Abstract

(Mrs. Oublier and Carol Turner) are favorably disposed to several of big ideas in California math framework and are already teaching in a manner consistent with these ideas; two teachers (Cathy Swift and Joe Scott) maintain their traditional style of math teaching with some minor adaptations to ideas in framework; and one teacher (Mark Black) has not responded at all to new ideas. We also learn that three of teachers have never seen the policy, as represented by Mathematics Framework for California Public Schools, K-12 (California State Department of Education, 1985) or by Mathematics: Model Curriculum Guide (California State Department of Education, 1987). One teacher has seen policy but openly disagrees with it, and in one case it is unclear. The materials teachers use also vary. Two teachers work out of a text entitled Math Their Way; one uses another text, Real Math; one works within a district-initiated instructional management system known as Achievement of Basic Skills (ABS) and uses a third text, California edition of Mathematics Unlimited; and with fifth teacher we are only told that he has a new math text. Responses to ideas in Framework include use of manipulatives and groupwork, together with greater attention to multiple representations of mathematical relationships and to problem solving. New content, including estimation and probability, makes an appearance in a few classrooms. But even most innovative teaching among these cases seems a far cry from full vision projected by policy. Here and there outer forms of reform are present, but nowhere is inner intent realized. There is little reflective, exploratory discourse about mathematics, teachers continue to dominate airwaves, groupwork does not promote mutual student engagement with complex problem-solving tasks, and aims of instruction remain focused on supplying students with correct procedures for obtaining right answers. This may appear as a familiar tale about trials and tribulations of implementation, particularly in early stages of a change effort, but buried in these narratives is a success story about instructional policy. The policy, of course, is not new math framework, but direct instructional modelalso known as clinical teaching, ITIP, or Madeline Hunter model-which is omnipresent in teaching described here. In each of these cases, teachers work quite consciously from a set of instructional principles purportedly validated through research and disseminated successfully through inservice education. In light of academy's generally gloomy view of translating new ideas (or policies) into practice, it seems quite remarkable that this model has spread so far, so fast. How ironic, then, that a brief moment's answer, supplied by science through policy,

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