The Early Childhood Mathematics Collaborative: Communities of Discourse
Copley, Juanita V., Teaching Children Mathematics
At 6:45 in the morning on the first day of the Early Childhood Mathematics Collaborative, I arrive at Jessup Elementary School and am greeted by several early kindergartners: "Hey, Mrs. Copley, is everyone coming?" "Where have you been? Hey, our class can get twelve people standing in the counting circle." "I've lost a tooth since you were here!" A first-grade teacher walks in with me, explaining that she has wonderful work from her students: "Just wait till we meet and you see their word problems. The students' thinking and reasoning are so obvious!" As we begin to unload, two very nervous undergraduate students wander in and explain that they have arrived more than ninety minutes early "so we wouldn't be late!" They quickly explain that they have been up all night worrying about teaching mathematics to real children and that if possible, they would like to observe today and perhaps teach on another day. I smile and assure them that everything will be fine. Within two hours, more than 800 students, 40 prese rvice teachers, and 50 faculty members arrive. Another semester of the Early Childhood Mathematics Collaborative (ECMC) has begun.
The ECMC has been active for seven years at the University of Houston. A unique professional development model, the collaborative has several components: (1) a university faculty member adopts a public school and conducts specific, standards-based professional development sessions; (2) five preservice teachers per classroom present games or activities to children in prekindergarten, kindergarten, and first and second grades; and (3) while the preservice teachers cover the classes, classroom teachers are involved in study groups with the university professor.
Putnam and Borko (2000) recently synthesized research on teacher learning. They describe communities of discourse" as effective vehicles for teacher change and further education. In their terms, communities of discourse provide settings in which teachers of all levels can discuss research-based knowledge, reflect on teaching practices, and share student learning experiences. When discourse in the community involves teachers' ideas meshed with research-based knowledge, teacher learning can result. Together, as a community of discourse, members of the Jessup and university communities assess student responses, evaluate specific teaching strategies, and reflect on student learning.
The Jessup Community
Jessup Elementary School is located in a large urban school district in a middle-class neighborhood. Jessup has three prekindergarten classrooms and includes up to fifth grade. This year, twenty-two different languages are spoken by the children of Jessup. English as a Second Language and dual-language Spanish and English programs are implemented in almost half the classrooms. Jessup, which has been involved with ECMC for two and a half years, is known as an innovative, exciting school filled with children from diverse cultures. Equally important, its teachers are diverse in background and education. Spanish is the first language for many of the teachers, and the United States is their second country. About half the teachers have more than ten years' experience; the other half have two years or less of teaching experience.
University Professor and the University Community
For more than twenty years, I have been involved in professional development for preservice and in-service teachers. I have served as a mentor, a model teacher, a coach, a teacher motivator, a workshop presenter, a professor of education, and an evaluator. I have seen numerous problems with each of these professional development roles. Ideas presented at "one shot" speeches or activity workshops often cannot easily be implemented or integrated in the daily classroom routine. Teachers frequently complain about the lack of time available to implement new ideas, to mentor or coach others, or to reflect on their students' understanding of mathematical concepts. Beginning teachers also experience teacher preparation that is less than satisfactory. They are often thrust into student-teaching experiences with little or no time to practice before they are evaluated. In addition, preservice teachers in early childhood classrooms have difficulty creating high-quality mathematics lessons, especially if they have not had positive experiences in mathematics as students. The ECMC model was devised to answer the problems encountered with teacher education, at both the preservice and in-service levels.
The collaborative experience involves one six-hour session every other week. In addition to the collaborative sessions, the university professor also models lessons in classrooms while the preservice and in-service teachers observe. A typical collaborative day involves the following activities: (1) a ninety-minute preparation time for the preservice teachers to review activities and games, (2) three hour-long meetings between the university professor and the in-service teachers by grade level (prekindergarten, kindergarten, and first and second grades) while the preservice teachers work in the classrooms, and (3) a reflection period at the end of the day for preservice teachers and the university professor.
Both planned and unplanned discourse occur continually throughout the day. The following paragraphs describe the discourse that occurred on the first day of the ECMC this past semester. (Note that all names used are pseudonyms.)
As preservice teachers arrived, the room was filled with nervous conversation, a few quiet laughs, and wide-eyed anticipation. Typical comments included the following: "I can't believe we have to teach math. Why couldn't we do reading stuff?" "I never was good at math. That's one of the reasons I decided to teach young children. I figured I could at least do first-grade math!" As soon as other preservice teachers arrived who had been in the collaborative the semester before, new conversations began. I started to hear comments like these: "Don't worry. The kids love these games." "Just watch the kids, and you will learn lots!" "I guarantee you will like this more than the classes you take!" "I used to be scared to death but not any more! I really like it." " I have even learned math I understand." I was generally quiet as I listened to peers teach one another the important lessons to be learned. When everyone arrived, I went over the activities in detail, assigned the preservice teachers to their classrooms, and assured them that they would be successful. When they returned an hour later, the nervous laughter had turned into questions and exclamations: "How smart the kids are!" "I wonder why they did that?" "Your group seemed to be playing so hard. What did you do?" They were excited about their conversations with "a real teacher and real kids" and the fact that "the teacher appreciated what I did with her class. I must have been OK!"
