This study presents a comparative analysis of classical reliability measures, including Cronbach's alpha, test-retest, and parallel forms reliability, alongside modern psychometric methods such as the Rasch model and Mokken scaling, to evaluate the reliability of C-tests in language proficiency assessment. Utilizing data from 150 participants…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

The quest for determining the degree of learning difficulty associated with different types of categories has been instrumental in our understanding of human categorization behavior and, more broadly, human generalization. For instance, we now know that the topological nature of the dimensions (e.g., whether these are integral or separable) that…

This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…

Large scale international assessments depend on invariance of measurement across countries. An important consideration when observing cross-national differential item functioning (DIF) is whether the DIF actually reflects a source of bias, or might instead be a methodological artifact reflecting item response theory (IRT) model misspecification.…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

An Angoff standard setting study generally yields judgments on a number of items by a number of judges (who may or may not be nested in panels). Variability associated with judges (and possibly panels) contributes error to the resulting cut score. The variability associated with items plays a more complicated role. To the extent that the mean item…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Executing actions in a specific order is a critical component of many action sequences that children must acquire, the majority of which are learned through observation and imitation of others. Although a wealth of evidence indicates that children can process and represent temporal order in memory, relatively little is known about the development…

The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra perspective in their teaching. However, PTs often show difficulties in algebra content knowledge,…

Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students' failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors' components such as the…

Much evidence suggests that, from a young age, humans are able to generalize information learned about a subset of a category to the category itself. Here, we propose that--beyond simply being able to perform such generalizations--people are "biased" to generalize to categories, such that they routinely make spontaneous, implicit…

Simulation-based learning offers a wide range of opportunities to practice complex skills in higher education and to implement different types of scaffolding to facilitate effective learning. This meta-analysis includes 145 empirical studies and investigates the effectiveness of different scaffolding types and technology in simulation-based…

This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize…