Quarterly for Education and Technology: Polyhedra City: A Mentoring Case Study

Polyhedra City: A Mentoring Case Study

Kay Toliver

Mentor (n) — A wise and trusted counselor or teacher. (vt) — To act as mentor, advise.

* Webster’s New World Dictionary

Mentor (n) — Friend, guide, communicator, listener, encourager, coach, friend, friend, friend.

* Kay Toliver, fourth-grade teacher

Even with the proliferation of staff development activities in recent years, it’s no exaggeration to say that many teachers still feel like they’ve been marooned, isolated in their classrooms. They may see demonstrations of the latest techniques. They may even get outfitted with the latest technology, but once they get into their classrooms, they are on their own.

New teachers are essentially given a room and a group of students and are expected to just get in there and teach. Too often, there’s no one to help them with the things that are the most overwhelming, from learning how to set up a classroom, to managing their time, to maintaining order or even finding and knowing how to use materials, like books or manipulatives.

Veteran teachers often need help as well. After years of being on their own, they can fall into a rote pattern. They may not have anyone in their school who has time to advise them or help them keep a creative and enthusiastic attitude about teaching.

About four years ago, a project in my school gave me the opportunity to address these truths. I was in my 30th year of teaching at P.S. 72/East Harlem Tech in New York City. I had just switched from teaching seventh-grade math to creating a fourth- through sixth-grade mathematics program, and I found myself assuming the role of mentor in a very unique way.

The mentorship centered around a project called “Polyhedra City,” which I instituted with two other fourth-grade teachers, Esther Murillo, a 17-year veteran, and Monique Coleman, who was starting her second year of teaching.

The program I was working on, “Challengers,” was unique to my school. It had originally been a language arts program. I turned it into an integrated program where language arts, history, writing, and oral speaking skills were stressed, but mathematics was the focal point from which everything else developed. Students who were interested in math would come to the Challengers program for five periods a week.


My teaching philosophy is simple. I believe that all children can learn. And I believe that they learn best by doing, by sharing, by being creative, by learning to think for themselves. When other teachers pass my room, they see an open door. They see children working in groups. Their desks may be filled with things I have provided for them to use to explore the concept at hand. They tend to be noisy, excited. They are driving the lesson forward through their own inquiry and discovery process.

My students also keep journals in which they write about what they are learning, what they may be having trouble with, even what they like and don’t like about what I’m doing. These journals give me an excellent measure of how I’m doing as a teacher.


Esther taught a combined class of bilingual third- and fourth-grade students. They tended to be timid and were afraid of the other fourth graders. It had gotten so bad that at lunchtime they didn’t want to play with them.

Esther would come to workshops I gave at school and share her concerns with me. She was a good teacher and she knew it, but she felt there was something missing. She wanted a little more challenge, a little bit more fun. She wanted her students to express themselves more, but she hesitated to make the changes that would allow it to happen. She was worried about the chaos that might result in her classroom if her students worked in groups. She would have all these manipulatives lying around. What would happen?

Monique walked into her first day in fourth grade facing a class of 38 students — a challenge for even the most experienced teacher. She had been a business major with a love of computers and only one course in education. She became a substitute teacher at my school temporarily while trying to decide what kind of business career she would pursue. A year later, she had hex’ first full-time teaching position. After that year, it was obvious she had what it takes to be a teacher. She loved it, and her students loved her.

During her first year, Monique had been assigned a mentor who came into her class only once or twice a week. As a result, she began to feel that she was stranded.

When she started teaching fourth grade, I was her math prep teacher, helping by doing the introductory part of math lessons with her students. I realized that Monique had hardly been prepared for teaching this enormous class of 38 inner-city children. I knew that with her skills, the business world might start looking really attractive.

My solution to Monique’s inexperience and Esther’s isolation was Polyhedra City. It involved all of our students working together. We assembled all 70 students in one room, gave them each a number, and assigned them to groups according to their numbers.

Right from the start, for the part of the day we were working on Polyhedra City, we were no longer three separate classes, but one group of students with three teachers. Esther, Monique, and I each filled a special need, and the students knew they could go to any one of us at any time.

As fate would have it, Esther had the largest room. So, in spite of her concerns about chaos, all 70 students were crammed into her room every day, dragging their chairs, supplies and ideas in loudly with them. We called her room “the family room.”


I created Polyhedra City as a yearlong project that involves math, history, reading, art, and writing. It’s a city made of polyhedra structures, built entirely by the students. They fashion everything themselves — even the polygons that comprised the bricks of each building. They use paper, cereal boxes, paper towel rolls, shoe boxes and any other material that we could find.

During the process, they read about the history of New York City and the immigrants who built it. This has a powerful impact on the children, many of whose parents are immigrants.

The best thing about this project is that the kids do it all; it is their ideas, their creativity, and we let them run with it. Students keep a journal describing what they accomplished for the day, what they learned. We get parents involved by inviting them to work on the project with their children. At the end of the year, there is a major event when parents are invited to see Polyhedra City, which by this time has tilled up an entire hallway. Astonished, they listen as their young children, even those who began the year with little English, explain the geometry behind their creation.

When we started working together — a rookie, a well-established teacher, and this “senior citizen” — we reed to develop a sense of community and family and to get kids who thought they were living in different worlds to be friends. I think the students have really responded to seeing three of their teachers working together, being friends, patting each other on the back and laughing together. They see us sharing ideas and sharing our materials. It’s the very thing that we’re asking them to do, and I think it’s really made an impact.


