This article describes a process called "Backing Up" which is a way to preassess student understanding of a topic and gauge student readiness to move forward in the learning process. This process of backing up begins with using responses to a word problem to identify categories of students' understandings in relation to the expectations…

An operational understanding of the equal sign can hinder learning its relational meaning. After providing examples that illustrate the folly of expecting students who know the operational meaning of the equal sign to intuit the sign's relational meaning, this article provides teachers with strategies that will help them effectively introduce…

Common Core State Standards for Mathematics (CCSSM) is different from the objectives that many teachers have previously experienced in their state frameworks. Although the mathematical topics of the two may be the same, the mathematical expectations within the Standards require a deeper understanding by teachers and students. In this article, the…

The advance of technology has caused many educators to question the time and energy expended for students to master the pencil-and-paper computation skills embodied in the long-division algorithm. In today's world, this mastery is truly a questionable goal. But understanding the conceptual infrastructure of the algorithm will add to students…