Making the Complexities of Teaching Visible for Prospective Teachers
Chval, Kathryn B., Teaching Children Mathematics
Most of the prospective teachers who enter my methods courses assume that teaching mathematics to elementary students will be easy. For example, Jenny wrote, "I thought, 'I can teach math. How can it be so hard? It's elementary math!' But I have been proven wrong." Based on comments such as Jenny's, I realized the importance of giving prospective teachers opportunities to understand that effectively teaching mathematics to elementary students is complex and challenging. I recognized that field experience in my mathematics methods courses had to make the complexities of teaching more visible for prospective teachers. In other words, prospective teachers must study teaching practices. Such study would not only require viewing, analyzing, and discussing practices but also include the opportunity for prospective teachers to practice and analyze their own teaching.
The purpose of this article is to discuss two approaches that have helped prospective teachers not only examine the complexities of teaching but also examine and improve their own teaching. The first approach involves repeatedly teaching the same mathematics lesson to small groups of students, and the second approach involves conducting the same interview with several children. Both approaches enable prospective teachers to focus their attention on students' development of mathematical understanding and how teachers' actions affect that understanding. Both approaches can also help teacher educators make the complexities of teaching more visible for prospective teachers.
Teaching the Same Lesson Repeatedly to Small Groups
Sometimes the most valuable lessons we learn are not the ones we set out to learn. In the late 1990s, the National Science Foundation (NSF) funded a program designed to enhance the mathematical learning of elementary students who were taught in small groups. The program called for prospective teachers to repeatedly teach the same lesson to several different small groups of four to six elementary students. Depending on the size of the classroom, prospective teachers taught the same lesson three to nine times. The program's impact on the prospective teachers was profound. The prospective teachers all agreed that their teaching improved as they taught the same lesson many times. Furthermore, they reported that the experience helped them view the work of teaching in ways that coursework never did. They also acknowledged that the groups taught later in the program received better instruction than did the initial groups who were taught the same lesson.
As a result of the initial observations of this program, NSF funded a research study to investigate (1) what prospective teachers learned from repeatedly teaching the same lesson and (2) how prospective teachers' instructional strategies changed from teaching the same lesson multiple times. During the study, selected lessons were observed and audiotaped. It should be noted that the lessons that the prospective teachers used were from NSF-supported curricula such as Investigations in Number, Data, and Space; Connected Mathematics; and Math Trailblazers. At the end of the teaching experience, the prospective teachers were interviewed. Figure 1 lists sample questions.
The prospective teachers reported learning important information about teaching, as well as about children and curriculum. Through this experience, the prospective teachers did not have to worry about managing an entire class and were therefore able to focus their attention on student thinking and communication. They found that children were capable of creating a variety of solution strategies and often approached tasks in ways that they had not anticipated. They had expected that every lesson would be the same and were surprised to find that every lesson was different. Children's contributions and struggles took the lesson in different directions for each small group.
In addition to learning about students, the prospective teachers recognized important aspects of their teaching. …