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…

The purpose of this descriptive study was to create and test questions on stoichiometry with number ratios for quick mental calculations and to identify students' problem-solving strategies. The present study was a component of a more comprehensive investigation in which 7,441 German senior high school students were asked to work on 154 test items…

Presents five activities focusing on mental computation and estimation for the K-3, 3-5, 4-6, and 6-8 grade levels that require the student, acting as a judge, to review solutions to problems and to pronounce and justify a verdict. Provides suggested materials, questions, possible extensions, answers, and worksheets for each activity. (MDH)

In this paper, formulas for computing the weights that maximize the reliability of a test with multiple parts are derived using a congeneric model. A direct derivation for the three-part test and case and a two-step derivation for the n-part case are presented, and results for these two approaches are shown to be consistent for the three-part…

This book addresses different types of thinking, including critical, creative, and analytical, and presents a variety of problem-solving strategies, along with specific ways they can be taught to students. The main emphases of the book are thinking and mathematics, problem solving, and the application of computational skills. The problem-solving…

Computer task automation is part of the natural progression of encoding information. This thesis considers the automation process to be a question of whether it is possible to automatically learn the encoding based on the behavior of the system to be described. A variety of representation languages are considered, as are means for the learner to…