In a German out-of-school laboratory, 293 medium-achieving 10th-grade students participated in a lesson unit about gene technology. They were divided into two groups (I-1, I-2), both of which followed the same hands-on lesson procedure. Students within I-2 were additionally confronted with alternative conceptions to central issues of the specific…

According to this author, when it comes to data-based decision making, many educators are looking in the wrong place. This is one reason why this potentially powerful practice has too often under-delivered. Many schools rush headlong into analyzing data without considering if the data they are reviewing is worth the effort, if other data might…

Techniques are developed for approximation and exact computation of the asymptotic limit of the item parameter estimates obtained by application of joint maximum-likelihood estimation to the Rasch model.

Two methods are presented for counting small "essentially different" sudoku puzzles using elementary group theory: one method (due to Jarvis and Russell) uses Burnside's counting formula, while the other employs an invariant property of sudoku puzzles. Ideas are included for incorporating this material into an introductory abstract algebra course.…

Are small and large numbers represented similarly or differently on the mental number line? The size effect was used to argue that numbers are represented differently. However, recently it has been argued that the size effect is due to the comparison task and is not derived from the mental number line per se. Namely, it is due to the way that the…

Uniformity, that is, equiprobability of all available options is central as a theoretical presupposition and as a computational tool in probability theory. It is justified only when applied to an appropriate sample space. In five studies, we posed diversified problems that called for "unequal" probabilities or weights to be assigned to the given…

In thinking about how best to support the changes in scholarly and scientific work and also to accelerate these changes as a way of advancing scientific progress, science funding agencies began speaking about the need to systematically invest in what they called "cyberinfrastructure." This included not just information technologies but…

In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

One of the major objectives of large-scale educational surveys is reporting trends in academic achievement. For this purpose, a substantial number of items are carried from one assessment cycle to the next. The linking process that places academic abilities measured in different assessments on a common scale is usually based on a concurrent…

Students with specific learning disabilities (SLD) tend to have difficulty with reasoning and communication across many mathematical domains. The purpose of this study was, through open response questions, to examine the mathematics reasoning performance of 4 th grade students with SLD. Using the learner centered principles outlined by the…

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

Apprentice and trainee data are reported by the State and Territory Training Authorities to the National Centre for Vocational Education Research (NCVER) on a quarterly basis, starting at the September quarter of 1994. The set of data submitted that quarter is referred to as Collection 1. The sets of data submitted in subsequent quarters are…

In order to ease the burden of electronic note entry on physicians, electronic documentation support tools have been developed to assist in note authoring. There is little evidence of the effects of these tools on attributes of clinical documentation, including document quality. Furthermore, the resultant abundance of duplicated text and…

As an undergraduate in the 1960s, the author mostly used a slide rule for calculations and a Marchant-brand motor-operated mechanical calculator for statistics. This was after an elementary education replete with learning multiplication tables and taking speed and accuracy tests in arithmetic. Times have changed and assuming even basic calculation…