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…

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…

Educational strategies have evolved over the years, due to research breakthroughs and the application of technology. By using the latest learning innovations, curriculum and instructional design can be enhanced and strengthened. The "Handbook of Research on Driving STEM Learning with Educational Technologies" is an authoritative…

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)…

This article describes the use of a Dutch pyramid model that may help teachers design assessment problems that go beyond reproduction and need mathematization, generalization, and insight. (Contains 4 figures.)

A procedure for the sequential optimization of the calibration of an item bank is given. The procedure is based on an empirical Bayes approach to a reformulation of the Rasch model as a model for paired comparisons between the difficulties of test items in which ties are allowed to occur. First, it is indicated how a paired-comparisons design…

Since 1985 several procedures for computerized test construction using linear programing techniques have been described in the literature. To apply these procedures successfully, suitable item banks are needed. The problem of designing item banks based on item response theory (IRT) is addressed. A procedure is presented that determines whether an…

Linear programming models with 0-1 variables are useful for the construction of tests from an item bank. Most solution strategies for these models start with solving the relaxed 0-1 linear programming model, allowing the 0-1 variables to take on values between 0 and 1. Then, a 0-1 solution is found by just rounding, optimal rounding, or a…

A "maximin" model for item response theory based test design is proposed. In this model only the relative shape of the target test information function is specified. It serves as a constraint subject to which a linear programming algorithm maximizes the information in the test. In the practice of test construction there may be several…

One means of learning about the processes operating in a multiple choice test is to include some test items, called nonsense items, which have no correct answer. This paper compares two versions of a mathematical model of test performance to interpret test data that includes both genuine and nonsense items. One formula is based on the usual…

Research related to the multiple choice test item is reported, as it is conducted by educational technologists in Japan. Sato's number of hypothetical equivalent alternatives is introduced. The based idea behind this index is that the expected uncertainty of the m events, or alternatives, be large and the number of hypothetical, equivalent…

The application of mathematical programming techniques is extended to the construction of measurement instruments in generalizability theory. Key concepts in generalizability theory are explained and a description is given of: (1) the one-facet crossed design; (2) the two-facet crossed design; and (3) a two-facet nested design. The optimization of…

Two optimalization models for the construction of tests with a maximal value of coefficient alpha are given. Both models have a linear form and can be solved by using a branch-and-bound algorithm. The first model assumes an item bank calibrated under the Rasch model and can be used, for instance, when classical test theory has to serve as an…

A multi-faceted model for the selection of answers for multiple-choice tests was developed from the findings of a series of exploratory studies. This model implies that answer selection should be curvilinear. A series of models were tested for fit using the chi square procedure. Data were collected from 359 elementary school students ages 9-12.…

Four discussions of test construction based on item response theory (IRT) are presented. The first discussion, "Test Design as Model Building in Mathematical Programming" (T. J. J. M. Theunissen), presents test design as a decision process under certainty. A natural way of modeling this process leads to mathematical programming. General…