In this paper, we propose a novel conceptual framework tailored for modeling the meaning of mathematical concepts in university-level mathematics, addressing their rigorous nature and their relationships with related concepts as well as interpretations in various contexts. Within this framework, we present a model of meaning for the concepts of…

This study analyzed the mediating role that implicit theories of intelligence and academic self-efficacy may play in the relationship between psychopathology and mathematical performance. The sample consisted of 838 students from first and second year of high school. A numerical calculation test was applied, followed by psychopathology self-report…

Diagnostic classification models (DCMs) are psychometric models designed to classify examinees according to their proficiency or nonproficiency of specified latent characteristics. These models are well suited for providing diagnostic and actionable feedback to support intermediate and formative assessment efforts. Several DCMs have been developed…

Diagnostic classification models (DCMs) are psychometric models designed to classify examinees according to their proficiency or nonproficiency of specified latent characteristics. These models are well suited for providing diagnostic and actionable feedback to support intermediate and formative assessment efforts. Several DCMs have been developed…

This study investigates the effect of 5E learning model enriched with coding (5EC), gender and their interaction on 4th grade students' mathematics achievements and permanence of their learning. It also examines the effect of the 5EC on participants' attitudes towards mathematics. The study group consists of 119 students. Mathematics achievement…

Correct specifications of hierarchical attribute structures in analyses using diagnostic classification models (DCMs) are pivotal because misspecifications can lead to biased parameter estimations and inaccurate classification profiles. This research is aimed to demonstrate DCM analyses with various hierarchical attribute structures via Bayesian…

Multiple-choice (MC) items are widely used in educational tests. Distractor analysis, an important procedure for checking the utility of response options within an MC item, can be readily implemented in the framework of item response theory (IRT). Although random guessing is a popular behavior of test-takers when answering MC items, none of the…

We conducted an experiment to determine the impact of short-term pressure on 1,228 Grade 8 students' outcomes when performing simple math exercises. We required all students to complete 100 simple math questions for 90 seconds. We analysed students' results and then divided them into three groups: (i) a control group who did nothing; (ii) a group…

A basic mental model (BMM--in German 'Grundvorstellung') of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific…

Knowledge tracing (KT) is a method to evaluate a student's knowledge state (KS) based on their historical problem-solving records by predicting the next answer's binary correctness. Although widely applied to closed-ended questions, it lacks a detailed option tracing (OT) method for assessing multiple-choice questions (MCQs). This paper introduces…

This article proposes a class of cognitive diagnosis models (CDMs) for polytomously scored items with different link functions. Many existing polytomous CDMs can be considered as special cases of the proposed class of polytomous CDMs. Simulation studies were carried out to investigate the feasibility of the proposed CDMs and the performance of…

A psychological framework for different types of items commonly used with mixed-format exams is proposed. A choice model based on signal detection theory (SDT) is used for multiple-choice (MC) items, whereas an item response theory (IRT) model is used for open-ended (OE) items. The SDT and IRT models are shown to share a common conceptualization…

This study aimed to address the need for a comprehensive assessment tool to evaluate the mathematical abilities of first-grade students through cognitive diagnostic assessment (CDA). The primary challenge involved in this endeavor was to delineate the specific cognitive skills and sub-skills pertinent to first-grade mathematics (FG-M) and to…

Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…

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…