Algebra teachers find themselves overwhelmed by the sheer volume of information that they have to teach their students. One way to address this issue is to have teachers teach for understanding by focusing on concepts. In this article, I share how language can help uncover the core ideas that define the concept of function and share activities…

In this article, the author reflects on her session at the 2006 conference, including the learning styles and strategies she observed. In her session, they explored some of the more unusual aspects of convex polyhedra (with regular faces), including the notions of "valence" and "species". Although the session was about shape and space, there was…

This article arises from a study whose overall purpose was to investigate the relationship between Colombian mathematics teachers' conceptions of "beginning algebra" and their conceptions of their "own" teaching practices. The teachers' understandings of their teaching practices were explored with a view to unravelling their…

With Simson's 1753 paper as a starting point, the current paper reports investigations of Simson's identity (also known as Cassini's) for the Fibonacci sequence as a means to explore some fundamental ideas about recursion. Simple algebraic operations allow one to reduce the standard linear Fibonacci recursion to the nonlinear Simon's recursion…

This article presents a rich geometry problem and discusses its solution. A variety of mathematically correct justifications for this answer are provided. (Contains 2 figures.)

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies…

As expectations for students to meet high academic standards have risen over the past two decades, so have the expectations for students to complete, and excel in, more rigorous mathematics courses. Once a course reserved only for the college-bound, algebra is now a graduation requirement for all California students as well as an early…

This paper addresses methodological issues arising from an experimental study of North Carolina's Early College High School Initiative, a four-year longitudinal experimental study funded by Institute for Education Sciences. North Carolina implemented the Early College High School (ECHS) Initiative in response to low high school graduation rates.…

Although an understanding of radiometric dating is central to the preparation of every geologist, many students struggle with the concepts and mathematics of radioactive decay. Physical demonstrations and hands-on experiments can be used to good effect in addressing this teaching conundrum. Water, heat, and electrons all move or flow in response…

This mixed methods study explores the relationship between ninth grade academy in South Carolina public high schools and student achievement in 84 high schools matched on poverty index and school size. The 2007 and 2008 South Carolina school report card data were used to gather information about the individual schools. The presence or absence of a…

In the No Child Left Behind Act (NCLB), Congress called for the U.S. Department of Education (ED) to conduct a rigorous study of the conditions and practices under which educational technology is effective in increasing student academic achievement. A 2007 report presenting study findings for the 2004-2005 school year, indicated that, after one…

The watchword of this year's Brown Center Report is caution--caution in linking state tests to international assessments--"benchmarking" is the term--caution in proceeding with a policy of "algebra for all eighth graders," caution in gleaning policy lessons from the recent progress made by urban schools. State and local budget…

The focus of this research is to develop an initial framework for assessing and interpreting students' level of understanding of mathematical equivalence. Although this topic has been studied for many years, there has been no systematic development or evaluation of a valid measure of equivalence knowledge. A powerful method for accomplishing this…

This study focused on examining the effect of two alternative school types on student success in Mississippi. To determine alternative school type, alternative program directors self-reported program design, and schools were divided into two groups. Type I schools were defined as "punitive-based" programs in which students receive…

This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers' pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete…