The "Building a System of Tens Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific mathematical…

Many teachers experience the tension between using published curriculum materials and teaching in ways that are responsive to children. Teachers are often expected to use a particular mathematics curriculum series, but they still want to be able to build on and connect to children's multiple mathematical knowledge bases (MMKB).…

How can we, as teachers, encourage students to move from drawing geometric objects to constructing them and thereby build their mathematical reasoning skills? One way to encourage students to construct instead of draw shapes and to help students develop more robust understandings of geometric relationships and constructions is to use interactive…

An undergraduate seminar was designed to help preservice teachers focus on students' learning. Preservice teachers planned and conducted weekly tutoring sessions with fourth graders and discussed their experiences in weekly discussions. The author investigated what preservice teachers learned about teaching mathematics from their focus on…

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these…

This study explores the use of video clips from teachers' own classrooms as a resource for investigating student mathematical thinking. Three dimensions for characterizing video clips of student mathematical thinking are introduced: the extent to which a clip provides "windows" into student thinking, the "depth" of thinking…

Students struggling with mathematics may benefit from early interventions aimed at improving their mathematics ability and ultimately preventing subsequent failure. This guide provides eight specific recommendations intended to help teachers, principals, and school administrators use Response to Intervention (RtI) to identify students who need…

This article describes how teachers can use students' conversations to assess their mathematical understanding. The authors draw on their own classroom experiences to show what they learned about planning for future lessons based on discussions in their own classrooms.

The activities contained in this document have been presented at several conference sessions. Participants engaged in hands-on activities for Grades 3 through 8 that utilized a deck of playing cards to meet mathematics content and process standards. Activities included variations of card games, but with a mathematical twist, and other card-based…

Teachers use the word assessment to describe any method of gathering information about student learning. Whether it be formative assessment (intended to guide instructional decisions) or summative assessment (a reflection on the entirety of student learning from prior instruction), teachers are constantly working to identify what their students…

This book provides targeted mathematics instruction for every child. This book combines formative assessment with practical activities to differentiate the elementary classroom. The formative assessments include student work samples at varying levels. The authors: (1) Illustrate the distinction between a "traditional" assessment and an "enhanced"…

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

A study was conducted with forty-seven preservice childhood (elementary) education teachers (42 F, 5 M) enrolled in two mathematics methods classes taught by the same instructor to determine the effect of these college students making curriculum materials appropriate for upper elementary students on the preservice teachers' knowledge of…

The Mathematical Sciences Education Board (MSEB) and the U.S. National Commission on Mathematics Instruction (USNCMI) took advantage of a unique opportunity to bring educators together. In August 2000, following the Ninth International Congress on Mathematics Education (ICME-9) in Makuhari, Japan, MSEB and USNCMI capitalized on the presence of…

This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated…