English Language Learners (ELLs) have an increasing presence in the nations' classrooms. From 1991 to 2004 the number of ELLs nearly doubled in grades K-12. Furthermore, new forms of accountability have school personnel concerned with the progress--or lack of progress--of the ELLs. "Principles and Standards" also reflects this concern: The Equity…

This article features Sweet play math, a "math by the month" activity that involves decorating and making sugar cubes. Teachers may want to substitute straws, paper squares, alphabet blocks, or such commercially made manipulatives as Unifix[R] cubes for the real sweets. Given no allergy concerns, teachers and students alike would enjoy some sweet…

Students from thirteen fifth-grade classrooms from six different elementary schools investigate the preferred escape routes of cockroaches. These identified routes of 90-, 120-, 150-, and 180-degrees are the research findings of Paolo Dominici, an Italian scientist. The students used rubber cockroaches and lizards to map out these escape routes.…

Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the…

During a two-week summer professional development workshop, teams of intermediate-level school teachers and college methods instructors crafted mathematics learning modules--activities, lesson plans, work sheets, and technology-oriented tasks--with the primary goal of strengthening students' understanding of various geometric concepts. They recast…

Online conversations help teachers engage in constructive criticism and attend more carefully to aligning lesson plans with problem solving. This article describes a strategy for using an online discussion board to help teachers evaluate one another's lesson plans. The online peer-review activity suggests that fostering critical pedagogical…

Analyzing student work can help teachers improve the teaching and learning of mathematics. Fortunately, the four authors have experienced professional development that supports teachers' professional growth and provides tools to begin the challenge of analyzing student work. However, as they began to assume leadership roles in their schools and…

Teacher educators are constantly searching for ways to better prepare preservice teachers to enter the education field. One way that has gained prominence in the last twenty years is through examining and discussing authentic student work samples. Research suggests that doing so helps preservice teachers to (1) gain insight into their own beliefs…

David Schwartz's classic book "How Much Is a Million?" can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2-5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of…

This article tells the story of an elementary school principal, a former high school mathematics teacher, who uses the geoboard in her work with a group of fifth-grade students. As the investigation of polygons progresses from symmetry to area to perimeter, hands-on applications of advanced mathematics topics such as the Pythagorean theorem and…

This article describes how Lego robotics, interactive multimedia, and a simple manipulative--string--can be offered to students through coordinated activities to help them build a conceptual foundation for measuring rate. (Contains 5 figures and 3 tables.)

A fifth-grade teacher describes what she learned from closely observing two students with different learning styles and kinds of understandings as they solve traditional fraction problems using a clock face. (Contains 5 figures.)