A learning trajectory describes the progression of student thinking and strategies over time in terms of sophistication of both conceptual understanding and procedural fluency. Currently, learning trajectories exist in the research literature for many mathematical domains, including counting, addition and subtraction, multiplicative thinking,…

Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

A team of teachers from the same New York City public school met to discuss and compare the Common Core State Standards for Mathematics (CCSSM) to their current math curriculum. The group consisted of four kindergarten teachers, a representative from the first-grade teaching team, and the school's math coach. During the first meeting, the…

High academic standards are an important first step in ensuring that all Alaska's students have the tools they need for success. These standards reflect the collaborative work of Alaskan educators and national experts from the nonprofit National Center for the Improvement of Educational Assessment. Further, they are informed by public comments.…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Fourth-grade students in Title I mathematics took 40-problem tests to determine types of persistent errors made in addition and subtraction. Tests, administered to 117 students (addition) and 104 students (subtraction), were analyzed for basic fact, random, or procedural errors. Findings are reported and discussed, and recommendations for…

An intensive 10-day peer tutor training component is described as a key element in the success of a peer tutoring program in mathematics for 21 low-achieving second graders. Results suggest the program's effectiveness in increasing the speed and accuracy of responses on written speed tests of addition facts. (Author/JW)

Describes a form of adaptive communication, referred to as single switch technology, as a method for assessing and developing mathematics skills of speech and motor disabled students. Provides a BASIC program to illustrate a basic single switch mathematics program. (MDH)