Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in…

Across the world, standards and practices for preparing teachers of mathematics emphasize the importance of math modeling (MM) in developing students' mathematical thinking. The aim of this research study was to develop the Mathematical Modeling Knowledge Scale (MAMKS), capable of determining preservice teachers' (PSTs') knowledge of MM. The study…

Mathematics modelling is a vital competency for students of all ages. In this study, we aim to fill the research gap about valid and reliable tools for assessing and grading mathematical modeling problems, particularly those reflecting multiple steps of the modelling cycle. We present in this paper the design of a reliable and valid assessment…

Educational reform priorities such as emphasis on quantitative modelling (QM) have positioned undergraduate biology instructors as designers of QM experiences to engage students in authentic science practices that support the development of data-driven and evidence-based reasoning. Yet, little is known about how biology instructors adapt to the…

A test battery with two different levels of adaptation is presented: a within-subtest level for the selection of the items in the subtests and a between-subtest level to move from one subtest to the next. The battery runs on a two-level model consisting of a regular response model for each of the subtests extended with a second level for the joint…

While research suggests that mathematical modeling is accessible to elementary grade students, questions remain about how to assess modeling competency. Our research addresses this need through the systemic design and empirical testing of a Mathematical Modeling Student Assessment (MMSA) for elementary grades 3 through 5. Research questions focus…

This monograph provides an epistemological rational for the Accumulative Manifold Validation Analysis [also referred by the acronym "AMOVA"] statistical methodology designed to test psychometric instruments. This form of inquiry is a form of mathematical optimization in the discipline of linear stochastic modelling. AMOVA is an in-depth…

This study is a pre test-post-test experimental control group design having a goal to analyze the role of problembased learning on students' mathematical problem-solving ability (MPSA) and self-confidence (MSC). The study involves 66 tenth grade students, a mathematical problem-solving test, a mathematical self-confidence scale, and perception of…

The aim of this paper is to present a shortened version of the SIS (support intensity scale) obtained by the application of mathematical models and instruments, adopting special algorithms based on the most recent developments in artificial adaptive systems. All the variables of SIS applied to 1,052 subjects with ID (intellectual disabilities)…

A definition of test validity as the ratio of a covariance term to a variance term, analogous to the classical definition of test reliability, is proposed. When error scores on distinct tests are uncorrelated, the proposed definition coincides with the usual one, but it remains meaningful when error scores are correlated. (Author/BW)

This paper considers some appropriate and inappropriate uses of coefficient kappa and alternative kappa-like statistics. Discussion is restricted to the descriptive characteristics of these statistics for measuring agreement with categorical data in studies of reliability and validity. (Author)

A procedure for inferring the validity of a selection test as a predictor of some criterion when the available data are limited due to prior selection is described. (Author/JKS)

A mathematical link between test reliability and test validity is derived, taking into account the correlation between error scores on a test and error scores on a criterion measure. When this correlation is positive, the "paradoxical" nonmonotonic relation between test reliability and test validity occurs universally. (Author/BW)

Adequacy coefficients can be derived by calculating the cosines of the angles between factors' actual and theoretically expected locations within factor space. The use of adequacy coefficients during instrument development is discussed. The development of an instrument to measure thinking interests provides a heuristic framework for the…

A simulation study compared the performance of the Mann-Whitney "U" test, Student's "t" test, and the alternate (separate variance) "t" test for two mutually independent random samples from normal distributions, with both one-tailed and two-tailed alternatives. Type I error probabilities were computed with equal and…