Based on the generating functions, for any positive integers "n" and "k", identities are established and the explicit formula for a[subscript i](k) in terms of Fibonomial coefficients are presented. The corresponding results are extended to some other famous sequences including Lucas and Pell sequences.

A generation of principals has heard the mantra that they should be instructional leaders, but rarely have they been encouraged to be learning leaders. While an instructional leader pays attention to the planning, implementation, and evaluation of instruction, a learning leader focuses on what is learned and how it is learned. These roles are not…

A group of teachers at Clifford Smart Middle School in Michigan's Walled Lake Consolidated School District have broken free from traditional grading in order to embrace a more meaningful grading practice. Using standards-based grading practices, they believe their grading now accurately communicates to students and parents the student's mastery…

Due to its complex and microscopic nature, genetics is a difficult subject for many learners to conceptually grasp. Graphics, animation and video material can be extremely helpful to their understanding. A wealth of educational online content about genetics has been created over the past decade in the wake of the human genome being sequenced.…

Every autumn, 50 million children load their backpacks and head off to public school. Most children embark on the adventure of a new school year with a mix of anxiety and anticipation. Many excuses are offered for the failures of public education. Still, on their very first day of school, kindergartners and new teachers alike arrive with the…

Using investigations in teaching mathematics has for many years become an established feature of most curricula around the world. Investigations can be a vehicle for enabling children to experience the genuine excitement that comes from mathematical discovery. The true spirit of inquiry and investigation lies in the mind-set that continually asks…

The purpose of this article is to share a learning-cycle sequence of lessons designed to convey the particulate nature of matter through use of physical models and analogical thinking. This activity was adapted from Conceptual Chemistry, a long-running professional development program for teachers of grades 4-9. Conceptual Chemistry's approach is…

In this Brief the authors first report on evidence about the effectiveness (or, unfortunately, in too many cases, the ineffectiveness) of remediation and then provide information about the progression of students through the developmental sequence. They discuss problems associated with the crucial assessments and make a brief statement about…

Landman Library is two-thirds of the way through a three-stage process of migrating to the Koha open-source integrated library system (http://koha-community.org). We are an academic library with roughly 143,000 volumes, six professional librarians, and three support staff. The migration to open source was driven by the desire to access our own…

Response to intervention is meant to be broad-based and preventative. However, as formulated and practiced the approach often is too limited in how it frames what needs to go on to enable learning, engage students, and keep them engaged. In particular, it pays too little attention to the need to strengthen the classroom and schoolwide context in…

The design of problems is crucial for the effectiveness of problem-based learning (PBL). Research has shown that PBL problems have not always been effective. Ineffective PBL problems could affect whether students acquire sufficient domain knowledge, activate appropriate prior knowledge, and properly direct their own learning. This paper builds on…

This article gives a general overview of an alternative instructional sequence that can be used to teach integer concepts and operations. The sequence follows three heuristics from Realistic Mathematics Education (RME) that encourage curricula to be reinforced with real-world applications (financial net worth): move students gradually, yet…

Despite all the speeches, articles, and meetings about data-based instructional decision making, the author's observation after more than 20 years of working with middle and high school teams is that teachers and administrators often make important instructional decisions on the basis of historical precedent, anecdotal information, experience, or…

Too many educators avoid using data when making decisions because they believe it is too time-consuming to do so. The authors present five steps that make it easier to use data in making school decisions. The first step is to review school improvement plan to identify the most salient issues a school wants to improve. The second step is to…

The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…