Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

Students need to be actively engaged to learn--intellectually curious, physically active, and emotionally involved in collaborative work that builds their capacity for empathy. What can teachers do to instill these elements in the classroom? "Active Learning: 40 Teaching Methods to Engage Students in Every Class and Every Subject" is the…

Students learn to read and write best when their teachers balance literacy instruction. But how do you strike the "right" balance of skills and knowledge, reading and writing, small and whole group instruction, and direct and dialogic instruction, so that all students can learn to their maximum potential? The answer lies in the…

Motivating adolescents to learn can be a challenge! Often distracted and easily bored, these kids are also critical thinkers capable of thriving in the classroom while learning 21st century skills. How do we hold their attention and develop their abilities? Research shows that all students--regardless of learning style, disability category, or…

This article describes the theoretical framework, research base, structure, and content of a video-based professional development program implemented during 2 consecutive years with sixth-grade mathematics teachers from five low-performing schools. First, difficulties teachers encountered in responding to video-based prompts during the 1st year…

This article describes the process of design and implementation of a hands-on unit on fractions in the sixth grade. The fraction unit, taught by a classroom teacher with the aid of a university professor, uses pattern blocks to help students develop conceptual understanding of fractions. Student misunderstandings and outcomes are presented, as…

Using collaborative critical reflection as an index, this study examines the asynchronous and face-to-face discourse of 28 suburban Chicago elementary teachers developing problem based learning (PBL) curriculum. Statistical analysis of the corpus produced by the 2 mediums shows that the asynchronous online network emerges as the medium of choice…

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…