Partially automated assessment is implemented via the 'Printable worksheet' mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct…

In this article, we extend Liao's test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be…

The concept of financial literacy, which has become popular as a 21st-century skill, is also a new field for mathematics education. Financial literacy, which has taken place in PISA [Program for International Student Assessment] since 2012, has not only been presented as a separate course and has also increased in density in related courses such…

Despite the call for an argument-based approach to validity over 25 years ago, few examples exist in the published literature. One possible explanation for this outcome is that the complexity of the argument-based approach makes implementation difficult. To counter this claim, we propose that the Assessment Triangle can serve as the overarching…

In this article we propose a framework for reporting mathematics results from national assessment surveys (NAS) such that effective use of the resulting reports can enhance teaching and learning. We explored literature on factors that may contribute to non-utilisation of assessment data as a basis for decision-making. In the context of South…

Educators are being encouraged to shift their instructional paradigm from teacher-centered to learner-centered through the use of technology. For online courses, legacy learning management products originally designed to support and deliver teacher-centered instruction may represent a constraint to implementing the learner-centered paradigm. Yet,…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

Developing a new assessment requires the expertise of both content experts and assessment specialists. Using the example of an assessment developed for Ontario's Colleges Mathematics Assessment Program (CMAP), this article (1) describes the decisions that must be made in developing a new assessment, (2) explores the complementary contributions of…

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K-12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem…

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

To address whether or not modifications in test administration influence item functioning for students with disabilities on a high-stakes statewide problem-solving assessment, a sample of 868 students (with and without disabilities) from 74 Georgia schools were randomly assigned to one of three testing conditions (resource guide, calculator, or…

In this article, we highlight the need for a precisely defined construct in score-based validation and discuss the contribution of cognitive theories to accurately and comprehensively defining the construct. We propose a framework for integrating cognitively based theoretical and empirical evidence to specify and evaluate the construct. We apply…

This paper introduces a utilitarian confidence testing statistic called Risk Inclination Model (RIM) which indexes all possible confidence wagering combinations within the confines of a defined symmetrically point-balanced test environment. This paper presents the theoretical underpinnings, a formal derivation, a hypothetical application, and…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…