The percentages were similar for eighth-grade students: teachers of 27 percent reported that students worked and discussed mathematics problems that reflected real-life situations “almost every day,” and teachers of 47 percent reported working and discussing these types of problems “once or twice a week.”61

As part of the 1996 NAEP, teachers were asked about their knowledge of the 1989 NCTM standards. The teachers of 46% of the fourth graders professed little or no knowledge of the standards, and only 5% of the fourth graders had teachers who indicated that they were very knowledgeable. In contrast, only 19% of the eighth graders had teachers who claimed to have little or no knowledge of the standards, and 16% had teachers claiming to be very knowledgeable.62

The accuracy of teachers’ self-reports of their practice can of course be questioned. Teachers have their own meanings for what they do. For example, in a recent survey of 85 elementary school teachers in two districts, 93% said that they were using cooperative learning, a practice in which students are grouped for instruction, are assigned roles in the group, work together on a task, are each assessed on their performance, are each held accountable for contributing to the work, and, in some versions, are taught skills for working together, promote each other’s contributions, and work collectively to improve their effectiveness.63 Interviews with 21 of the teachers who had indicated they were using cooperative learning (17 of whom said they used it for mathematics) revealed that all but one had their own version of the practice, which they distinguished from the “more formal” version. Primarily, they almost never attempted to make sure that individual students were held accountable for contributing to the work. From their own descriptions, the majority of the teachers were using a form of cooperative learning that differed substantially from the forms described in the literature by the researchers who had developed the practice. Similar discrepancies have been documented between teachers’ reports of implementation of other reform practices and the observation of those practices in their video lessons.64

Overall, teachers’ reports give at best a mixed picture of mathematics teaching in U.S. elementary and middle schools: heavy attention to traditional content accompanied by modest and possibly idiosyncratic use of practices endorsed by advocates of standards-based instruction. Regardless of how teachers are interpreting these practices, most do appear to be at least somewhat aware of recent proposals for change. Self-report data address isolated practices only, however; observational data are needed if one is to get a sense of how lessons are organized and conducted.

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