The classic film "Powers of Ten" is often employed to catalyze the building of more accurate conceptions of scale, yet its effectiveness is largely unknown. This study examines the impact of the film on students' concepts of size and scale. Twenty-two middle school students and six science teachers participated. Students completed pre- and…

A method called the Remainder Method is proposed for the calculation of sample quantiles of a given order, for example, quartiles, hexatiles, octatiles, deciles and percentiles assuming that all the observations are distinct. Proof is given for a special case of deciles. The criterion "equisegmentation" is proposed, namely that the number of…

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…

The purpose of this article is to present a collection of problems that allow students to investigate magic squares and Latin squares, formulate their own conjectures about these mathematical objects, look for arguments supporting or disproving their conjectures, and finally establish and prove mathematical assertions. Each problem is completed…

The MathPacks program at the Science Museum of Minnesota provides students with in-depth understanding of real-world applications of mathematics and science. Students measure museum specimens and investigate ratios, patterns, and mapping while simulating the work of scientists.

This article reports on a sample of fourth graders' responses to the 2003 NAEP exam. Readers are invited to analyze the responses to assess students' concepts of fractions.

Has it ever seemed to you that some students are hardwired to dislike math? If so, then here's a book that explains how negative attitudes toward math get established in the brain and what you can do to turn those attitudes around. Math teacher and neurologist Judy Willis gives you over 50 strategies you can use right away in any grade level to:…

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge…

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 investigated the comparative efficiency of Web-based instruction (WBI) and traditional teaching methods on preservice teachers' fraction knowledge. Students' knowledge of fractions was measured using a Fraction Knowledge Test. The test consisted of 32 items and was administered as pre- and posttests to a total of 42 preservice teachers…

The present paper examines the difficulties Greek senior high school students identify in learning Statistics and how these difficulties are related to the course's level of difficulty. Also it examines the difficulties students identify that teachers face while teaching Statistics, their suggestions for changes and how these difficulties and…

The article "Is Google Making Us Stupid?" in last Summer's "Atlantic Monthly," raised a number of provocative, and indeed worrisome, questions about computer usage and cognitive development. For instance, persons with considerable experience of reading for the sake of pleasure report that, after a couple of years using computers a great deal, they…

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…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

The premise underlying this article is that identifying and using the "five practices model" can make discussions of cognitively challenging tasks more manageable for teachers. By giving teachers a roadmap that they can follow before and during whole-class discussions, these practices have the potential for helping teachers more effectively…