No one could have been happier about the arrangement than Monique, who had already been getting a good deal of support from me. Before school started, I had given her pointers on setting up her classroom. Since her class was so big and the room so small, I suggested that she create “learning centers” — one for reading, one for computers, and so on. We arranged the desks in a certain way, to situate the children. I invited her to come into my classroom anytime, and she would show up about twice a week and then talk to me afterwards. I’d ask her what she learned — what she saw that I was doing that she did, and what she wasn’t yet doing.

When the three of us began working together, Esther or I would often visit Monique’s classroom to observe. It made her nervous at first, but we told her that our comments weren’t to put her down or make her feel bad; they were simply to help her improve. There was a time when I was new, too, and I remember those teachers who were the old-timers. At lunchtime I would be alone in my room trying to figure out how to do things, and they would see me and say, “Come in Kay, and sit with us. What is the problem you’re having? What do you need help with?”

We tend to think in terms of new teachers being influenced by more experienced ones but, in our case, it went the other way as well. Monique, the technology specialist in our little group, somehow managed to get hold of a computer and put it into Esther’s classroom. She helped the students use it to write stories about what they were doing on Polyhedra City. She coached Esther as well.

Esther would visit my classroom often, and take the things she watched me do back to her students. For instance, I always ask my students to answer questions, not with just a yes or a no, but in whole sentences. She made the same request of her students and expanded it — not only to answer in whole sentences, but also to explain, and even to write about, why and how they came up with their answers. I was extremely impressed by her ability to take ideas and go beyond them, applying them to her own way of teaching.

That’s one of the biggest challenges with staff development. Every teacher wants her students to succeed, to do well. But sometimes it’s easier to do it the same old way. You can work with teachers, they can come to workshops and get excited about learning new techniques, but often they don’t take what they have learned back to their classrooms and make it their own. Staff development should be a catalyst that gets teachers to be more creative, to use what they have seen to develop their own activities. That’s where mentoring can help.

When we started working on Polyhedra City together, I took the lead. I wanted to show Esther and Monique how we could get this group of students together to work to produce a product that would be something that everyone would be proud of. I modeled how you get started on a project. I did a lot of introductory lessons with all the children in one area. Esther and Monique took it from there.

All the students improved significantly. When Monique’s students began fourth grade, the class as a whole was in the 20th percentile. At the end of the year, they had met the school average.

Esther’s bilingual third and fourth graders held their own on year-end assessments. Only two of her third graders did not pass, and every student showed improvement. Since these tests are based entirely in written language, she was especially pleased. At year-end, her class was in the 60th percentile.

One of my fondest memories from my time mentoring Esther and Monique was in the mornings, when I would be in charge of getting all of the fourth, fifth and sixth graders into line. Each day would start out with something we called “word of the day,” where I would offer a new word for students to go to their computers or dictionaries and discover. It never failed that Monique’s, Esther’s, and my students were the first ones ready. They took pride in school, they were all friends, and they knew their education was important.


Whether we want to admit it or not, there are still too many doors that are closed between teachers, too many ideas that are not being shared. For Esther and Monique, I have tried to be there as a model. I’m someone who can talk about curriculum. I’m there to share what I know about discipline, and to listen to any ideas they might have. If a student was really troublesome, Monique knew she could send him over to Esther’s room and he could sit there and work. My room was the cool-out room for all the kids who might need a minute.

We were equal partners, because our mission was the same — we all wanted to have the best fourth-grade students. It is this type of mentoring experience that I believe will open the doors between our classrooms and help new and veteran teachers alike.


Of all the ways a teacher can learn — workshops, mentoring, team teaching, reading articles — what has been most effective for me is taking back whatever it is that I saw Kay doing and then trying it myself, in my own way.

When I tried doing this, my students were a little noisy, but as I walked around I found they were talking about the project, about what they’re supposed to be doing. They were talking to each other: “Why don’t you do it this way?” “Look what I did over here everybody!” “Look what Louis did!” They would call me over. Suddenly, the children were excited about what they were doing, and what they were discovering.

At first I was nervous about working with Kay. Was I going to be able to meet her expectations? But then I realized that she does what she does because she loves the children. And I knew then that this is a teacher at heart and someone who I would like to be like.


When Kay and Esther would come to my class to observe what I was doing, I would get nervous just knowing they were there. Sometimes I’d get tongue-tied. But they told me the critique wasn’t to put me down or make me feel bad, it was to help me improve. If I didn’t have Kay or Esther around, and I was in a school where teachers were more isolated from each other, I would definitely be more scared.

I’ve learned a lot from Kay, especially about appropriating time. I used to have difficulty with getting my lessons in order. I would go into Kay’s room and see how she would break down her lessons — how she would start with one thing, like reading, and then go into another subject, like science or math or social studies.

I’m still learning, still getting lots of help with my timing, my pacing, and also in introducing more lessons. The most valuable thing I think I’ve learned from Kay is about control and management. I tell my kids, if you want respect, you have to respect me first, and then I’ll give you respect.

I want to be a better teacher. Kay’s bringing things out of me that I never thought I had. What have I learned from her? Patience, control, great lessons, creativity. That’s a whole lot.

Kay Toliver has been teaching at East Harlem Tech/P.S. 72 in New York City for more than three decades. Her teaching honors include Presidential, Disney, and Kilby Awards. Working with the Foundation for Advancements in Science and Education (FASE), she has contributed to nearly 40 video programs that feature her innovative lesson plans and her eager and inquisitive East Harlem students. Included among these are two award-winning series for staff development use, The Kay Toliver Files and Teacher Talk. Surveying the body of work that Ms. Toliver has created with FASE, School Science and Mathematics wrote: “Each of the programs in this collection is independently superb, and collectively they are extraordinary in their perspective and vision.” For more information on these resources, call 1-800-404-3273.

Racquel Skolnik is a senior research associate at FASE.

COPYRIGHT 1999 Agency for Instructional Technology

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