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…

Chalmers recently published a critique of the use of ordinal a[alpha] proposed in Zumbo et al. as a measure of test reliability in certain research settings. In this response, we take up the task of refuting Chalmers' critique. We identify three broad misconceptions that characterize Chalmers' criticisms: (1) confusing assumptions with…

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 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…

Fuzzy-set qualitative comparative analysis (fsQCA) has become one of the most prominent methods in the social sciences for capturing causal complexity, especially for scholars with small- and medium-"N" data sets. This research note explores two key assumptions in fsQCA's methodology for testing for necessary and sufficient…

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 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 subject of the research is to build methodologies to evaluate the student knowledge by testing. The author points to the importance of feedback about the mastering level in the learning process. Testing is considered as a tool. The object of the study is to create the test system models for defence practice problems. Special attention is paid…

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…

Previous studies have suggested that dorsal hippocampal areas CA3 and CA1 are both involved in representing sequences of events that compose unique episodes. However, it is uncertain whether the contribution of CA3 is restricted to spatial information, and it is unclear whether CA1 encodes order per se or contributes by an active maintenance of…

The idea of test consistency is illustrated, with reference to two sets of test scores. A mathematical model is used to explain the relative consistency and relative inconsistency of measurements, and a means of indexing reliability is derived using the model. Practical aspects of estimating reliability are considered. (TJH)

A necessary and sufficient condition for a perfectly homogeneous test in the sense of Loevinger is stated and proved. Using this result, a formula for computing the maximum possible KR-20 when the test variance is assumed fixed is presented. A new index of test homogeneity is also presented and discussed. (Author/BW)

Simulated data based on five test score distributions indicate that a slight modification of the asymptotic normal theory for the estimation of the p and kappa indices in mastery testing will provide results which are in close agreement with those based on small samples from the beta-binomial distribution. (Author/BW)