In the American Federation of Teachers' Thinking Mathematics collaboration, teachers have become equal partners with researchers to create staff development aimed at mathematics instruction. Researchers and 5 visiting practitioners have cooperated to create mathematics foundations materials conceptualized in 10 guiding principles for mathematics…

Describes the Philadelphia Public Schools' formative testing program, used to diagnose students' difficulties under mastery learning, especially in mathematics. Discusses in turn the classroom, school, and district aspects of the program and summarizes the program's essential features. A full-page chart outlining aids and hindrances to formative…

Policy initiatives from Kentucky to California are espousing curriculum based on NCTM-backed core concepts that students understand through induction rather than memorization, teaching based on guided mastery rather than didactic instruction, and assessment that is open-ended rather than machine-scorable. This article highlights obstacles to…

At a suburban school near Atlanta, Georgia, three different types of tutors (adult, cross-age, and peer) helped resolve the problem of continued math failure among at-risk elementary students. Tutors filled in gaps and clarified critical misunderstandings when students were unsure of math processes. Using adult tutors as mentors motivated some…

While working to reconcile developmentally sound curricula and instruction with district and state requirements, faculty at a Dalton, Georgia, primary school were hindered by mandated standardized tests. Since uncovering several negative aspects of such testing, faculty have been struggling to teach a developmental and test-driven math program…

Thinking Mathematics is an American Federation of Teachers program that united teachers and researchers in face-to-face dialogue aimed at translating mathematics research into professional development material for teachers. Teachers played an increasingly prominent role, evolving into the primary decision makers about content, style, and the…

Describes a research project in a third-grade classroom that explored a spontaneous, bottom-up approach to developing and testing performance measures. After establishing project goals for reading and math instruction, the 14 participating teachers worked with University of Colorado researchers to develop summarizing activities, open-ended math…

The National Council of Teachers of Mathematics recently published two documents emphasizing solving nonroutine problems in meaningful contexts. "Curriculum and Evaluation Standards for School Mathematics" (1989) describes what students should know and a framework for developing appropriate curricula. "Professional Standards for…

To make sense of the complex information taught in the upper elementary grades -- and to understand the language that increasingly appears in high-stakes tests--students must be proficient in academic English. English language learners are at a serious disadvantage. Two word problems in mathematics illustrate the difficulties that these students…