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…

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…

This study addresses a gap in the literature on mathematical modeling education by developing the mathematical modeling knowledge scale (MMKS). The MMKS is a quantitative tool created to assess teachers' knowledge of the nature of mathematical modeling. Quantitative instruments to measure modeling knowledge is scare in the literature partially due…

This article describes the development, initial validation, and psychometric evaluation of the mathematical modeling attitude scale (MMAS). Specifically, both qualitative and quantitative techniques were used to generate relevant items. The MMAS assesses K-12 teachers' attitude toward mathematical modeling and examines their experiences with…

This paper presents the design and development of a rubric for assessing mathematical modelling for mathematical modelling tasks at the secondary level. A rubric was crafted based on the mathematical modelling competencies synthesised by the researchers identified from four sources. The rubric was fine-tuned following an interview with three…

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)…

The axioms of a three-set Guttman simplex model are presented and the effects of relaxing the axioms for one of the three sets are examined. This model can be used to define longitudinal developmental scales. (NSF)

Generating a test from an item bank using a criterion based on classical test theory parameters poses considerable problems. A mathematical model is formulated that maximizes the reliability coefficient alpha, subject to logical constraints on the choice of items. Theorems ensuring appropriate application of the Lagragian relation techniques are…

This paper examines the properties of the Item Efficiency Index proposed by Neill and Jackson (1976; EJ 137 077) for minimum redundancy item analysis. (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…

Samples of 356 management students and 102 managerial employees were used to assess the hierarchical structure of the Negative Affectivity scale of J. Stokes and I. Levin (1990). Data suggest that a higher-order model is the most satisfactory representation of the underlying structure of the scale. (SLD)

An index measuring the degree to which a binary response pattern conforms to some baseline pattern was defined and named the Pattern Conformity Index (PCI). One way of conceptualizing what the PCI measures is the extent to which each individual's particular response pattern contributes to, or detracts from, the overall consistency found in the…

This paper attempts to provide some initial information about the use of a variety of item response theory (IRT) models in the item selection process; its purpose is to compare the information curves derived from the selection of items characterized by several different IRT models and their associated parameter estimation programs. These…