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…

Designing a theory-based assessment with sound psychometric qualities to measure a higher-order cognitive construct is a highly desired yet challenging task for many practitioners. This paper proposes a framework for designing a theory-based assessment to measure a higher-order cognitive construct. This framework results in a modularized yet…

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)…

While linear programming is a common tool in business and industry, there have not been many applications in educational assessment and only a handful of individuals have been actively involved in conducting psychometric research in this area. Perhaps this is due, at least in part, to the complexity of existing software packages. This article…

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.)

This second volume of the 31st annual proceedings of the International Group for the Psychology of Mathematics Education conference presents research reports for author surnames beginning Alc- through Hal-. Reports include: (1) How Do Your Students Think about Proof? A DVD Resource for Mathematicians (Lara Alcock); (2) Teachers' Conceptions of…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…