The discourse in the study groups with the in-service teachers was equally exciting, although more content focused. At this time in the semester, the Jessup teachers had decided to focus on children's reasoning, problem-solving, and estimation skills. In each grade-level meeting, teachers brought samples of student work, reflections from their own experiences, and questions about the modeled lessons and about their own instruction.
Maria explained a pompom jack game that I had played with her class. In fact, she brought a Hula-Hoop and filled it with pompoms so that we could play, too. She asked each of us to estimate the number of pompoms that we could put outside the hoop in groups of five as she bounced a ball five times. Then we tested our estimates as we played the game. Although our estimates were close, many of us discussed why our reasoning was not exact. Maria said, "That's just what happened in my class! They automatically discussed how they made the sets ('I made a two and a three so I could do each set of five fast!') and how they estimated ('I thought each of us would make two sets so that would be five, ten, and then if there were four kids, that would be ... ten, twenty, thirty, forty! But some people made more than I thought.')" She continued to explain how she saw the activity: "At first, I thought Nita was just doing a fun game, and then I saw all kinds of math. Kids were making sets of five, estimating using sampling , using prior knowledge to make good decisions, and then mentally counting by fives to see if their estimations were reasonable." We discussed other reasoning opportunities that could be involved in this simple type of game.
I then asked about the estimating jars that were part of the in-service teachers' daily routines. A lively discussion ensued about how that activity could be made more meaningful to children and involve more reasonable estimates. We talked about sampling, setting parameters, and letting children change their estimates after they had time to talk with their peers.
In the prekindergarten and kindergarten group, we began by sharing children's reasoning that had been overheard during routine classroom activities. Kenneth said that he heard amazing vocabulary used at the block center. A four-year-old child explained to his friend that he needed a "big block put like ... you know, a bed" to bridge the gap between two vertical blocks. His friend responded, "You mean like a fat rectangle?" We talked about the use of meaningful vocabulary and the "looks like" vocabulary used by the young child. Dottie brought up the use of the word big. She said that one of the kindergarten students had asked if she was "bigger than" another teacher. When Dottie had responded, "Do you mean taller?" the child said, "No--more numbers!" After we stopped laughing about our "old age," we again discussed the idea that children's meanings are often different from ours and talked about the importance of questioning and listening to young children.
Another teacher, Marianne, shared discoveries that her pupils had made while counting the number of objects that they could hold in their hands. One five-year-old said, "Isn't it weird ... you put big things in your hand, and you get little numbers. You put little things in your hand, and you get big numbers!" Everyone wanted to know what types of questions she had asked that supported this rather mature reasoning by a five-year-old. Marianne laughed as she responded, "You all know me well and how much I talk! This time, I didn't ask questions. I simply suggested that he try the small blocks immediately after he had tried the big blocks. Then I stood back and looked puzzled. He took my reaction as a cue, was silent for a few seconds, and then said his discovery!" We discussed the importance of silence and modeling, along with other methods that we could use to encourage discovery and reasoning. Everyone promised to report other ideas at our next meeting.
When the preservice teachers returned after that first day, I saw a definite difference in their demeanor and excitement. Words rushed out as they told me about their new students and the mathematics that they had learned. Materials were packed up, new plans were discussed, and successes were reviewed. Together, we reflected about our day and prepared to learn more the following week.
What Are the Results?
From its earliest conception, the ECMC was created to adhere to the professional standards for teaching early childhood mathematics described by Copley and Padron (1999). Jessup Elementary School is just one of four sites
currently involved in the collaborative program, and many more are on a waiting list for participation in the future. Formative program evaluations of ECMC have revealed changes in in-service teachers' beliefs about mathematics and a greater emphasis on standards-based mathematics instruction, increased confidence of preservice teachers in their abilities to teach mathematics to young children, and growth in student achievement in problem solving and mathematical reasoning. From my perspective, I have greatly enjoyed introducing both new and experienced teachers to mathematics and teaching. Most important, I have witnessed teachers who have become empowered to implement ideas that result in both teacher and student learning through communities of discourse. All the program needs is a willing ness to connect universities and elementary schools and a community of learners!
Juanita Copley, firstname.lastname@example.org, teaches at the University of Houston, Houston, TX 77204-5872. She conducts research in early childhood settings.
Copley, Juanita, and Yolanda Padron. "Preparing Teachers of Young Learners: Professional Development of Early Childhood Teachers in Mathematics and Science." In Dialogue on Early Childhood: Science, Mathematics, and Technology Education, pp. 117-29. Washington. D.C.: American Association for the Advancement of Science and Project 2061, 1999.
Putnam, Ralph T., and Hilda Borko. "What Do New Views of Knowledge and Thinking Have to Say about Research on Teacher Learning?" Educational Researcher (January-February 2000): 4-13.…
Questia, a part of Gale, Cengage Learning. www.questia.com
Publication information: Article title: The Early Childhood Mathematics Collaborative: Communities of Discourse. Contributors: Copley, Juanita V. - Author. Magazine title: Teaching Children Mathematics. Volume: 8. Issue: 2 Publication date: October 2001. Page number: 100. © 1999 National Council of Teachers of Mathematics, Inc. COPYRIGHT 2001 Gale Group.