Editorial

Demonstrates the value of a recent graphing innovation, the hat plot, a simplified version of the box-and-whisker plot, in representing and interpreting data sets. Students used a software tool to demonstrate understanding of data representation and they were able to effectively communicate group characteristics of data sets.

Describes a unique task structure that helps foster classroom discourse and reveals students' mathematical conceptions. The example involves a proportional reasoning task set within a best-buy context. Three versions of the task are provided which encourage students to consider the meaning of ratios in multiple ways. Several student responses are provided and analyzed.

Describes the advocacy work of NCTM and the input that NCTM has provided to policymakers. In addition, the roles of the Principles and Standards for School Mathematics and the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics are addressed.

An illustration of how the difference and completion (or missing addend) interpretations of subtraction may be used with chips of two colors to understand subtracting negative and positive numbers. Several visual representations are provided.

Describes fifth- and sixth-grade teachers involved in lesson study, in which they collaboratively planned, observed, and analyzed a lesson using multiple representations to teach decimal number sense. The lesson described uses 10X10 grids to represent decimals as well as a game to practice adding and subtracting.  The setting for this lesson study included many ELL and special needs students so the authors describe how to build representations and vocabulary with these students.