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…

Teacher, peer, and student reports of the quality of the teacher-student relationship were obtained for an ethnically diverse and academically at-risk sample of 706 second- and third-grade students. Cluster analysis identified four types of relationships based on the consistency of child reports of support and conflict in the relationship with…

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…

This book re-examines the dichotomy between the everyday and the disciplinary in mathematics and science education, and explores alternatives to this opposition from points of view grounded in the close examination of complex classroom events. It makes the case that students' everyday experience and knowledge in their entire manifold forms matter…