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…

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…

An interpretation is provided of the philosopher L. Wittgenstein's analyses of mental states. The theoretical implications of these analyses for cognitive development and qualitatively oriented researchers are discussed. The mental states examined are: (1) pain; (2) remembering; (3) calculating/adding; (4) following a rule; and (5) reading.…

The usefulness of joint and conditional maximum-likelihood is considered for the Rasch model under realistic testing conditions in which the number of examinees is very large and the number is items is relatively large. Conditions for consistency and asymptotic normality are explored, effects of model error are investigated, measures of prediction…

Criteria for prediction of multinomial responses are examined in terms of estimation bias. Logarithmic penalty and least squares are quite similar in behavior but quite different from maximum probability. The differences ultimately reflect deficiencies in the behavior of the criterion of maximum probability.

It is common to assume during statistical analysis of a multiscale assessment that the assessment has simple structure or that it is composed of several unidimensional subtests. Under this assumption, both the unidimensional and multidimensional approaches can be used to estimate item parameters. This paper theoretically demonstrates that these…