Olympia, Washington

I give students their weekly homework assignments on Monday, and they have until Thursday to complete them. They know ahead of time what they need to do and when it needs to be done by. This helps my college-bound students budget their time and learn better time-management skills. Students who have to work an extra shift just let me know ahead of time to get an extension. When a reading assignment is due the next day, I encourage students to take their books to work and read during their break. I have found that if I am flexible and understanding, my students tend to live up to my expectations of them.

Laura Ann Curran
Junior and senior English teacher
Belleville, New Jersey

When I see that students' late work hours are affecting their studies, I call their parents to voice my concern. Most parents in our area are very cooperative and appreciate my calling. They talk with their children and frequently have them cut back on the number of hours they are working or make them quit working until vacation time.

Marjorie Rios
Spanish teacher
Livingston, Tennessee

Got an Answer?

How do you handle chronic tardiness?

E-mail your answer to dilemma2@neatoday.nea.org. You can also fax to 202/822-7206 or use regular mail. Please include your name, city, state, job title, and grade level, if applicable.

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How I Did It

Lawrence Volpe
Seven Trees School fifth grade teacher
San Jose, California

I found a way to take my inner-city kids on wonderful excursions, with lots of help from the Sierra Club.

In my first year of teaching, I wanted to get my inner-city kids into the outdoors.

I organized, planned, shopped, and rented camping gear and a van, so that I could take 13 students to a national forest for a camping wilderness experience.

I did all the work myself, and it was tough!

It was well worth it, though. I had parents of three students on the trip--and they still go on my trips, three years later.

But it was too much work.

Searching for an alternative, I found Inner City Outings, a part of the Sierra Club that provides outdoor experiences for kids who would not otherwise have them.

The program's philosophyis that the wilderness exists as a resource for everyone, and all people should have access to it. Students develop their interpersonal skills and self-esteem through teamwork and an active relationship with the outdoors.

Inner City Outings supplies all the necessary gear for outdoor adventures. They provide well-trained leaders with experience and a love for the outdoors--at least two come on each trip in case something goes wrong.

If you're not a trained leader, you can go as a volunteer.

The Sierra Club also provides liability insurance.

Although the Sierra Club pays most of the expenses, I ask students to contribute $5 to $20, "or whatever you can afford."

In the year I have been involved with Inner City Outings, I've taken my kids on about a dozen trips.

We've been camping, backpacking in the Sierras, sea kayaking, whale watching, and sleigh riding, and we went on an excursion to San Francisco Bay for International Migratory Bird Day. There are almost 50 ICO local groups across the United States and Canada, conducting as many as 700 outings a year.

For more about Inner City Outings, contact ICO National coordinator Debra Asher, 415/977-5568, E-mail debra.asher@sierraclub.org.

Or contact Lawrence Volpe, lvolpe@fmsd.k12.ca.us, or visit http://www.sierraclub.org/ico/.

Can't We All Just Get Along?

Hoosier teachers and administrators build mutual trust and boost student achievement.

Marion Teachers Association President Judy Creviston and Superintendent Gene Denisar meet regularyly to solve district problems.

The small city of Marion, Indiana, home to several large factories, witnessed some long, bitter strikes in the '70s and '80s, complete with mass arrests of picketers and union leaders. Not in front of its plants, but in front of its public schools.

Warlike labor relations prevailed in the Marion district until the mid-'90s, reports UniServ Director Sharon Casey.

"When I arrived here in 1990," she recalls, "120 grievances had been filed, 30 of which went to arbitration. The head of the American Arbitration Association regional office couldn't believe our local Association. We had the thickest file in his office, with 350 cases!"

Well, times change, and so have relations in Marion. In 1995, the district hired a progressive new superintendent, Charles Coleman, and worked with the Marion Teachers Association to forge a collaborative partnership grounded in interest-based bargaining. That's a process through which the parties identify common concerns, build mutual trust, and use open communications to resolve problems and reach agreements.

This partnership, which remains strong under the leadership of current Superintendent Gene Denisar, has turned this 6,100-student district around in the face of big-city challenges, including the loss of industry, declining tax rates, and a growing number of low income students.

Today, student test scores are rising, suspensions are down, and the graduation rate has increased, and that's just for starters.

Over the past six years, leaders of the 450-member MTA and district administrators have used the interest-based process to tackle every issue that can pop up in a school system.

This relationship starts with a labor-management Communications Committee that irons out problems before they become grievances and extends to a series of joint panels that carefully research individual issues and devise solutions acceptable to all school stakeholders.

One joint committee, composed of teachers, parents, and administrators, has implemented a new, earlier elementary schedule more suited to young risers: 8:00 a.m. to 2:35 p.m. "It's research-based," notes MTA President Judy Creviston. "We haven't seen the results yet--the latest student test results aren't in--but the kids like this schedule better."

Another panel has studied grade-level alignment among elementary, middle, and high schools and discovered the need for a smoother transition between each new level, notes Creviston, a remedial math and language arts teacher at McCulloch Middle School.

Yet another joint committee, involving top administrators and MTA leaders, is planning the district's response to a new Indiana law requiring every school building to draw up an improvement plan with a professional development component.

"We don't want to set buildings up to compete with one another," says Creviston. "We want to allow each school to write a plan that serves its children and area population."

Making this planning process far easier will be an innovative new teacher "review" or evaluation procedure drawn up by, yes, a joint committee after two years of laborious research. The new system, piloted among veteran educators last year and new teachers this year, replaces the old principal-with-a-checklist evaluation with an open-ended process based on peer support.

In a nutshell, this process permits each teacher--with the exception of those vets who prefer the old checklist--to select a support team for the year consisting of two or three colleagues and the building principal. The teacher meets with this team a couple of times a year and is free to request support tailored to his or her needs, from mentoring to classroom observation.

The review process, when fully developed, will involve stiffer training requirements and larger support teams for new teachers and vets who need extra help. But the basic philosophy of the system will be "people helping people," stresses Creviston.

"It's a professional development approach that puts each teacher in control of his or her destiny, based on the idea that good teachers can do an even better job and grow with support."

That kind of backing, coupled with the relaxed atmosphere that grows out of the interest-based process, can only benefit students in the end.

"Whatever we and administrators do, we do together," Creviston concludes. "And in whatever we do together, we keep student achievement foremost on the agenda."

--Dave Winans

For more information, contact Judy Creviston or Sharon Casey at 765/664-1244 or by E-mail at marionta@comteck.com.

What do you do with colleagues who constantly put down good ideas?

In my earlier days, I probably would have dismissed them as "old fossils" or spent energy trying to debate the issue. Now, after 23 years in the profession and finding I could be called the "old fossil," I view these negative opinions quite differently. I have begun to realize the value of listening to criticisms as a troubleshooting opportunity.

We are eager to do what's best for children and may overlook negative points that should be addressed. I try to look at an idea thinking about both the worst- and best-case scenarios.

In addition, if that "negative" colleague begins to see that his or her ideas are given consideration, he or she may become more open.

If the colleague is voicing negative opinions honestly, then at least you will always be sure of where that person stands in any policy discussion. You won't be surprised by an unexpected challenge.

Kathleen Keefe
Fourth grade teacher
Casper, Wyoming

When I have colleagues who put down ideas that I think are good, I try to avoid bringing up new ideas around them. I seek out people who will help me brainstorm new ideas.

June Hunter
First grade teacher
Washington, Iowa

First, I play devil's advocate, acknowledging right up front the potential difficulties we would have to overcome to make it work.

Second, I garner support from other colleagues before presenting ideas to the group.