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…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

Each year, Montana students participate in testing as part of the state's assessment program. This past spring, students in grades 4, 8, and 10 took Montana Comprehensive Assessment System (MontCAS) tests in reading and mathematics. These tests serve as an important measure of student achievement for the state's accountability system. Results from…

Each year, South Carolina students participate in testing as part of the South Carolina assessment program. Students in grades 3 through 8 take the Palmetto Achievement Challenge Tests (PACT) in English/Language Arts and Mathematics. Students in grade 10 take the High School Assessment Program (HSAP) in English/Language Arts and mathematics. These…