| This study was designed to gather information about mathematics instruction and learning in a classroom where one of the teacher's major goals was that children understand mathematics. In a naturalistic study based on informal observations made during 74 classroom visits over a 7-month period, I observed and described what one teacher and his fifth- and sixth-grade students did during mathematics. I had eight formal interviews with the teacher, Barry, and at least one formal interview with each of 20 students. Every mathematics lesson was audiotaped during the last 45 visits, and I videotaped three lessons, as well.;Unbeknownst to Barry or the children, I focused more deeply on seven students to gain a clearer insight into their individual and unique experiences and views on mathematics and learning. Analysis of the data collected about these individual students, as well as the data collected for the class in general, led to the following conclusions: (1) While Barry's statements about, and use of, grouping seemed to belie it, the class was actually a rather whole-class, teacher-directed event. (2) Neither Barry nor his students focused on what children did and did not understand in mathematics. (3) A number of Barry's professed beliefs about mathematics, its instruction, and how children learn were inconsistent with each other and/or with observed behavior.;Those of Barry's beliefs most clearly reflected in his mathematics instruction included the following: (1) Knowledge is built socially. (2) It is impossible for teachers to simultaneously help individuals understand mathematics and teach the whole class. (3) It is often more productive for students to work together to learn a topic than for a teacher and student to work together. (4) A teacher's power lies in providing the proper environment and the right activities. (5) A teacher has little direct and immediate influence on children' s attempts to understand mathematics.;The implications of this study's findings as they pertain to the issues of children's mathematics inventions, peer collaboration, teachers as mentors, and the most recent mathematics education reforms are discussed. Suggestions for future research emphasize the need to include teachers as partners in data collection and analysis. |
