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 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…

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…

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)

Across the field of educational assessment the case has been made for alternatives to the multiple-choice item type. Most of the alternative types of items require a subjective evaluation by a rater. The reliability of this subjective rating is a key component of these types of alternative items. In this paper, measures of reliability are…

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…

Urry's procedure for approximating latent trait test models is shown to tend to underestimate item discriminatory power and overestimate item difficulty. A method for correcting these biases is provided, and implications of the procedures are discussed. (Author/JKS)

Conditional item independence, also known as local independence, is necessary for the accurate estimation of item parameters within item response theory (IRT). Given that the condition of local independence will be violated to at least some degree when unidimensional models are used to represent multidimensional data, it is important to study the…

Describes four measures of test unreliability that quantify effects of question selection and guessing, both separately and together--three chosen for immediacy and one for greater mathematical elegance. Quantifies their dependence on test length and number of answer options per question. Concludes that many multiple choice tests are unreliable…

Designing a test using three-parameter item response theory (IRT) is discussed. A brief review of IRT is followed by a discussion of two types of test design: (1) selecting items using confidence envelopes (confidence envelope method); and (2) using item characteristic curves and their confidence intervals (test envelope method). The confidence…

A least-squares solution for the method of paired comparisons is given. The approach provokes a theorem regarding the amount of data necessary and sufficient for a solution to be obtained. A measure of the internal consistency of the least-squares fit is developed. (Author/CTM)

Scoring of response vectors to give maximum test-retest correlation is investigated. A general method is given for finding the best scores, deriving them for the normal factor model, and showing that for a standard model for binary response it is easy to approximate the best scores. (SLD)