The Council of Chief State School Officers (CCSSO), through its Interstate Teacher Assessment and Support Consortium (InTASC), offers this set of combined resources that define and support ongoing teacher effectiveness to ensure students reach college and career ready standards. This document includes the "InTASC Model Core Teaching…

The process of instructional design has parallels in other design disciplines. Software design is one that has experienced intense attention in the last 30 or so years, and many lessons learned there can be applied to ID. Using software design as a springboard, this concept paper seeks to propose a new approach to ID. It suggests that…

This article, which describes integrating virtual manipulatives with the teaching of probability at the elementary level, puts a "virtual spin" on the teaching of probability to provide more opportunities for students to experience successful learning. The traditional use of concrete manipulatives is enhanced with virtual coins and spinners from…

Charles Dodgson (Lewis Carroll) discovered a "curious" method for computing determinants. It is an iterative process that uses determinants of 2 x 2 submatrices of a matrix to obtain a smaller matrix. When the process ends, the result is the determinant of the original matrix. This article discusses both the algorithm and what may have led Dodgson…

The geometric problem of finding the number of normals to the parabola y = x[squared] through a given point is equivalent to the algebraic problem of finding the number of distinct real roots of a cubic equation. Apollonius solved the former problem, and Cardano gave a solution to the latter. The two problems are bridged by Neil's (semi-cubical)…

In this article, the authors consider the exponential curves y = ba[superscript x] where a, b [is a member of] R, a [greater than] 0, a [not equal to] 1, and b [not equal to] 1. The authors show that by fixing one of a or b the points (x[subscript 0],y[subscript 0) of tangency of y = ba[superscript x] and the line passing through the origin lie on…

In this article, the author presents a six by six array in which individuals can obtain 182 in total even if they use a different set of numbers. The author then explain why this is possible. The author uses the k-translation of a sequence for this equation. (Contains 8 figures, 2 tables and 6 footnotes.)

In this article, we show how "Laplace Transform" may be used to evaluate variety of nontrivial improper integrals, including "Probability" and "Fresnel" integrals. The algorithm we have developed here to evaluate "Probability, Fresnel" and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals…

In this article, the author relates how he found "MT202" full of interest and how he was fascinated by the number of threads he found running through it. He then describes how he weaved together these threads. (Contains 1 table.)

Two problems in projectiles are discussed which generate interesting loci.

The aim of this paper is to present a simple way of establishing the general solution of the linear, second-order differential equation without using complex numbers.

A technique is presented, which is different from the well-known Ferrari's method, to solve a general quartic equation. Formulae for the four roots of quartic are derived. A numerical example verifies the formulae obtained.

Action research places a powerful tool for school improvement in the hands of teachers. By highlighting the outcomes that are possible and presenting clear steps in the research process, this book is one to encourage anyone who is seeking to implement evidence-based school improvement. Eileen Piggot-Irvine uses her Problem Resolving Action…

In the past, if a question is asked of a student, and that student needed a few minutes to think, that student's thinking would be interrupted by somebody else who'd be shouting out. Now, teachers at St. Johnsbury School in Vermont are really focusing on think time for students and really working with other students in the classroom to be…

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…