This paper focuses on using technology to support mathematics instruction. Technologies such as computers and calculators are widely used in the teaching of mathematics. The educators advocate the use of these tools to reduce tiresome computations and tasks so that class time can be more effectively used for learning mathematics. The purpose of…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

Background: Teachers' work overload has been the subject of intense research, and the results of these studies show that a substantial proportion of teachers perceive their job as very stressful. Aims: To investigate how different formulations of high demands and low decision latitude was related to teachers' burnout, and to estimate the possible…

The procedures required to obtain the approximate posterior standard deviations of the parameters in the three commonly used item response models for dichotomous items are described and used to generate values for some common situations. The results were compared with those obtained from maximum likelihood estimation. It is shown that the use of…

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

This paper describes the construction of a slide-rule computer that allows one to quickly determine magnitudes of several effects that result from the detonation of a nuclear device. Suggestions for exercises are also included that allow high school and college-level physics students to explore scenarios involving these effects. It is hoped that…

In this article, the author describes integrated science and mathematics activities developed for fourth-grade students to explore and investigate three-dimensional geometric shapes, Bernoulli's principle, estimation, and art with and through bubbles. Students were engaged in thinking and reflection on the questions their teachers asked and were…

The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain…

This article investigates several methods of identifying individual guessers from their response data. Both the posterior probability method and the likelihood ratio method are based on the two-state mixture modeling approach to response times. The accuracy method is based on response accuracy data. Results from the simulation study showed that…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Different computational tools may offer teachers and students distinct opportunities in representing, exploring and solving mathematical tasks. In this context, we illustrate that the use of dynamic software (Cabri Geometry) helped high school teachers to think of and represent a particular task dynamically. In this process, the teachers had the…

Risks of life on the street caused by inclement weather, harassment, and assault threaten the unsheltered homeless population. We address some challenges of enumerating the street homeless population by testing a novel capture-recapture (CR) estimation approach that models individuals' intermittent daytime visibility. We tested walking and…

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

Hydrogen activation on the (100) surface of MoS[2] structures was investigated by means of density functional theory calculations. Linear and quadratic synchronous transit methods with a conjugate gradient refinement of the saddle point were used to localize transition states. The calculations include heterolytic and homolytic dissociation of…